[]A SURVEY OF EXPERIMENTAL PHILOSOPHY.

CHAP. I. Of Matter and its Properties.

LET us for a moment compare this univerſe to a palace, erected by the divine Architect, and the unphiloſophical ſpectator to a foreigner, who ſees but the external part of the building. From ſo ſuperficial a view it is evident he can have but an unſatisfactory idea of the ſkill and contrivance of the great De⯑ſigner; he may perceive its beauties, but can have no idea of its conveniences. To have a more exact conception therefore, it is neceſſary to enter the building, to view each apartment ſeparately, to con⯑ſider the convenience of every room ſingly, with the ſymmetry and elegance of the whole.

[18]IN the ſame manner the beauties of Nature ſtrike our view, we find our cu⯑rioſity allured by a variety of objects. Animals, vegetables, minerals, air, wa⯑ter, and fire, all put on different appear⯑ances to pleaſe, aſſiſt or aſtoniſh us; in order to come at a knowledge of their nature we muſt approach them cloſely; we muſt firſt conſider each as diveſted of all their accidental qualities of figure and colour, and turn from Nature's external ornaments to view her internal ſim⯑plicity.

IN this ſearch, the firſt thing we find is Matter, that inert ſubſtance which ſerves as the foundation of all bodies, and which, while itſelf is unſeen, gives ex⯑iſtence to all other qualities that ſtrike the ſenſes. Of this all bodies have been originally compoſed, and it is probable that whatever different forms things may aſſume either in earth, air, fire, or water, yet matter is alike ſimple in all, and that every part of nature is compoſed from ſimilar materials.

[19]HOWEVER this be, certain it is, that no efforts of ours can make any alterations in matter, though we eaſily can in the ſenſible qualities with which it is cloath⯑ed. We may, for inſtance, deſtroy the figure and colour of a globe of gold, and diſſolve it into a fluid like water, yet ſtill every part of matter in it remains un⯑changed, and fills up as much ſpace as before. If we ſhould attempt to force any other body into the place it poſſeſſes, the united ſtrength of millions would not be able to prevail till itſelf were re⯑moved, to give the forcing body admiſ⯑ſion. If the ſofteſt ſubſtances, ſuch as air or water, be fixed between our hands, theſe cannot be brought to touch, till the air or water find a vent on one ſide or another. The academy of Florence having encloſed water in a globe of gold, preſſed it by the extreme force of ſcrews on every ſide. The fluid thus compreſſed by the approaching ſides of the engine, at laſt, finding no other paſſage, oozed out through the pores of the metal, and ſtood like a dew upon its ſurface. Thus [20] no art can deſtroy that property of body by which it keeps out all others that tend to enter the place it poſſeſſes; and which is called ſolidity.

ANOTHER property which cannot be ſeparated from mere matter, is its in⯑activity, or that incapacity it has to move of itſelf, or to ſtop its own motion. It is true, we may eaſily put one body into motion, which may communicate the ſame to another, which may commu⯑nicate to a third, and ſo on; yet ſtill this matter is perfectly inactive, it only goes forward with the force impreſſed at firſt by ourſelves, and whatever motion it may communicate, it loſes ſo much of its own. No art, however, can give it a power of creating or generating new motion; a ſtone till removed will continue to lie inertly on the ground, and if thrown forward will continue to move forward till the air or ſome other obſtacle hinders it from proceeding. If there had been nothing to ſtop its motion, it would continue to go on for ever.

[21]AS we are capable of giving Motion to matter, ſo alſo are we able to divide it; for Diviſion is, properly ſpeaking, only the moving of one part away from another. This Diviſibility may be carried to great lengths by art: a ſingle grain of muſk ſhall ſo divide its parts as to fill a whole room with its odour, and yet loſe but little of its weight in the expe⯑riment; a ſingle grain of gold ſhall cover a ſurface of thirty yards ſquare; a ſingle grain of copper ſhall give a beau⯑tiful blue tincture to many millions of times its own quantity of water. Thus matter is extremely diviſible; and after all, when the artiſt is thus fatigued with dividing a body into minute parts, the imagination can eaſily take up the taſk, and continue the operation without ever coming to an end.

LET us then call ſolidity, inactivity, the capacity of receiving motion, and divi⯑ſibility, properties of matter of which it can never be deprived; properties which we mention here rather for the ſake of [22] method than information; ſince they are all obvious to the moſt ſuperficial ob⯑ſerver, and ſince every moment's experi⯑ence convinces him of their exiſtence. In ſuch ſubjects the learner wants to be informed of little more than the import of the names, for the things themſelves they knew before. In fact, each of theſe properties implies the exiſtence of all the reſt; for if a body has been divided, it muſt have been put into motion; if put into motion, it muſt have been in a ſtate of inactivity; if inactive, it muſt have reſiſted the preſſure of the moving force, and the reſiſtance to this preſſure im⯑plies ſolidity.

CHAP. II. Of Attraction.

THE properties of matter, men⯑tioned in the laſt chapter, are ſuch as offer themſelves to every obſerver, and which can be known to reſide in every ſingle part of it, independant of the reſt; [23] for I can feel, move, and divide a piece of wax or an apple, though there were no other in the world. But, beſides theſe, there is another property of matter leſs obvious, and which, though reſiding in every part of body ſingly, yet cannot be made known to us, but by the opera⯑tion of one body upon another. The property I mean is Attraction, or that power by which we ſee one body ap⯑proach another, without any apparent force impelling it. Thus we ſee motes and ſtraws, of themſelves, fly to amber or ſealing-wax, at a conſiderable diſtance; we ſee iron move towards the loadſtone, and water to glaſs. What it is that thus impells theſe ſubſtances to approach each other, or in other words, what it is that cauſes this attraction between them, re⯑mains a ſecret that human ſagacity has not yet diſcovered; we are certain of the fact, we ſee plainly that the ſubſtances do approach, and all that we can aſſign as the cauſe of their coming thus together is but conjecture.

[24]IT may be aſſerted, for inſtance, as the cauſe of this, that there is an extremely ſubtil fluid, much thinner than air, which is diffuſed throughout the uni⯑verſe, and even enters the pores of the hardeſt bodies. This being granted, it follows, that ſuch parts of this fluid as are thus ſtrained through hard ſubſtances, muſt be neceſſarily much finer, and more ſubtil, than thoſe parts of this fluid which are diffuſed into ſpaces leſs crowded with matter; as the liquor that is filtered through the pores of a marble rock, muſt be much finer than that which is unfiltered. Wherever this fluid is moſt denſe, therefore, it will drive all ſolid bo⯑dies towards thoſe places, where they find the leaſt reſiſtance; namely, where the fluid is leaſt denſe; that is, to the ſurfaces of the hardeſt bodies; and the particles of this fluid being alſo ſuppoſed elaſtic, its impelling force will be increaſed to what degree the imagination thinks pro⯑per to give it.

[25]IT was thus that Newton attempted to explain this appearance in nature^*, a me⯑thod of accounting for things, perhaps, originally borrowed from Des Cartes, and which wants only to have the exiſtence of a ſubtil fluid proved, to make it bear the reſemblance of truth. In fact, in other parts of his works, he ſeems to lay no ſtreſs upon this theory, and aſſerts, that a body attracted, is drawn in propor⯑tion to the quantity of matter it contain⯑ed; while bodies impelled by a fluid, are driven with more or leſs force in propor⯑tion to their ſurfaces.

BUT though we cannot account for the cauſe of this attraction, or this tendency of one body to another, yet the experi⯑ments that ſerve to prove it are inconteſt⯑able, though we ſhall find it various in different ſubſtances. The wonders of the load-ſtone, of electricity, of capillary tubes and cohering bodies, will at once confirm the exiſtence of attraction, will [26] excite our ſurpriſe, and will introduce us to more important diſcoveries.

CHAP. III. Of the Magnet or Load-ſtone, with the attraction of Magnetiſm.

THE power which the load-ſtone has of attracting iron, or of one load-ſtone attracting another, has excited the admiration of every age; and even induced ſome of the ancients to aſſert, that it was an animated ſubſtance. Ariſ⯑totle aſſures us that Thales, the moſt an⯑cient philoſopher of Greece, made men⯑tion of it, and Hippocrates ſpeaks of it under the title of the ſtone which attracts iron. Pliny was ſtruck with the wonders of its attractive qualities, which was all the ancients knew of it, and thus finely exclaimed ^*, What can be more rigid, [27] and inactive than ſtone? Yet, for all this, nature has granted it ſenſe, and power? What can be more obſtinate than the hard⯑neſs of iron? Yet it is brought to obedience, and becomes tractable. For it is com⯑manded by the load-ſtone, and that ſub⯑ſtance, which conquers all things, flies to ſomething, I know not what, incorporeal. In fact, theſe powers might well excite ſurprize, they were inexplicable from the beginning to this day, and remain ſo: poſterity, inſtead of being able by experi⯑ment, to inveſtigate the cauſe, have only by the ſearch, found out new wonders equally inexplicable; therefore all that now remains, is rather to ſum up the qualities of the load-ſtone, than to ac⯑count for them.

EVERY load-ſtone hath two poles, in which, the greateſt ſhare of its magnetic or attractive virtue reſides. Theſe poles, or oppoſite points, may be found out by rolling the load-ſtone in the filings of iron, by which the filings will be ſoon ſeen to adhere to the poles, in greater [28] abundance, than to the other parts; and though it be broke into a thouſand pieces, yet each part of it ſhall ſtill have its poles, as before.

THESE two parts of the load-ſtone have received their name from the two poles of the earth, and like them, one is called the north, and the other the ſouth pole. Nor are theſe terms applied arbi⯑trarily; for they have a moſt ſenſible affinity with the poles of the globe, whoſe names they bear. A load-ſtone, ſo con⯑trived as to float upon ſmooth water, (which may eaſily be done by making it with a broad ſurface) will have its poles always directed, each to its kindred pole of our earth; one to the north, and the other to the ſouth. And if they be turned never ſo often, ſo as to make them point in different directions, yet the in⯑ſtant this external force is taken away, they will recover their former poſition.

THIS polar direction was utterly un⯑known to the ancients, but has by the [29] moderns been converted to the moſt uſeful and amazing purpoſes. For another pro⯑perty of the load-ſtone is, that it com⯑municates its virtues to iron, merely by rubbing; and converts it, to all intents and purpoſes, into a magnet like itſelf, with all the ſame attractive properties. A piece of iron, thus impregnated with the magnetic power, and nicely ſuſpended on a ſharp point, ſo as to leſſen the friction, and to give it the greater advantage of playing and turning in every direction, becomes what is called the mariner's needle, and will be ſeen to ſettle itſelf in a direction nearly north and ſouth. I ſcarcely need obſerve, how abſolutely neceſſary ſuch an inſtrument muſt be in directing mariners in long voyages; and it was for want of it, that the ancients were obliged to coaſt along in their courſes from one country to another; and ſeldom ventured to leave ſight of land.

BUT though load-ſtones, or iron im⯑pregnated with magnetiſm, have a ſtrong [30] attractive force upon each other, yet they have a repulſive force alſo; for if we ſhould attempt to make the two north poles, of two different magnets, approach each other, we ſhould ſoon perceive them to fly off with ſome violence, as if afraid of the touch; and in the ſame manner alſo, would the two ſouth poles repell each other: ſo that in fact, two magnets only attract mutually, by the poles of different denominations; that is, the north pole of the former, will attract only the ſouth pole of the latter; and the north pole of this, in turn, will have the ſame influence upon the ſouth pole of the other. But two poles of the ſame name, like two men of the ſame trade, are ever at enmity, and repell each other.

IT is for this reaſon, therefore, when a magnetic virtue is to be communicated to iron, that the ſouth pole in the load-ſtone, ever gives a north pole to the im⯑pregnated body; as we ſee, for inſtance, that end of the mariner's needle, which is touched by the ſouth pole of the ſtone, [31] always points northward. There is therefore ſomewhat friendly and ſym⯑pathetic, between the two poles of dif⯑ferent denominations. Univerſally, when artificial magnets are made by rubbing, each pole in the making magnet, begets its ſympathetic pole of a different name in the newly made magnet. And when two magnets are left to remain together, they ſhould always be placed with their ſympathetic, or oppoſite poles together, like pins that lie head to point, and this rather encreaſes their energy; whereas, if they lie with their diſagreeing ſimilar poles together, their power will be wea⯑kened, and at laſt totally deſtroyed.

THE fineneſs of theſe magnetic effluvia is ſuch, that they pervade the hardeſt bo⯑dies; a magnet attracting iron, though glaſs, gold, water, or any other ſubſtance be interpoſed between them, and equally operating, in vacuo, as in open air. There is a curious method of rendering the directions of theſe effluvia viſible. Strew ſome ſteel filings over a ſheet of [32] white paper, and underneath, let a mag⯑net be placed; then gently tap the paper with the finger, or otherwiſe, ſo as to give the filings a little motion, and they will ſoon be ſeen to form a regular ſtriated figure upon the paper; as repreſented in the diagram. (See plate I.) From the regularity of the figure, which theſe efflu⯑via aſſume, ſome have been of opinion, that the earth itſelf is one great magnet, ſending forth effluvia in the ſame man⯑ner; and that all magnetic bodies, lying in the current of theſe, aſſume a polar direction: as a piece of timber, carried down a rapid ſtream, generally floats lengthwiſe.

IT has been tried alſo, but with no better ſucceſs, to determine, to what ex⯑tent the ſame magnet diffuſes its attract⯑ing powers; and it has been found, that one day, the ſphere of its power is much more extenſive than another; that upon one trial, it would attract ſteel filings, at fourteen feet diſtance; and upon a ſecond, it could ſcarcely reach them at ſeven feet, without any apparent alteration in the weather. Some magnets alſo are found to act with much force upon bodies near them; but with very little, if they are removed to the leaſt con⯑ſiderable diſtance; while others are re⯑markable for contrary properties, having an extenſive reach, though no great force in approximation or contact. Doctor Helſham's load-ſtone attracted iron four times more ſtrongly, at one inch diſtance, than at two; or in a ſimilar proportion. Sir Iſaac Newton's, attracted ſix times more ſtrongly, at one inch, than at two; [35] while that of M. Du Tour, attracted but twice as ſtrong, at ſimilar diſtances. For this reaſon, no general law can be formed concerning the increaſe of mag⯑netic power; the properties in each magnet being ſo very various, and often the ſame magnet, at times, differing ſenſi⯑bly from itſelf.

BUT, beſides the virtue given to iron by rubbing upon a magnet, it may acquire the ſame powers, without the aſſiſtance of any load-ſtone whatſoever; and the beſt needles may be made artificially, merely by rubbing againſt other iron. A piece of ſteel, for inſtance, rubbed hard, for ſome time, all one way, by a poliſhed ſteel inſtrument, will, by this kind of friction, conceive ſo great a degree of virtue, as to become an artificial magnet; of greater force than the natural one. Or, if a bar of iron be left to ſtand for a long time, in the ſame unaltered per⯑pendicular poſition (as we ſee the bars of windows) it will acquire a magnetic power, and attract iron. But there is [36] a method, which gives a power to ſteel, far beyond what the natural magnet is able to produce; and which may be per⯑formed as follows.

PROCURE a dozen bars, ſix of ſoft ſteel, each three inches long, one quarter of an inch broad, and one twentieth of an inch thick; with two pieces of iron, each half the length of one of the bars, but of the ſame breadth and thickneſs; and ſix bars of hard ſteel, each five inches and an half long, half an inch broad, and three twentieths of an inch thick; with two pieces of iron, of half the length of one of the bars, but its whole breadth and thickneſs. And let all the bars be marked with a line round them at one end.

FOUR of the ſoft bars, being impreg⯑nated after this manner, lay the other two parallel about one fourth of an inch from each other, on the table, between the two pieces of iron belonging to them; a north, and a ſouth pole, againſt each piece of iron. (See Plate II. fig. 2.) Then take two of the four bars, already made magnetical, and place them, with their flat ſides together, ſo as to make a double bar in thickneſs; the north pole of the one, even with the ſouth pole of the [38] other. Then lay the two remaining ones, on each ſide of theſe, ſo as to have two north, and two ſouth poles together. You muſt then ſeparate the two north, from the two ſouth poles, at one end, by thruſting a large pin between them; and place them perpendicularly, with the ſeparated end downward, on the middle of one of the parallel bars; the two north poles towards its ſouth, and the two ſouth poles, towards its north poles. In this poſition, ſlide them backward and forward, three or four times, the whole length of the bar, and finiſhing in the middle; remove them from the middle of this, to the middle of the other parallel bar, and go over that in the ſame man⯑ner; and turning both bars the other ſide upwards, repeat the operation. This being done, take the two parallel bars from between the pieces of iron, and placing the two outermoſt of the perpen⯑dicular touching bars, in their room; let the remaining two now be made the outer⯑moſt, and thoſe that were parallel become the innermoſt of the four to touch with. [39] The proceſs with theſe, being repeated as before, till each pair of bars have been touched three or four times over, which will give them a conſiderable magnetic power; put the half dozen together, three poles on one ſide, and three poles on the other; and in the former manner, touch with them, the two pair of hard bars placed between their irons, at the diſtance of about half an inch from each other. Then lay the ſoft bars aſide, and with the four hard ones, let the other two be impregnated, holding the touching bars apart at the lower end, near two tenths of an inch; to which diſtance, let them be ſeparated after they are ſet on the parallel bar, and brought together again, before they are taken off. With this precaution, proceed in the method de⯑ſcribed above, till each pair has been touched, two or three times over.

THE bars, though now impregnated with ſtrong power, yet may receive ſtill greater, by touching each pair, in their parallel poſition between the irons, with [40] two of the bars, one in each hand, held horizontally; (ſee Plate II. fig. 3.) and a north and ſouth pole being approached to each other, and laid upon the middle of the parallel bar, the hands are drawn aſun⯑der, ſliding the north pole of one touch⯑ing bar, to the ſouth of the parallel; and the ſouth pole of the other touching bar, to the north pole of the ſame. This is repeated three or four times, and it will make the bars as ſtrong as they can poſ⯑ſibly be made. The whole of this may be gone through in half an hour, and each of the bars, if well hardened, may be made to lift above two pound; a power, much greater than any load-ſtone can confer. Such a method there⯑fore of communicating magnetiſm, will anſwer all the purpoſes of navigation, and experimental philoſophy in the compleateſt manner, with leſs trouble, and more certain ſucceſs.

AS the magnetic power may be thus eaſily communicated, ſo may it as eaſily be deſtroyed. By making the load-ſtone [41] or iron red hot, the power is quite taken away, though it often returns upon the body's growing cold. A ſmart blow of a hammer, often diſpatches this virtue alſo; and in general, any operation which alters the form or texture of the body, diminiſhes the magnetic power. Thunder ſometimes gives it, and ſome⯑times takes it away; in ſhort, nothing can be more uncertain and capricious, than the phaenomena of this amazing power. Almoſt every new experiment on the ſubject, diſcovers new wonders, ſome of the moſt ſtriking are here men⯑tioned; it would take up a volume but to name thoſe that remain ^*.

CHAP. IV. Of Electricity.

A Magnet attracts iron, without any previous rubbing, and its effluvia pervades the pores of all other ſub⯑ſtances, how denſe ſoever. But, beſide this, there are other bodies which attract different ſubſtances, tho' they require ſome preparation to make their power ſenſible; and the effluvia which they emit, can pervade only ſome particular ſubſtances. This ſpecies of attraction is called Electricity. For upon rubbing amber, called in Latin Electrum, it is found to attract any very light ſubſtances that are near it; and this property was known to the naturaliſts of antiquity, as well as the moderns. Upon further enquiry it was found, that not amber only, but ſeveral other ſubſtances, had the ſame properties, in a high degree; that glaſs, reſinous ſubſtances, wool, ſilk, and hair produced the ſame effects. That any of theſe, when dry, and rub⯑bed [43] for a ſhort time, were always ſeen to attract motes and ſtraws to their ſur⯑face, from a pretty conſiderable diſtance; and ſometimes repel them again with equal force. The ſame trials were made upon other bodies, moſt of which, after being very well dried and rubbed with long perſeverance, ſhewed a ſimilar power of attraction. Two kinds of ſubſtances alone were to be found in nature, that could not become attractive; and theſe were fluids, which could not be ſubjected to the trial of rubbing; and metals, which by no arts uſed could be brought to ſhew any ſigns of this electrical property.

AS ſome bodies were thus perceived to have theſe electrical properties more eaſily excited in them than others, thoſe which quickly became attractive by rubbing, were called electric bodies. Of this kind, were all precious ſtones, glaſs, porcelane, reſins, bituminous ſub⯑ſtances, wax, certain parts of animals, ſuch as ſilk, feathers, hair, or wool; all theſe eaſily becoming electrical, when [44] rubbed, and exerting their power in a high degree. On the contrary, thoſe which took a long time to have this pro⯑perty excited, or which ſhewed no ſigns of it at all, received the name of non-electric bodies. Of this kind, were all fluid ſubſtances, ſuch as water, ſpirits or mercury; all metals, and ſemi-metals, marble, lime-ſtone, all living animals, all green plants and trees, and ſubſtances made from them; ſuch as thread, paper, and linen cloth.

SUBSTANCES being thus claſſed, ac⯑cording to their electrical powers, it was then tried to how great a degree, bodies of the electric kind, ſuch as glaſs, for inſtance, could be impregnated with an attracting power. A glaſs tube, about an inch and an half in diameter, and three feet long, being heated by rubbing, was found alternately to attract and repell all light bodies, at ſeveral inches diſtance. As this, however, was but a trifling power, in⯑ſtead of uſing a tube, experimental philo⯑ſophers procured an hollow globe of glaſs, [45] moderately thick, and about a foot dia⯑meter; which being made to turn upon an axle, in the manner of a cutler's grind-ſtone, and like that, being whirled round by means of a large wheel and ſtrap, the palm of the operator's hand kept dry by a glove, or Spaniſh white be⯑ing kept upon it, a great degree of fric⯑tion was thus excited. The globe being rubbed in this manner, was ſeen to acquire a very great electrical force, and Doctor Helſham long ſince found, that woollen, or ſilken threads, being held on one ſide near it, while thus turning, they would dart themſelves into ſo many ſtraight lines, all pointing towards the center of the globe. The effluvia were even perceiv⯑able to the ſmell and the touch; and theſe were the firſt ſteps, which were made in purſuit of the wonders that were after⯑wards diſcovered, in this part of phi⯑loſophy.

IF, while the globe was thus turning, or ſoon after, it was touched with a piece of ſealing-wax, reſin, amber, or any other electrical ſubſtance, this made no [46] alteration in its effects; the globe con⯑tinued to attract leaf gold, motes, or ſtraws, as before: on the contrary, when it was touched with a man's hand, a piece of metal, a ſtick, or any other non-electric body, all its attracting power ceaſed in an inſtant, and it required to be rubbed anew. It was, however, ſoon after perceived, that if the touching non-electric body, was placed in ſuch a manner as to touch nothing but the electrified globe or tube, and to have no communication with any other body, it then became electric itſelf, attracted motes and ſtraws, and its touching did not in the leaſt diminiſh the efficacy of the glaſſes attracting power. If, for inſtance, a piece of metal, or any other non-electric body, was fixed on the top of a glaſs tube, taking care that it touched nothing but the glaſs only; and then the tube, being electrified, by rubbing with the hand, the metal above was ſeen itſelf to become electric; and like the glaſs to attract and repel light ſubſtances; and like it, when the finger was brought near [47] it, about the diſtance of half an inch, to ſnap and crackle. But if the metal, while it touched the globe, touched alſo the earth, or any other non-electric body that communicated with the earth, as a man ſtanding on the ground, a chair, a table, or ſuch like, all its new acquired virtue, inſtantly ran into the man, or the table, and from thence down to the earth; where, like ſpilled water, it vaniſhed, and was loſt in an inſtant, and was no longer capable of its former exertions.

IN order, therefore, to ſtop this cur⯑rent of electrical effluvia from running into the ground, ſomething was to be placed between the man's feet and the earth, that would prevent the electrical ef⯑fluvia from going any farther. Now it was found, that all electrical ſubſtances could do this; for though they become electri⯑cal by rubbing themſelves, yet they never admitted the effluvia from another electri⯑cal body, but reſiſted its further progreſs. If, therefore, a cake of reſin, wax, or [48] any other ſtrongly electrical ſubſtance, be placed under the man's feet, while he touches the electrified globe, he becomes filled with the electrical effluvia, which has no power to eſcape downward, as the cake reſiſts it, and he is as capable of attracting light ſubſtances, to the ſurface of his body, as the globe itſelf. A piece of metal, inſtead of the man, will do the ſame, ſo will all non-electric ſubſtances.

IN general therefore we may obſerve, that the electrical effluvia can be poured into all non-electric ſubſtances at pleaſure by communication; that they receive it ſimply, at the approach of the electric globe or tube, which is heated by fric⯑tion, and communicate it to all other non-electric bodies, with which they are united, though this union ſhould be never ſo extenſive. On the contrary, electric bodies, whoſe power can be excited by rubbing, will receive no effluvia by communication from other electrified ſubſtances, but repel all their emanations.

[49]LET us now then ſuppoſe the whole electrical apparatus prepared, the glaſs globe turning ſwiftly upon its axle, by means of a wheel, and rubbed by the hand of the operator, while the perſon to be electrified ſtands upon a cake of reſin, wax and ſulphur, mixed together, of about fifteen inches diameter, while he touches the upper part of the globe, or ſome non-electric ſubſtance, that com⯑municates with it. The weather being dry, and the room ſpacious, we ſhall ſee the following wonders enſue. In a few ſeconds, the man will be filled with ef⯑fluvia; he will become perfectly electrical; his hands, and every part of his body will attract and repell light ſubſtances at four feet diſtance, and even farther, if the weather be extremely dry. Each of theſe little ſubſtances, ſuch as ſtraws, motes, and leaf gold, are at firſt drawn towards the electrified body with great ſwiftneſs, and then when they have been ſaturated with the electric vapour, and have become equally electric themſelves, they are repelled with equal force.

[50]WHATEVER non-electric body, the man electrified holds in his hand, be⯑comes electrified like himſelf, provided it has no other communication but with himſelf, or ſome electric body, into which its effluvia cannot enter. And this extenſion of the electrical effluvia, inſtead of diminiſhing its quantity, ſeems rather to increaſe its force, as well in the man, as whatever he holds in his hand. So that if a thouſand men ſhould take hold of each other's hands, provided they be all placed upon cakes of reſin, or ſome other electric body, the laſt man will be as ſoon electrified as the firſt, and the greateſt number rather more ſtrongly than one at a time. However, if any one of them have the ſmalleſt communi⯑cation with a non-electric body, which leads to the ground, if, for inſtance, one of theſe thouſand men ſhould have a linen thread, reaching from the ſkirt of his coat to the earth, the whole effluvia would eſcape through that narrow con⯑ducter, to be loſt entirely. If theſe men, inſtead of holding hands, ſhould each [51] hold an iron chain between them, they will be electrified with equal velocity and ſucceſs.

IF now, the electrified man, who ſtands foremoſt, ceaſes to touch the turn⯑ing globe, he will, nevertheleſs, continue for a good while impregnated with the electricity he has received, as well as all the reſt to whom it has been communi⯑cated; however, their power of attracting and repelling light ſubſtances, will in⯑ſenſibly begin to diminiſh, till, after ſome time, it totally ceaſes. Metallic ſubſtances are found to hold this electri⯑city, infuſed into them, much longer than animals; probably, becauſe their electric matter does not tranſpire, as in animals, by perſpiration. But to make all electricity ceaſe in a moment, in either, it is ſufficient juſt to touch them with any non-electric ſubſtance that communicates to the ground.

IF one, who is not electrified, brings his hand near the face of the perſon under the operation, he will perceive [52] the impreſſion of a fluid atmoſphere about it; and continuing to approach his finger to ſome protuberant part, the noſe for example, if the room be darkened, the finger and the noſe will appear en⯑lightened; and when they approach ſtill nearer, there will proceed, from the perſon electrified, with ſome noiſe, a bright ſtream like fire, which will affect both parties at once, with a ſmall ſen⯑ſation of pain, and which will be painful in proportion to the ſtrength of the elec⯑tricity. This ſtream will be equally pro⯑duced by the touch, from any part of the body, and even through the clothes; all that is required, being only that the touching perſon be not electrified himſelf.

IT is by this ſmall ſtream, that the effluvia migrate from one body to another; ſo that if the barrel of a gun, or any other metallic body which is non-electric, be ſuſpended by ſilk cords which are electric, and ſtop the progreſ⯑ſion of the effluvia, it becomes electrified, by a ſingle touch from the man, under the operation; and what is more extra⯑ordinary, [53] the greater this non-electric body is, the more powerful is its electricity.

IF a ſteel wire of five or ſix hundred yards, be ſuſpended in like manner, by ſilken cords, the inſtant it receives elec⯑tricity at one end, it is felt at the other; for the remote end will be found to attract leaf gold, the moment the nearer end touches either the man or the globe; and the effects, thus inſtantly excited, may be as inſtantly repreſſed, by the touch of a perſon who ſtands on the ground. If a man, ſtanding on a cake of reſin, ſhould, with the point of a ſword, approach the wire thus electrified, yet without touching, he becomes him⯑ſelf equally ſo; from whence it appears, that the effluvia can paſs from one ſub⯑ſtance to another, without either coming into contact.

HITHERTO we have ſeen how elec⯑tricity flows, either back or forward, with amazing velocity, and that it can be accumulated in any body at pleaſure, by ſimple infuſion. It will be found alſo, to [54] exert all theſe powers in a vacuum, or place free from air, with a greater force; for if a globe be placed in ſuch a manner in a receiver, exhauſted of its air, that it may ſtill continue to be rubbed with the hand, while the rubbing continues, and while the air is kept away, the globe will ſend forth a very bright light, in great quantities; but its brilliancy will become more feeble in proportion as the air is admitted, though the rubbing ſhould be continued all the while.

WHEN the conductor, or any other non-electric body, has been thus electri⯑fied, and has received as great a quantity of effluvia as it can bear, the overcharged effluvia, which is continued to be poured in from the turning globe, flows out, either from the whole ſurface, like a bright light, or from ſome point or angle of its ſurface, in a ſtream, like that which is excited by the approach of the finger. The flame reſembles in form that of a hiſſing ſquib, (ſee fig. 4.) narrow upon iſſuing out, but diffuſing its rays as it goes farther. If the finger be now ap⯑proached to this ſtream, another wonder will appear. A ſtream of fire will proceed from the finger, in an oppoſite direction to the other; narrow upon leaving the finger, but diffuſing its rays as it goes forward. When both flames have ap⯑proached ſo near as that they join, they then quickly condenſe, and an appear⯑ance [56] is excited, that every way reſembles lightning; the flaſh is ſudden, the noiſe is loud, a ſulphureous ſmell enſues, a great pain and ſhock is felt, and a ſlight burn remains upon the finger that ſuſ⯑tains the experiment. We may kindle ſpirits of wine a little warm, gunpowder, or any other inflammable ſubſtance in the ſame manner, by holding them near a ſtream of fire, iſſuing from ſome point or angle of the conductor.

BUT the flame excited in this way, is but a ſpark, compared to that excited by the famous Leyden experiment; the cauſe of which, no philoſopher has yet been able exactly to account for. A perſon holds by the bottom, in the broad of his hand, a decanter or bottle almoſt filled with water, in ſuch a manner, as not to touch any of the empty part of the bottle with his fingers. Then an iron wire, that touches the globe or the con⯑ductor with one of its ends, is made to dip the other end into the water contained in the bottle, but ſo as not to touch the glaſs in any part. While the perſon holds [57] the bottle thus, in the left hand, and the globe being ſtrongly electrified, if he touches the conductor or the wire with the knuckle of his right, he will imme⯑diately feel a moſt violent ſhock enſue, the force of which ſeems diffuſed over his whole body; ſo great is its force, that Mr. Muſchenbroke, who was the firſt who publiſhed this experiment, thought, when he firſt felt it, that it had killed him. This experiment was, ſome-time after, improved by Doctor Bevis; who, inſtead of a bottle with water, made uſe of a large ſquare pane of glaſs, and a different non-electric, namely, a me⯑tallic ſubſtance, in this manner. A large ſquare pane of glaſs, of about twenty inches diameter, though the larger the better, is tinned on both ſides, as we ſee the back ſide of a looking glaſs; on both ſides however, there is a margin left all round untinned of about two inches broad. The glaſs being thus prepared, is placed flat upon a metal ſtand, ſo that the under ſide of the pane lies upon a non-electric body, which itſelf commu⯑nicates [58] with the ground. The upper ſide of the glaſs parte, is made to communi⯑cate with either the electrifying globe itſelf, or its conductor, by means of an iron chain. Things being thus diſpoſed, the chain is ſtrongly electrified by turn⯑ing the globe, and thus communicating with the upper ſide of the pane, is elec⯑trified alſo. Now ſhould a man be ſo raſh, things being in this ſituation, as to touch the under ſurface of the pane with one hand, while with the other he touches the chain that communicates be⯑tween the upper ſurface and the globe, the ſhock would be ſo terrible, that it would ſtrike him dead in an inſtant. But to avoid this, the operator takes a bent iron wire, curved ſomewhat in the form of a C, which is fixed in a glaſs handle that prevents the effluvia from coming to his hand; he takes, I ſay, this wire thus bent, and blunted at both ends, and with this touches at the ſame time, the under ſurface and the upper chain that leads to the globe. The moment of the touch a flaſh of lightning enſues, which [59] dazzles the eyes with its ſplendour; the noiſe may be heard at a great diſtance, and its force is ſuch, that it can penetrate ſeveral ſheets of paper laid upon the upper ſurface of the glaſs, or melt leaf gold, when properly placed to receive the flame.

AS nothing we have hitherto men⯑tioned ſerves to explain the phaenomena of this and the former amazing experi⯑ments, and as it in ſome meaſure departs from the uſual laws of electricity; ſeveral very learned men have been much per⯑plexed to account for it. Here we ſee glaſs, which in the uſual inſtances is un⯑touched by the electrical effluvia, in this experiment tranſmitting it, or at leaſt, ſtrongly affected by it. The Abbé Nollet, Doctor Watſon, Mr. Jallabert, and Mr. Franklin, have all attempted to account for it, and each in a different way from the reſt: it would be impertinent here to recite or confute any of their opinions, we ſhall only give an explanation later than theirs, namely, that of Mr. Monier, [60] who delivers it himſelf as a mere con⯑jecture, and as ſuch we repeat it. It is true, he ſays, that glaſs reſiſts the admiſ⯑ſion of electric effluvia, when thoſe effluvia touch its ſurface but in one or two points; but when it is united with a non-electric body, ſending forth its effluvia more cloſely, ſo as to touch ſurface againſt ſurface; in ſuch a caſe, the glaſs imbibes the effluvia like a non-electric body. For inſtance, as the ſurface of the water in a bottle, touches the internal ſurface of the glaſs in every part, when this water is ſtrongly electrified for ſome time, the glaſs will alſo imbibe a part of the effluvia from the water. Now this being admitted, and experiments ſhew it to be true; after it has thus for ſome time imbibed the effluvia on its inner ſurface, this will make it begin to imbibe them on its outer ſurface alſo; ſo that if the bottle be held in the hand, it will alſo imbibe the effluvia of the hand. Now it ap⯑pears, that this current of effluvia coming from the hand is greater than that coming from the water within; ſo that [61] the two currents meeting in oppoſite directions, the ſtronger ſtream will over⯑power the weaker, and the whole current will run from the hand to the outer ſurface of the bottle, from thence to its inner ſurface, and ſo inward to the water. If now, while the whole bottle is thus imbibing the effluvia from the hand that holds it, the man, with the other hand, touches the conductor, and charges him⯑ſelf in this manner with a freſh quantity of effluvia, the whole torrent running towards the hand with the bottle; the hand that holds it will receive a moſt vio⯑lent ſhock as the increaſed effluvia enters the ſurface of the glaſs, and at the ſame time that the other hand which touches the conductor, receives alſo a ſlight ſhock from this quarter, ſo that the whole body feels at once two concuſſions; and this produces the violence that is felt in the experiment of Leyden.

HOWEVER this be, the great reſem⯑blance which the flame thus excited, in every reſpect, bore to that which flaſhes [62] from thunder, gave philoſophers the firſt hint of trying whether lightning was not actually the reſult of electricity. Upon examination, it was found that the air is often charged with vaſt quantities of electrical effluvia; that an iron wire ſuſpended by electrical ſtrings, often im⯑bibed this fluid from the clouds in great plenty; that in times of thunder it was particularly charged with it, and often with ſo much more than it could contain, that the fluid ſtreamed over from its points in great abundance. All this proved in⯑conteſtably that lightning is no other than the electrical flaſh of ſome non-electrical uncharged body in the air touching another made electric by friction, or charged by communication. And this may be eaſily enough conceived, if we ſuppoſe a large quantity of dry air be⯑come perfectly electrical, and touched by a non-electric cloud, as in an iron conductor applied to a glaſs globe, the flaſh enſues, and the inſtantaneous loud noiſe is heard, which being echoed ſeveral times among the clouds, before it [63] comes to us, gives the continuing ſound of thunder. If the flaſh ſhould reach ſo low as the earth, and a perſon ſhould un⯑fortunately be in the place of its exploſion, he is generally ſtruck dead in a moment, and feels the moſt inſtantaneous of all kinds of death.

BUT this theory is not only amuſing, but uſeful; for as in ſome countries the damages ſuſtained by thunder are frequent and terrible, Mr. Franklin has invented a method of ſecuring the houſes, and conſequently the inhabitants, from its violence. It is no more than procuring a long iron rod, which reaches from the cloud to the earth, and is ſo erected in or near a houſe, as to touch no non-electric ſubſtance whatever, except the ground below, and the cloud above. The end of this rod, touching the electrified cloud, imbibes the electric fluid with which the cloud is charged, and carries it down to the earth; where it is diſſipated without farther miſchief.

[64]SOME other meteors are the reſult alſo of this electrical fluid. The Aurora Borealis for inſtance, or that ſhining light which is often ſeen by night in the heavens, and which the vulgar call ſtreamers, may be thus accounted for from its effects. For it muſt be obſerved, that ſometimes electric bodies ſuck in the electric fire, and ſometimes they throw it out: if, for inſtance, after rubbing an unpoliſhed tube of glaſs, you approach it with the finger, the ſtream of fire comes from the finger to the glaſs; if on the contrary, this tube be poliſhed and then rubbed, the ſtream of fire will come from the glaſs to the finger. Now ſhould we ſuppoſe, in the ſame manner, two electric clouds with different ſurfaces, and there⯑fore one of them attracting the other's effluvia, if we ſuppoſe an intervening non-electric cloud as the conductor of the fluid from one cloud to the other, it will ſhine like the overcharged iron conductor, and put on the appearance of the meteor we attempt to account for.

[65]FROM electricity alſo, we may account for that fire, ſo often ſeen by ſailors, called St. Anthony's fire, which is no⯑thing more than the electrical fire ruſh⯑ing into a place exhauſted of its air, and there putting on a luminous appearance, as it always does in a vacuum. However, after all, in attempting to account for any of thoſe meteors, we have but pro⯑bable conjectures to ſupport us; there is not hitherto enough known of the phae⯑nomena of electricity to build any ſyſtem upon, and we are deſirous of ſaying ſomething rather to excite, than ſatisfy curioſity.

IT has not leſs embaraſſed philoſophy to account for the nature of this fluid, than to aſcertain its properties. Some have ſuppoſed electrical fire to be a diſtinct fluid, as diſtinct from all others in nature, as the magnetic fluid is known to be; others will have it to be merely elementary fire, or ſuch as is collected by the burning glaſs; others that it is a culinary; and others that it is no other [66] than the Ether of the ancients, or of Sir Iſaac Newton, which is diffuſed through the whole ſyſtem of the world; and the motions of which, give movement to all the reſt of matter. To explain the reſem⯑blance between Ether and electricity, it has been in a former chapter obſerved, that this Ether is ſuppoſed to be in greateſt quantity, or denſeſt, in the moſt porous bodies; and on the other hand, more fine and ſubtil in denſe bodies, ſuch as gold. It is alſo known by experience, that upon heating or rubbing any ſub⯑ſtance whatever, it ſwells under the operation, grows bigger, and conſe⯑quently becomes more porous. Now, ſay ſome, in proportion as the body becomes porous, the ſurrounding Ether ruſhes into it, and accumulates within, till the heat or the rubbing ceaſing, the body gradually ſhrinks to its former dimen⯑ſions, and the Ether is again ejected. Now this, they continue, is exactly what happens in electricity; the ſurface of the body is encreaſed by rubbing, the elec⯑trical fluid ruſhes into its pores, and there [67] remains for ſome time, till the effects of the rubbing ceaſes. And as the body, which by its dilatation receives this fluid, is, during the time of rubbing, continually taking in an overplus; and conſtantly, after the rubbing has ceaſed, by contracting itſelf, is ſqueezing out what remains, a part will be thus forced into whatever body comes in contact with it: it will, they ſay, be forced into all bodies that communicate, except ſuch as have an extremely denſe atmoſphere ſurrounding them, which like a ſhell defends them from the incurſions of this fluid that would thus force an entrance. But it is, they add, known by experience, that of all ſub⯑ſtances, thoſe which contain light within them have the denſeſt atmoſphere; of this ſort are glaſs, reſin, diamonds, and in ſhort, all highly electrical bodies. Bodies like theſe are ever found to reſiſt the incurſions of this fluid, except their pores are opened and their atmoſphere rarified by rubbing. This denſe atmoſ⯑phere which ſurrounds them effectually, prevents the entrance of the fluid by [68] communication; and in like manner, when the fluid is introduced by rubbing, keeps it a long time ſhut up in the body, and prevents it from eſcaping. For this reaſon we find electrical ſubſtances never receive the fluid by the touch alone, but when they have been other⯑wiſe excited, they hold the fluid a longer time than non-electric bodies are found to do.

THESE are the outlines of the diſ⯑coveries in electricity; a ſubject which has of late employed the attention of philoſophy, and which is yet but in its infant ſtate. Thoſe various appearances which it aſſumes, probably ariſe from [70] ſome one leading cauſe, which is yet un⯑known: that it is of uſe in the ſyſtem of nature, muſt be granted, for we find it hitherto, either medicinally or mechani⯑cally, of no peculiar benefit to mankind, and nature does nothing in vain. But what its uſes in nature may be, whether it regulates her motions, or puts her into motion; whether it vivifies her produc⯑tions, or continues their exiſtence; whe⯑ther it ſupplies animal heat or elementary fire, are ſubjects not yet illuſtrated; and may perhaps continue unknown while man ſees but in part. Some of the con⯑jectures on this ſubject are given; all would be endleſs.

CHAP. V. Of the Attraction of Coheſion and Ca⯑pillary tubes.

WE have hitherto ſeen attraction to prevail in every part of nature, that has fallen under our notice; magnets to attract bodies at a diſtance without rubbing, electric ſubſtances performing the ſame effects upon being rubbed: but beſides theſe powers in nature of form⯑ing large maſſes by uniting bodies to⯑gether, there is one of another kind, in which bodies that at the leaſt ſenſible diſtance have no power of attracting each other, yet being touched together cloſely join and unite with a kind of ſympathetic fondneſs.

WE perceive ſeveral bodies when ap⯑plied to each other ſtick cloſely, while others, though united never ſo cloſely, or never ſo long, cannot be made to adhere after the force that kept them together is taken away. This power of coheſion, [72] by which bodies are held together, has perplexed the philoſophers of every age, and every age has attempted the ſolution. Some have aſcribed this tena⯑city of bodies, to a kind of hook'd for⯑mation in the atoms that compoſed them; ſo that two atoms like burs ſtick to each other, the hooks in one catching thoſe of the other. As this however was explaining one difficulty by a ſtill greater; Bernouilli aſcribed all coheſion to the uniform preſſure of our atmoſ⯑phere. This theory he endeavoured to ſupport by an experiment of two poliſhed marbles, which would co⯑here in the open air, but would drop aſunder in vacuo, or a place where the air was exhauſted. But unfortunately for him, this fact happens to be falſe. Others were for aſcribing coheſion to an occult quality in bodies, by which they aimed at a ſtate of reſt; and others again aſſerted, that the attempt at motion in all the parts of a body pro⯑duced the reſt of all, and thus they hap⯑pened to unite into maſſes of peculiar [73] ſizes and hardneſs. Such were the former weak attempts to ſolve this difficulty. Newton however ſaw, with the greateſt degree of probability, that this tenacity of bodies might be produced by the ſame cauſe by which we ſee iron fly to the load-ſtone, or ſtraws move to amber; in ſhort, that it was produced by attraction, a cauſe unknown to us indeed, but of which, in numberleſs inſtances, we ſee the effects. The ſurfaces of all bo⯑dies, ſaith he, are unequal, which cauſes that they touch only in a ſmall number of points, when placed one upon the other. The leſs une⯑qual the ſurfaces of the bodies the more they touch, and conſequently the more they attract each other. Thus we ſee, that thoſe which have the eveneſt ſurfaces, have the greateſt power of coheſion; and if, to render theſe ſur⯑faces ſtill more uniform, the pores be filled up with ſome liquid, the power of coheſion will be ſtill greater.

[74]IN the ſame manner all ſolid bodies when brought into contact, as well as all liquids whatſoever, adhere to each other. Theſe attract ſolid bodies, and are mutually attracted by them; from whence it appears, that this attracting power is diffuſed over all parts of nature, at leaſt ſuch as we have hitherto exa⯑mined. If we apply the ſurfaces of two looking glaſſes to each other, being pre⯑viouſly well poliſhed, cleaned and dryed, it will be found that they adhere to each other with a very ſenſible tenacity. The ſame effects will happen in vacuo (or a ſpace emptied of its air) as well as in the uſual manner. If two leaden balls be cut ſo as to have even ſurfaces, and they be preſſed againſt each other with a twiſt, it will be ſeen that they adhere with a force equal to forty or fifty pounds weight. In general, all bodies whoſe ſurfaces are even will thus ſtick to each other, and if a liquid be ſmeared over either ſurface, their coheſion will be ſtill the ſtronger.

[75]IT is this liquid or thick oil which is contained in the bodies of all plants and vegetables that holds their parts together; and we are taught by chymiſtry, that if this be burned away the reſt will fall into aſhes, and without the reſtoration of ſome other fluid, the parts cannot again be united. The bones of animals alſo, if calcined in ſuch a manner as that all their oil ſhould be exhauſted, while their form is preſerved, will be found to become extremely brittle, but they will in ſome meaſure recover their former ſtrength if they be dipt in oil. Thus we find that ſome bodies are thus perceived to cohere, and to be more tenacious than others, by means of this fluid, or elſe from their internal conformation, by which the ſurfaces of every particle of matter contained in them, touch the ſur⯑faces of the neighbouring particles in the greateſt number of points.

Muſchenbroek has made many experi⯑ments to find the force with which the parts of many bodies are found to cohere [76] to each other; or in other words, how much force is required to pull the parts of any body aſunder, drawing them accord⯑ing to the length of their fibres. In theſe trials he found that the beech and aſh were the tougheſt of all woods; next to them the oak, then the linden and alder, then the elm, and laſtly the fir; the weight required to pull a piece of aſh aſunder, being more than double what was ſufficient to break the fir. He alſo made ſimilar trials on metals; of theſe, gold was the moſt tenacious, then iron, ſilver, yellow braſs, copper, tin, lead.

But bodies are found to attract each other at minute ſenſible diſtances, as well as in contact. If we place between two glaſs plates, ſuch as thoſe which have already been mentioned, a fine ſilk thread, then we may eaſily conceive thoſe two plates will not touch, ſince they will be ſeparated from each other by the whole thickneſs of the thread; but however, notwithſtanding this ſe⯑paration, the two plates will mutually [77] attract each other, though with leſs force than if there were nothing between them. Place between the plates two threads of the ſame twiſted together, and afterwards three; the glaſſes will ſtill attract, but with leſs force than before.

IT is by this power, ſaith Newton, that the ſmall particles of bodies act one upon another, at ſmall ſenſible diſ⯑tances, and cauſe ſeveral phaenomena in nature. This opinion has been driven as far as it could well bear, by Freind and Keil, and been brought to explain all the theory of chymiſtry, as well as ſome other obvious appearances. Some bodies, ſay they, have a greater power of attracting certain kindred bodies than others. Thus water, in which the gall-nut has been diſſolved, attracts the parts of iron, and forms the black liquor called ink; but if we pour into this ink ſpirits of nitre, with which the iron has a greater affinity, or by which it is more ſtrongly attracted, then the iron, before diſſolved in the gall water, flies to its [78] more kindred fluid the ſpirit of nitre, and ſinks with it to the bottom of the veſſel, leaving the water at top quite clear of any colour, except that given it by the gall-nut originally. If again we pour into this compoſition ſpirits of vitriol, between which and ſpirits of nitre there is the utmoſt affinity, the nitre ſpirit immediately quits the iron which it before united itſelf to, in order to join with the more kindred ſpirit of vitriol; and the iron, thus let free, is once more ſuſpended like a black fluid in the gall-water, as before. By this me⯑thod alſo of reaſoning, we may account for all thoſe changes wrought in the co⯑lour and taſtes of liquors, upon their be⯑ing mixed with each other. For whether they be naturally fluids, or only bodies diſſolved or ſuſpended in fluids, the kindred bodies fly to their peculiar kindred bodies. But if the affinity between the fluids and the body ſuſpended, be greater than be⯑tween the particles of the body itſelf, the body ſtill remains ſuſpended or diſſolved; but if the parts of the body attract each [79] other with greater force than the liquid attracts them, then they begin to cryſtalize, or to unite into maſſes of ſuch figures as the peculiar kinds of ſalt are uſually found to be. Laſtly, when, continue our authors, upon the mixture of two bodies in the ſame liquor, which are both more ſtrongly attracted by each other than by the fluid that ſurrounds them, they happen to ſtrike againſt each other, if they happen to be elaſtic they will conſequently be driven back with a degree of force almoſt equal to that with which they have been attracted; and this alter⯑nate attraction and repulſion will produce a fermentation in the whole. In this man⯑ner ſome Engliſh philoſophers have at⯑tempted to account for many chymical phaenomena; much has been objected againſt their theories, and the truth is, when examined cloſely, they have neither that preciſion nor perſpicuity which ſubjects of this nature require; however, this diſquiſition belongs more properly to chymiſts than natural philoſophers, and with them we leave it.

[80]BUT to prove the attracting power of one body upon another beyond all poſſi⯑bility of doubt; if a glaſs bubble be ſet to float on water contained in a glaſs veſſel, at a ſmall diſtance from one ſide of it, though at firſt it appears motionleſs, yet after a very ſhort time, from a ſtate of reſt it will begin to move towards the ſides of the veſſel, and that with a velo⯑city encreaſing as it approaches the power attracting, till at laſt, it ſhall ſtrike the ſide of the veſſel with ſome force. This approaching of the drop to the ſide of the veſſel is alſo the more re⯑markable, as it in ſome meaſure moves up hill, the water in the glaſs veſſel riſing all round the edges, as is obvious to every minute's experience.

TO ſhew this attracting power in an inſtance or two more. If two poliſhed plates of glaſs, ſuch as we have men⯑tioned above, be both placed edgeways in water, their ſurfaces very near and parallel to each other, a ſmall part of the [81] glaſſes being only thus immerſed, the water will riſe up between them, and the leſs the diſtance between the two ſurfaces of the glaſſes, the higher will the water riſe. If the diſtance between them be about the hundredth part of an inch, the water will riſe to about an inch; if the diſtance be but half that, the water will riſe but half as high.

AS water or any other fluid (except mercury) thus aſcends between poliſhed plates of glaſs, ſo it does likewiſe in ſlender pipes of glaſs open at both ends, (commonly called capillary tubes.) Theſe capillary tubes of glaſs may be drawn to an exceſſive fineneſs, much ſlenderer than the fineſt wire of an harpſichord, by means of a blow pipe and candle. If one of theſe hair-like tubes be dipped at one end into water, ſpirit of wine, or any other convenient fluid, the liquor will riſe to conſiderable heights, the narrower the tube the higher the liquor. This ſpontaneous elevation of the fluid, [82] which is in appearance contrary to its natural weight, demands our moſt parti⯑cular attention. The body of man may be compared to an hydraulic machine, it it may be conſidered as a collection of tubes with their proper fluids running through each. In the almoſt infinite number of pipes which thus compoſe the human frame, thoſe of the ſmall capillary kind, are without doubt the greateſt in number; for this reaſon therefore, a thorough knowledge of theſe, intereſts us the more.

THE ſubject is difficult, and requires patience and reviſion. The aſcent of the fluids, in capillary tubes, has been by the beſt philoſophers aſcribed to the power of the ſides of the tubes attracting the fluid; but there are ſome things which embarraſs this opinion, and Doctor Jurin was the firſt who treated the ſubject with much accuracy and preciſion. Before the method of explaining this phaeno⯑menon was broached by Newton, ſome [83] aſcribed the riſing of the fluid in the nar⯑row tube to the unequal preſſure of the atmoſphere; the air, ſaid they, is com⯑poſed of parts which ſtick to each other, and conſequently cannot enter the narrow tube where it is open at the top, there⯑fore not being able to preſs upon the fluid within the tube, as it does upon the fluid without, the fluid is puſhed up by the external preſſure being greater than the internal. This whole hypotheſis is de⯑ſtroyed by a ſingle experiment, for the fluid riſes in vacuo, where there is no air, as well as in the ordinary manner.

ANOTHER ſet of naturaliſts have ima⯑gined, that upon the tube's being im⯑merſed in water, that part of the water in immediate contact with the internal ſurface of the tube, loſt its weight down⯑wards by its adherence to the ſides of the glaſs; that it was therefore puſhed up⯑ward by that part of the water immedi⯑ately below it, which coming into the place of the former, loſt its own weight [84] in the ſame manner, by adhering to the inner ſides of the tube, and that thus ſuc⯑ceſſive columns of water were forced up and ſuſpended. But if this ſyſtem were true, the tube, by being plunged into the water in ſuch a manner as would cauſe the fluid to adhere to it in greateſt quan⯑tity, would be moſt filled with the fluid. However, the tube which is but ſlightly dipped becomes as well filled as that which is deeply immerſed in the fluid. Theſe ſyſtems being found inadequate to the purpoſes of explaining this appear⯑ance, later philoſophers have had recourſe to attraction, all agreeing that the fluid is attracted by the tube, but they differ in the part by which the tube attracts. Some have ſaid, (ſuch as Hawkſby and Morgan) that the internal ſurface of the tube at⯑tracts the fluid and cauſes it to riſe, till the weight of the fluid, ſo raiſed, be⯑comes equal to that power, which thus lifts it above its level, and then it ſtops without riſing. This explication, how⯑ever, is by no means ſatisfactory; for, as [85] we have ſaid before, the narrowneſs of the tube and the height to which the water riſes are always in the ſame pro⯑portion; as for inſtance, if a tube the hundredth part of an inch diameter, raiſes the water to one inch, a tube the fiftieth part of an inch will raiſe juſt half an inch of water. Now the internal ſurfaces of the tubes cannot be the cauſe of the water's riſing in either, for in the narrow tube, the ſurface applied to raiſe the water, is greater than in the wide one; whereas, in the latter, the quantity of water raiſed is greater; wherefore, if the ſurfaces were the cauſe of attraction, the greateſt ſur⯑face would raiſe the greateſt quantity.

DOCTOR Jurin perceiving the inſuffi⯑ciency of this explication, has given one of his own; but firſt, a very remarkable experiment is neceſſary towards explain⯑ing it. Dip the tube A B (fig. 5.) of two different diameters into water. Though a tube of the diameter of the part C B could elevate the water only to the point [86] E, yet if it be filled with water up to D, this water will not ſink again, but con⯑tinue ſuſpended in the tube as high as if it were only of the ſmall diameter of the parts A C throughout. By this ex⯑periment it is obvious, that the liquor does not remain ſuſpended, by the attracting power of the whole internal ſurface, ſince here there is no proportion between the thing which raiſes, and the thing which is raiſed; the quantity of ſurface attracting, being very trifling in this ex⯑periment, and the quantity of water raiſed very great. Our judicious philo⯑ſopher, therefore, is of opinion, that as the fluid riſes in proportion to the diameter of the tube in its upper part, that it is attracted by that ring of the internal ſur⯑face of the tube, which is touched by the upper ſurface of the fluid as it aſcends. As this ring is narrow the water riſes high, as it is wide the water ſinks in proportion.

MR. Clairault is ſtill for another hy⯑potheſis, and thinks the inferior end of [87] the tube is the chief elevating power; like the former, however, he allows attraction to be the cauſe; but ſtill it muſt be confeſſed that the laws of this attrac⯑tion, at what diſtance it acts, or how the ſame acknowledged force is found to raiſe, in one inſtance, a large weight of water, and in another, is incapable of ſupporting a much leſs, are things not yet clearly made out; we know enough of the general appearances of capil⯑lary tubes, to aſcribe their power to at⯑traction; ſome exceptions only raiſe doubts, and teach us to ſuſpend our entire aſſent; only ſtill let us appear ſenſible that ignorance is better than error.

WHATEVER be the cauſes of the aſ⯑cent of fluids in capillary tubes, the ex⯑periment is obvious, and in the explica⯑tion of many parts of nature, we ſhall find the doctrine of fluids aſcending in ca⯑pillary tubes of great utility. The human frame, as we have already remarked, is a machine compoſed of numberleſs tubes of [88] different diameters, with fluids circu⯑lating through them. Through the largeſt of theſe, the force of heat, or their own power of contraction, or the im⯑pulſe of the ſucceeding parts of the fluid driving on that before it, are the cauſes of circulation; but when the diameters of thoſe veſſels become ſo ſmall as to loſe all elaſtic contracting power, or when they are at too great a diſtance from the heart, which is the propelling power, or when placed at ſuch angles that the ſuc⯑ceeding maſs of fluid no longer preſſes from behind, it is then that circulation is carried on in the ſame manner as fluids riſe in capillary tubes, the minute veſſels of the body taking the blood and other juices through them, by means of this capillary ſuction, if I may ſo call it, and then emptying themſelves in the larger veſſels again.

IN the ſame manner, every plant and vegetable may be conſidered as a bundle of capillary tubes united, with their ends placed in the earth, from whence they [89] imbibe their moiſture; and if each of theſe tubes be conſidered as indefinitely ſmall, it is apparent that ſuch will raiſe the fluids to any indefinite heights, ſo that the ſap will riſe by the ſame means in the talleſt oak as well as in the lower ſhrub. But it may be aſked, how ſome vegetables extract one kind of ſap from the earth, and others a ſap every way different? In anſwer to this it may be obſerved, that glaſs capillary tubes of all other fluids are found to raiſe water to the greateſt height; now if we ſup⯑poſe every vegetable like the glaſs tube, thus endued with a property of raiſing ſome particular fluids to greater heights than others, we may, with equal pro⯑priety, ſuppoſe that ſome vegetables are ſo formed, as to raiſe only fluids of one particular kind, and that this is the cauſe of that variety which is found in their juices.

THE theory of capillary tubes has alſo been brought to explain the aſcent of [90] liquors in a ſponge, in a loaf of ſugar the under ſurface of which is placed in water, and ſuch like ſubſtances, which being porous, may be conſidered as com⯑poſed of a number of little canals or tubes, each of which acts in the manner already explained. Perhaps this doctrine may alſo be of uſe in explaining the origin of fountains, the waters of which are thus imbibed by the earth, and riſe through its ſubſtance till they come to its ſurface, to ſupply the neceſſities of man, or to adorn his habitations. As the earth may be thus conſidered acting like a ſponge upon the waters placed below its ſurface, ſo the air has been compared to a ſponge raiſing waters to great heights above its ſurface. This has been aſſigned as the cauſe of vapours, clouds, and ex⯑halations. A ſponge or capillary tube, when filled with its fluid, continues to attract no longer; in the ſame manner the air, when charged with rain, has no power of abſorbing moiſture, but con⯑tinues thus charged till the cold condenſ⯑ing, [91] it acts upon it like preſſure upon a ſponge, and thus obliges it to fall in rain.

WE could adapt this theory to the explanation of ſeveral other phaenomena not yet well underſtood, but we would not embarraſs the learner, in his very entrance upon this pleaſing ſtudy, with unſupported conjectures. They who can wreſt ſuch experiments as theſe to ex⯑plain all that they ſee, would, with equal eaſe, have explained appearances of a contrary kind, upon the very ſame principles; the cauſes of meteors are as yet but little underſtood, and in fact, for many years paſt, have been very little ſought after.

CHAP. VI. Of the Attraction of Gravity.

WE have hitherto ſeen an attrac⯑tion prevail at ſenſible diſtances between iron and the load-ſtone; we have ſeen it prevail in a more general manner between electric and non-electric ſubſtances; it has been found exiſting ſtill more generally in almoſt every body that can be ſubjected to experiment, operating moſt ſtrongly in coheſion, and loſing its force in proportion as the two bodies un⯑der experiment were removed from each other. If now, therefore, we would de⯑ſire to enquire into the reaſon that all bo⯑dies continually fall to the ſurface of the earth, would we aſk the cauſe that impells them rather downwards than upwards, the anſwer will be obvious, namely, attraction. The ſame ſecret cauſe that impells iron to the load-ſtone, or motes to amber, influences all bodies on the ſurface of the earth to fly to it. It is a rule adopted by philoſophers and con⯑firmed [93] by common ſenſe, that more cauſes than one are not to be aſſigned for ſimilar effects; here we ſee nature ope⯑rating in many inſtances entirely like her operations in others, and therefore we muſt account for her operations by the ſame rule in both caſes. Let us, there⯑fore, for a moment, conſider the earth as one great attracting body, drawing like a magnet every thing to its ſurface; a ſtone when forced up into the air, by the ſtrength of the ſlinger's arm, comes down again by the earth's attracting power; a cannon ball ſhot upwards, is brought back by the earth's influence, with almoſt equal velocity. Let us ſuppoſe, I ſay again, that the earth acts upon theſe bodies in a manner, ſimilar to that with which amber acts upon ſtraws, or a mag⯑net acts upon iron. Let us be allowed this for a ſhort time, and it will ſoon receive almoſt inconteſtible evidence from a variety of reaſons.

TO have an idea of this, let us begin by conſidering by what laws the attractive [94] power of the globe, which we inhabit, may be ſuppoſed to be, and in fact is regulated. Let us then, firſt, conceive our earth as a great ſphere or ball, and its attracting power as iſſuing forth from all parts of it in ſtraight lines, as rays do from the ſun, as heat from fire, or ſmells from a perfume; in ſhort, diffuſed every way in right lines from the center of the globe under conſideration. This being conceived, it is obvious, the force by which any body on its ſurface is at⯑tracted, will be greater or leſs in propor⯑tion to the quantity of the attracting rays; but all rays iſſuing from a center, recede from each other, as the ſquare of their diſ⯑tance from that center encreaſes; that is, a body at twice the diſtance of another body, will be attracted only by a fourth part of the rays that attract the latter, at thrice the diſtance, with only a ninth part, at four times the diſtance, with only a ſix⯑teenth, and ſo on. Thus if I deſire to know how much a body, which at one ſemi-diameter of the earth's diſtance weighs or gravitates four pound, will weigh at two [95] ſemi-diameters diſtance; I take the in⯑creaſed diſtance two, and ſquare it, that is, multiply the number by itſelf, thus, twice two is four, and then ſay, as this ſquared diſtance is encreaſed, ſo much is the gravity or the weight of the body dimi⯑niſhed; that is, the body weighs four times leſs than it did at firſt, viz. one pound. Now ſhould it be aſked how much this ſame body will weigh, at three ſemi-dia⯑meters diſtance, I again take this diſtance three, and ſquare it, which is nine, and then ſay, that the body only now weighs a ninth part of its original weight; that is, ſix ounces, or thereabouts. In ſhort, to ſay all this in different words, the force of gravity increaſes in a duplicate proportion as it approaches the attracting power.

ALL bodies upon this earth tend to it in a line perpendicular to its ſurface; the lighteſt will fall, if unſupported by ſome ſurrounding fluid, ſuch as air or water, as well as the heavieſt. The ſmoke of a candle which aſcends in [96] the air pump, before the air is exhauſted, yet upon a vacuum being made, will fall down plumb to the bottom of the receiver. If we drop a piece of gold and a feather from the top of an exhauſted receiver, they will both fall to the bottom at the ſame time; by which it appears that a body, which is ten thouſand times heavier than another, yet is attracted with equal eaſe and celerity. The force, therefore, which has cauſed the heavy body to deſcend, has acted upon it with ten thouſand times the degree of power which has been applied to move the lighter, in the ſame manner, as it requires ten times more ſtrength in me to lift ten books than one. Gravity, therefore, acting in proportion to the quantity of matter in all bodies, and the earth, which is almoſt infinitely greater than all other bodies on its ſurface, acting with a comparatively infinite force, muſt attract all to itſelf, with almoſt an infinite de⯑gree of ſuperiority.

[97]BUT although theſe be the laws by which gravity acts, at conſiderable diſ⯑tances from the center of the earth, yet we cannot pretend to aſcertain them by experiment; the difference, perceivable by us at the ſurface, is ſo ſmall, that it ſcarce makes any alteration in the deſcent of bodies. We, on the ſurface, are diſ⯑tant from the center of the earth, near four thouſand miles, and at the height of one mile, our diſtance will be four thou⯑ſand and one miles; now ſhould we re⯑gulate the difference of gravity by the ſquares of theſe numbers, they at the ſurface will find their gravity to be about ſixteen thouſand, and they a mile higher ſixteen thouſand and eight, a difference too ſmall to be perceivable by our ſenſes.

BUT though this difference is not per⯑ceivable by us, in the deſcent of bodies at the ſurface of the earth, yet when we aſcend to the heavenly bodies, particu⯑larly to the moon, which we know by the means of the teleſcope, to be nearer [98] the earth than any of the reſt, we ſhall find theſe laws of attraction to guide it in all its motions. We ſhall find that all the pla⯑nets turn round the ſun, which is infi⯑nitely larger than themſelves; by the ſame law, we ſhall ſee thoſe ſmaller planets, which are the attendants upon other planets, guided by the laws of gra⯑vity; if we meaſure their diſtances from each other, and the times of their tra⯑velling round their reſpective center of revolution, we ſhall find all concur in proving that the larger bodies attract the ſmaller, in proportion to the difference of their quantities of matter, and that they are attracted the nearer they approach, with a force increaſing, as the diſtance ſquared decreaſes. If this be true, and it will ſhortly appear that it is, the deſcent of bodies to the ſurface of the earth, re⯑ceives a new proof of its ariſing from that power we call attraction. For if we find this attraction to prevail amongſt all bodies in the heavens, as upon all on the earth, it would be bad philoſophy [99] to ſay, that in the ſingle inſtance of a body's falling to the ſurface of the earth, nature acted upon different principles, ſince natural effects of the ſame kind muſt be allowed to proceed from the ſame cauſes. If I ſee a ſtone gravitate here, and another gravitate or fall in America, I allow the fall in both to pro⯑ceed from the ſame cauſe. But if I ſee the moon gravitate towards the earth, (as will ſhortly be ſeen ſhe does) if I ſee the earth gravitate towards the ſun, if I ſee his attendant planets gravitate towards Jupiter, if I ſee motes gravitate to amber, and iron to the magnet, it would be abſurd not to grant that the ſame cauſe which makes all theſe gravitate or fall towards each other, makes alſo a ſtone gravitate or fall towards the earth; nature acts ſimply, and we ſhould reaſon with a ſimplicity conformable to her operations.

CHAP. VII. Of the power of Attraction in Celeſtial Bodies.

WE ſaid that the laws of gravity prevailed in guiding the motions of all the celeſtial bodies of our ſyſtem; an aſſertion which requires to be proved. However, as it is a ſubject which belongs rather to aſtronomy than natural philoſo⯑phy, we muſt explain it with the utmoſt brevity. To enquire whether it be the ſame principle which guides the moon in her orbit, and makes an heavy body fall towards the ſurface of the earth, and whether they be moved by the ſame laws, it is firſt neceſſary to examine what ſpace a body falling to the earth, would move through in one minute, and what ſpace the moon, which is ſixty ſemi-diameters of the earth diſtant, would move through in the ſame time; and if they are both found regulated in ſimilar proportions, they may both be aſſerted to ariſe from one ſimilar cauſe.

[101] Newton, the great inventor of the ſyſ⯑tem, ſet himſelf diligently to meaſure both. He was taught that a body falling to the ſurface of the earth, ran through ſixteen feet in a ſecond, for this experi⯑ment had been made with exactneſs by Galileo before him. But in meaſuring the motion of the moon he had more trouble, for it was firſt neceſſary to know her pre⯑ciſe diſtance from the earth, and to attain a knowledge of this, it was requiſite to have the exact meaſure of our globe. In this he was led aſtray, for from wrong meaſures the geographers of that time were taught to reckon but ſixty miles to a degree, whereas they ſhould have reckon⯑ed ſeventy; theſe erroneous calculations therefore, were found by Newton utterly repugnant to his ſyſtem, and he was wil⯑ling to abandon his theory for a while, rather than force nature to conform to it. However, the true meaſure of a degree being ſome time after found out, Newton again reſumed his calculations, and found them all agreeing with the utmoſt exact⯑neſs [102] to the appearances of nature. The moon is ſixty ſemi-diameters of the earth diſtant from us; now it is known by computation, that if the moon fell per⯑pendicularly towards the earth, inſtead of being puſhed round in a circle, it would at its preſent diſtance begin to fall at the rate of ſixteen feet and an half in a minute. But in going through this ſpace, it moves nearly thirty times ſlower than a body falling at the ſurface of the earth is found to do, which moves ſixteen feet and an half in a ſecond. The moon, therefore, falling at its preſent diſtance, and the body falling at the ſurface of the earth, fall by the ſame law, for the ſquare of the moon's diſtance will be found exactly in proportion to the dimi⯑niſhed force of its attraction. If the ſtone, which falls ſo ſwiftly at the earth's ſurface, were carried up as high as the moon, it would take half a minute in falling ſix⯑teen feet and an half, as the moon is now found to do.

[103]THIS law of attraction which prevails between the earth and the moon, may be extended to all the other planets, and it will be found to explain their motions with equal preciſion. We ſhall find that the attendant planets are attracted to⯑wards their primary planets, and that they, earth and all are attracted towards the ſun by a force increaſing as the diſ⯑tance ſquared decreaſes.

BUT it will be ſaid, that we talk of the moon's being attracted or drawn towards the earth, and the planets to⯑wards the ſun, when in fact they only move round them in circles. If the earth or the ſun, it may be aſked, attract the celeſtial bodies towards themſelves, why do they not fall upon their ſurfaces, as we ſee heavy bodies fall to the ſurface of the earth? To anſwer this, we muſt ob⯑ſerve, that the great Creator of all things, when he firſt formed the univerſe, per⯑mitted all bodies that compoſe our ſyſtem to be actuated by two different powers. [104] One, that inert force in matter, by which, when once moved, it would con⯑tinue to go on in a ſtraight line for ever, if not turned out of its way by ſome obſtacle; the other, this power of attrac⯑tion, by which every body tends towards ſome other. Now then, let us for a moment imagine that in the forming our ſyſtem, the ſun was firſt made and placed in the center; after this, let us ſuppoſe that the mighty Architect took this ball of earth and puſhed it from him in a right-lined direction. It is obvious, that by its own inert force it would go ever ſtraight forward into endleſs ſpace, if nothing hindered; but while its im⯑preſſed force drives it forward, the attrac⯑tion it feels from the ſun draws it with an equal degree of force inwards; and between thoſe two oppoſite forces it is found to go wholly in neither, but as a ſtone whirled by a ſling it deſcribes a circle round the ſun. That force by which a body endeavours to recede from the center of its motion, is called [105] the centrifugal force, that by which it tends towards the center is called the centripetal force; they both go by one common appellation, namely, that of central forces, which, if we would have a more preciſe idea of the manner in which the planets revolve about the ſun, muſt be examined more mi⯑nutely.

CHAP. VIII. Of Central Forces, as far as they tend to explain the Univerſal Syſtem.

WE have often had occaſion to in⯑culcate, that matter is of itſelf entirely paſſive, incapable of moving itſelf, or ſtopping its own motion; a ball thrown by the hand would continue to go on for ever, did not the force of attraction, or the reſiſtance of the air, at laſt deſtroy the motion it received from the flinger's arm. Matter, in ſhort, follows whatever direction is impreſſed upon it, and is af⯑fected by every impulſe in its way. As it is incapable of moving itſelf, ſo it is incapable of changing the direction of its own motion, that is, it muſt move forward in a ſtraight line in the direction it firſt received. If then at any time we ſee a body moving in a circle, or any curve whatever, we conclude that it muſt be acted upon by two powers at leaſt, one to put it into motion, and the other [107] to draw it out of its rectilinear direction, in which it would have moved on for ever. Let us therefore conſider the direction a moving body will receive, that is put into motion by two powers at the ſame time. Suppoſe, for inſtance, a boat (ſee fig. 6.) is drawn up the ſtream of a river, by two men on oppoſite banks and with equal force on both ſides; it is evident it would follow the direction of neither entirely, but go in a line be⯑tween both, exactly in the middle of the ſtream.

TO carry this yet farther, ſuppoſe a ſhip at A (ſee fig. 7.) driven by the wind, in the direction of the line A B, with ſuch a force as would carry it to B in a minute. Then ſuppoſe a current driving this ſhip, at the ſame time, in the direc⯑tion A D, with an equal force. By theſe two forces acting together at right an⯑gles, the ſhip will go in neither direction, but deſcribe the longer line A E C, running from corner to corner in a [108] minute; or in other words, it will deſcribe the diagonal of a ſquare.

IF theſe equal forces, inſtead of acting upon the body A (fig. 8.) at right angles, act in more conſpiring directions, one having a tendency to drive it through the ſpace A B, at the ſame time that the other has a tendency to move it through an equal ſpace A D, it will then deſcribe the diagonal A G C, in the ſame time that either of the ſingle forces would have cauſed it to deſcribe its reſpective ſide; and this, it muſt be obſerved, is a greater ſpace than if the forces had acted upon it at right angles. Univerſally there⯑fore, the more conſpiring the united forces that drive a body forward are, the greater ſpace the moving body will deſcribe.

IN a manner ſimilar to this, bodies revolving round a center, are attracted by two powers. If a leaden bullet, fixed to the end of a ſtring, be ſuſpended upon a pin, and then receive a blow from a battledore or other inſtrument, it will [109] thereby deſcribe a circle about the central pin, and while its circular motion con⯑tinues, it will endeavour to fly off from the center; and in fact, if the ſtring which holds it to the pin, happened to break, we ſhould ſee the bullet fly off, and hit the wall, cieling, or ſome other part of the room; but it is held by the ſtring, with a force equal to that by which it is drawn away; theſe forces, I ſay, are equal, for if one prevailed, the body would circulate no longer. Now the primary puſh, if I may ſo call it, which a planet has firſt received, reſembles the blow given to the bullet; while the attraction, which draws it to the ſun, the center of its motion, may be com⯑pared to the ſtring.

TO illuſtrate this by an example: ſup⯑poſe I want to compare the central forces of two bodies of different magnitudes, different velocities, and moving in unequal circles. The firſt body weighs 2, has ſwiftneſs as 2, and moves in a circle, the ſemi-diameter of which is 2. The ſecond body weighs 3, with a ſwiftneſs equal to 3, with a ſemi-diameter of 3. I take the ſwiftneſs of the firſt body, and multiply it by itſelf thus, twice two is four. Then I multiply this by the weight 2, and the produce is 8, this I divide by the ſemi-diameter 2, which [112] gives 4. What has been done to the firſt body muſt be done to the ſecond, and the reſult will be 9, and as 4 is to 9, the central force of one body will be to the central force of the other.

THIS being underſtood, if we apply this rule carefully we ſhall find, 1. that if two bodies of equal weight deſcribe unequal circles in equal times, the central force will be greateſt in that which deſcribes a circle of the greateſt diameter; and of conſequence, if the central forces of two bodies, which deſcribe unequal circles, are in proportion to their diameters, the two bodies will revolve in equal times.

2. IF two bodies deſcribe unequal cir⯑cles, their central forces will be directly as the ſquares of the velocities, and in⯑verſely as their diameters. From whence it follows, that if the velocities are equal, then the central forces will be inverſely as the diameters alone; but if the dia⯑meters are equal, and the velocities un⯑equal, [113] the central forces will be as the ſquares of the velocities alone. And if the central forces of two bodies, which move in unequal circles, are equal, their diameters will then be as the ſquares of the velocities.

3. IF two bodies moving in unequal circles have equal central forces, the time employed in deſcribing the greateſt circle, will be to the time employed in de⯑ſcribing the leaſt, in the ſame proportion as the cube of the greateſt diameter, is to the cube of the leſs. But if the reader conſiders, he will find in this caſe the times and the velocities the ſame; but we obſerved before, that the diameters are as the ſquares of the velocities, therefore the diameters here are as the ſquares of the times.

FROM hence it follows, that in com⯑paring the motions of the planets, and their diſtances from the center of their motions, this law has been eſtabliſhed, [114] That the ſquares of the periodical revolu⯑tions of two planets, are as the cubes of their diſtances from the center, round which they move.

THIS law is of infinite uſe to aſtrono⯑mers; for if they know the periodical time, that is, the time of the circular revolution, of two planets, and the diſ⯑tance of one of them from the center, they can by this find out the diſtance of the other, which before was not known. For inſtance, we know the periodical time of the moon to be 27 days, and the peri⯑odical time of the earth to be 365 days. The diſtance of the moon from the center of its motion we alſo know to be 60 ſemi-diameters of the earth. Now I deſire to know the diſtance of the earth from the center of its motion, namely, the ſun? I know by my rule, that the proportion of the ſquares of the periodical times, will give the proportion of the cubes of the diſtances. Then I find out the ſquares of the periodical times of the two planets. [115] The periodical time of the moon is 27, and the ſquare of that number 729; the periodical time of the earth is 365, and the ſquare 133225. Then I find the diſtance of the planet, already known, 60, and cube it, which makes 216000. Now by a rule in arithmetic, I find out a certain number which will bear the ſame proportion to this, that the ſquares 729, and 133225 bear to each other; that proportional number is 39460356, and the cube root of this laſt number, which is 340, will expreſs the diſtance of the ſun from the earth, which was what I wanted to know, ſo that the earth is diſtant from the ſun, 340 of its own ſemi-diameters.

THIS law, of ſuch great benefit in aſtronomy, was found out by Kepler, but far from being able to give the cauſe of it, which the reader has already ſeen; as we have taken it from Newton and the Marquis de l' Hopital. Kepler ſuppoſed that the ſun was poſſeſſed of a kind of [116] vegetating ſoul, and that turning round itſelf it attracted the planets, and that the planets would actually fall upon its ſurface, but that by turning upon their own centers, (as we ſee a top) they by this means reſiſted the ſun's attracting power.

THE laws we have hitherto laid down ſuppoſe that all the planets move in cir⯑cles; but in truth this is not the caſe, for while they are attracted by the bodies reſpectively in their centers, at the ſame time they are in a leſſer proportion at⯑tracted by each other. For this reaſon they do not move in circular orbits, but in ſuch as are elliptical, of the figure A in the plate, the diameter of which is greater one way than another. (Fig. 10.)

BY this we ſee, that though the uni⯑verſe may be reſembled to a nice ma⯑chine, in which all parts are wiſely adjuſted, yet the conſtant and paternal inſpection of the great Architect is ever [117] requiſite, his regulating hand is always over all his works, and ſhould he leave them but for a time, their order and re⯑gularity would be at an end. The planets would neceſſarily diſturb each others motions, and when ſeveral of them came to the ſame quarter of the heavens, they would attract the ſun with united influence, and perhaps at once deſtroy the common regulator of their motions. In this manner the uniformity of nature would be deſtroyed, and as it could never repair its own breaches, the whole ſyſtem would run into endleſs confuſion. Of this diſturbance we had a remarkable inſtance in the comet which lately appeared; which, in receding from the ſun, went ſo near the planet Jupiter, as to be greatly affected by its attraction. But a ſolicitude for the diſarrangement of the univerſe, belongs only to him who is above all concern.

CHAP. IX. Of the Figure of the Earth, and the different Weights of Bodies upon its Surface.

EXPERIMENTAL Philoſophy is not, at firſt ſight, ſo pleaſing as that amuſing ſcience which is formed upon conjecture; but it improves as it proceeds, and the mind, by firſt more painfully meaſuring the effects of bodies upon each other, at laſt comes to arrive at the cauſes. We have ſeen how by means of the attraction of bodies upon each other, all nature ſeems to put on uniformity; but this power makes the heavenly bodies not only move in circles round a diſtant center, but alſo regulates the motion of the earth upon itſelf. For the earth, moon, and planets have two motions, as we ſee ſometimes when boys are whipping a top, which, while it is ſpin⯑ning upon itſelf, is at the ſame time go⯑ing round a circle chalked on the floor.

[119]THIS motion which the earth has upon itſelf, is that which cauſes day and night, as either ſide is turned toward, or from the ſun. Now while the earth is thus whirling round, that part upon its ſurface will have the greateſt ſwiftneſs, which is moſt diſtant from its center of motion. As for example, a body placed upon the circumference of a chariot wheel, while it is turning, will have twenty times the motion of a body placed upon the nave. A body, if placed upon the equator of the earth, is like this body at the circumference of the wheel, while another at either of the poles, is like one placed upon the nave. Now this body placed at the equator, it is evident, would fly off, by reaſon of the earth's centrifugal force, with great velocity, were it not held to the earth by the infinitely ſtronger power of attraction. However, though it ſtill holds to the earth by its gravity, yet by its centrifugal force, it in fact loſes a part of its tendency to the earth, and is diminiſhed therefore in a part of its [120] weight. Thus if weighed at the equator, a body is ſenſibly lighter than the ſame when weighed at either of the poles, and this has often been meaſured, by the means of pendulums, in a method which ſhall hereafter be ſeen. Let it ſuffice here to obſerve, that a body, which at Paris would weigh two hundred and twenty pounds, would at the equator only weigh two hundred and nineteen.

SUCH is the difference of gravity on different parts of our globe; from whence it appears, that bodies placed at the equator, have a greater tendency to fly off from the ſurface of the earth, than ſuch as are placed at either of the poles. Now, if inſtead of bodies flying off at the ſurface of the earth, we ſhould ſup⯑poſe the parts of the earth itſelf were moveable among each other, and the whole, for inſtance, compoſed of a great heap of running ſand; then it is obvious, that while the earth turned round its axis, her parts would attempt moſt to fly off [121] where the motion was greateſt; it would ſwell under the equator, for the greateſt quantity of materials would run to that part.

WHAT is ſaid here of the earth's ſwel⯑ling at the equator, is actually found to be true; for though we often call it a globe, yet it is by no means perfectly round, but widened out at the equator, and flatted at both poles, like a turnip; or, if the learner is fonder of a hard name, its figure may be called an oblate ſpheroid. Aſtronomers and natural phi⯑loſophers had long been of a different opinion with regard to the figure of the earth; the French and Italian geogra⯑phers univerſally conſidered it as a ſphe⯑riod rather lengthened than flatted, rather like an egg, than the figure men⯑tioned before. Huygens and Newton however, perſiſted in affirming the con⯑trary. The diſpute continued long, but was at length determined, highly to the honour of the latter; ſeveral members [122] of the academy of ſciences having been ſent, in 1735, to the polar circle, and others to Quito, for the purpoſes of de⯑termining the figure of the earth; they concurred in affirming with Newton, that the earth was flatted at the poles. Nor was this a ſmall conqueſt gained in fa⯑vour of the Engliſh philoſopher's ſyſtem. For it muſt be obſerved, that if the earth's figure were proved not to be flat, a part of his doctrine of gravity would be falſe. For it ſeems the earth has yet another motion; its poles are found to point ſlowly, to different parts of the heavens, in a ſeries of years, like a top going to fall, which while it ſpins round itſelf, nods alſo, with a ſort of circular motion. Of this nutation of the poles, which it is not our buſineſs here to examine, he had ſhewed that gravity muſt be the cauſe, provided the earth were flat, which he believed it was.

BUT though the earth is allowed by the generality of modern philoſophers to [123] be an oblate ſpheroid, yet ſome latter ob⯑ſervations have induced many of them, and thoſe among the foremoſt, to think it of a more irregular figure. Of this opinion, we find Buffon, Condamine, Maupertuis, and Boſcovich. The prin⯑cipal reaſon upon which this opinion is founded, is, that a degree juſt meaſured on the meridian of the globe in Italy, by Boſcovich, was found to differ from that meaſured in France in the ſame lati⯑tude, 70 French toiſes. Could we be certain that the admeaſurements of theſe two different meridians were made without error, this would, undoubtedly, be a demonſtrative proof of the irregu⯑larity of the earth's figure. But an error of two ſeconds will produce the difference now complained of; and where is the ob⯑ſervator that can anſwer for two ſeconds? The opinion therefore, of the earth's ob⯑late figure ſtill remains uppermoſt, yet not with ſuch entire conviction, as before this laſt admeaſurement was made.

CHAP. X. Of the Deſcent of Bodies to the Surface of the Earth.

THUS far we have ſhewn the ge⯑neral cauſe why bodies fall to the earth, and proved that the force of gra⯑vity which draws them down becomes leſs, as the diſtance, when ſquared, be⯑comes greater: That a body, which at one ſemi-diameter of the earth, weighs one pound, will have four times leſs weight at two ſemi-diameters, and nine times leſs at three. This difference in weight, we ſaid, might be ſenſible at great diſtances, but not at any diſtance we can remove from the earth's ſurface; for though we could remove a mile above the earth, and weigh a body there, yet this encreaſed diſtance would take but little from its gravity, for a body on the ſurface of the earth, is already removed four thouſand miles from the center of the earth, by which it is attracted; and [125] removing it one mile more will be but making a decreaſe of one mile's attraction from four thouſand, a difference too mi⯑nute for ſenſe to diſcern. This decreaſe of gravity, therefore, as we remove from the earth, is only an object of the imagi⯑nation, or if we have any ſenſible proofs, they are obtained by meaſuring the hea⯑venly bodies around us.

IT ſuffices us therefore to know that bodies, though to ſenſe they have not more gravity in the loweſt pit than upon the higheſt mountain, in general fall by that power. But the cauſe why bodies fall with greater force as they fall from higher places, which we ſhall now ſee to be another law of falling bodies, is founded upon quite other principles, diſcovered long before the principle of gravity was thought of.

THE moſt unlettered ruſtic is ſenſible, that the fall of a ſtone is to be dreaded in proportion to the height from whence [126] it deſcends; that if it falls from a place a foot above his head, it is not ſo likely to be fatal, as if it fell from the houſe-top. From this it is obvious, that the body thus falling, acquires new ſwiftneſs the longer it falls; and in fact, it has been found by trial, that a leaden bullet, let fall from the top of the ſteeple in Weſt⯑minſter Abby, acquired ſuch velocity to⯑wards the end of the fall, that it pierced through a deal board that was fixed beneath.

THE exact quantity of ſwiftneſs, which a body thus falling acquires, was firſt de⯑monſtrated by Galileo, and his experi⯑ments confirmed by Grimaldi and Riccioli, who, by letting heavy bodies fall from high towers, and then by computing the time in which they fell, and the heights of the towers they fell from, determined the quantity of ſwiftneſs gained in every inſtant of the fall. In determining theſe laws however, they ſuppoſe that the bo⯑dies were free from that reſiſtance in [127] their fall, which they receive from the air through which they move, and which reſiſts the falling body with greater force, the quicker the body deſcends; as when walking we feel the wind ſtronger when we go faſt than when we move ſlow.

BUT though, as was ſaid, this ſwift⯑neſs, which deſcending bodies acquire, is obvious to common experience; the exact quantity, thus acquired, is not ſo eaſy to be determined. In order to find this out, we muſt conſider that as a body deſcends, the power of gravity is con⯑ſtantly and uniformly increaſing its ſwift⯑neſs; the impreſſion gravity gives it in the firſt inſtant of its fall, would alone be ſufficient to make it deſcend, though it received no new impreſſion; (as a ſtone, impreſſed by the hand, moves ſtill forward, after the moving cauſe ceaſes to act) but gravity ſtill operates upon it, and a new impreſſion is added in the ſecond inſtant of the fall, which conſpires with the firſt impreſſion, and doubles it; [128] and in the third inſtant, the body goes on with the double impreſſion, and re⯑ceives alſo a new one which triples it; ſo that we may ſuppoſe every body fall⯑ing, to receive a new impreſſion every moment of the fall, and that the velocity increaſes as the moments increaſe.

NOW then let us imagine a bullet dropped from the tower of Weſtminſter Abby, and that in the time of one ſecond it falls the ſpace of one pole (ſixteen feet and an half,) its velocity is ſtill in⯑creaſing; at the end of this fall it will have acquired as much ſwiftneſs as in the next ſecond would have carried it two poles, or double the former, although no new impreſſion from gravity were added; but a new impreſſion being added, will make it fall, through three poles. As the velocity is increaſed to⯑wards the end of every fall, in the beginning of the third ſecond, it will have acquired as much velocity as would have carried it through four poles, and [129] the uniform impreſſion from gravity being added, will make the body fall through a ſpace of five poles. At the beginning of the fourth ſecond, it will have acquired as much velocity as would have carried it through a ſpace of ſix poles, and one, which is the uniform im⯑preſſion, being added, will make the body fall through a ſpace of ſeven poles. At the beginning of the fifth ſecond, it will have as much velocity as would have carried it through eight poles, and the new impreſſion being added, will make it fall through nine poles. Thus in the firſt ſecond, it will fall through 1 pole, in the next 3, in the third 5, in the fourth 7, in the fifth 9 poles. All theſe being added together, make 25 poles, or 300 feet; ſo that if the tower be 300 feet high, the bullet will fall from its top, in about five ſeconds. And the velo⯑city it will have acquired in the laſt ſe⯑cond of the fall, will be five times greater than that which it had in the firſt. Thus the, velocities, like the times, in⯑creaſe [130] uniformly, 1, 2, 3, 4, 5, but the ſpaces, through which the body falls, taken ſeparately and in order, increaſe by odd numbers, 1, 3, 5, 7, 9, &c.

TO prove all this by experiment: A B, and C D, (fig. 11.) are cords made of the beſt catgut about twelve feet long, tightly extended, parallel to each other, at ſome inches diſtance, and making an angle of about 22½ with the ſurface of the earth. G is a weight which ſlides very freely, by means of two pulleys, along the cord A B, and its weight is ſo contrived to fall below, that its upper part always retains the ſame ſituation. H is a pendulum of a moderate weight which moves upon two pivots A a, and its rod is lengthened a little towards f. The length of the pendulum ought to be ſuch as to vibrate once, while the weight G, runs through the ninth part of the cord A B. To meaſure this exactly, the cord ſhould be carefully marked out into nine equal parts, and upon the other [131] parallel cord, and juſt oppoſite the firſt mark, is to be fixed the little bell K, which, by means of a ſcrew, can be placed at any part of the cord at pleaſure; this muſt alſo have a little clapper, which the weight G, as it runs down its own cord, may ſtrike againſt. On the other hand, the pendulum H alſo ſtrikes a bell of a different tone, and the tail of the pendulum rod that is lengthened to f. cuts as it paſſes a ſmall ſilk thread, that holds the weight G from ſliding. In this manner the whole being well adjuſted, the weight G no ſooner begins to move, than the pendulum ſtrikes its bell I for the firſt time, while the other bell K gives its ſound, juſt as the bell I gives its ſecond alarm. Thus between the firſt and ſecond ſound of the bell I, there intervenes a time, of which we have the exact meaſure, and alſo we have a mea⯑ſure for the ſpace the weight ſlides. We then ſcrew the bell K to that place of the cord where the weight G ſhall make the ſe⯑cond ſound of the bell K, anſwer the third [132] of the bell I, and thus of the reſt; ſo that we may thus meaſure the ſpaces run through, with the times of the deſcent. It will by this appear, that during the firſt vibration of the pendulum, the weight G ſhall run over a ninth part of the cord; if it continues to move for⯑ward during the ſecond vibration, it will arrive at 3, and in the third vibra⯑tion at 5, in the fourth at 7, in the fifth at 9; ſo that the ſpaces taken ſeparately, go on increaſing by odd numbers.

BY theſe means, if a body is let fall from a tower, and if we know the time of its falling, we are enabled to tell what velocity it has acquired in every moment of its deſcent, what ſpace it has run through in each part of time taken ſepa⯑rately, and how much theſe ſpaces make when added together; or in other words, how high the tower is, from whence the body falls.

[133]YET this height may be eſtimated by an eaſier method. For it is plain that the longer the time the body has taken to fall, and the greater the velocity with which it moves, the greater muſt be the height from which it falls: now then we may multiply the time of the fall by the velocity, and the product will give us the height or ſpace through which the body has fallen. Thus if the time a bullet has taken to fall from the top of Weſt⯑minſter tower be 5 ſeconds, and the velo⯑city it has acquired (which is always in⯑creaſing as the time) be 5 times greater than in the beginning, if the bullet fell 1 pole in 1 ſecond, (which all bodies by the force of gravity nearly do) then at the end of 5 ſeconds, it would have fallen 5 multiplied by 5, that is 25 poles, or 300 feet, the height of the tower.

IT was ſaid that the times and the velocities are always equal: as that is the caſe, it will be more expeditious ſtill, to [134] multiply the time of the bullet's fall, by the time itſelf, that is, ſquare its number, and the product will give the ſpace through which the bullet has fallen, as exactly as if the time were multiplied by the velocity. We may therefore con⯑clude univerſally, that the whole of the ſpaces deſcribed by a falling body, is as the ſquares of the times, or the ſquare of the velocities, it is indifferent which.

LET us only add one poſition more on this difficult ſubject, and we have done with its intricacies. From all that has been ſaid, it will follow, that the velocity acquired by an uniformly accele⯑rated body at the end of the fall is ſuch, as if it continued to move forward with that velocity, without any new acceleration, it would, in an equal time, move through a ſpace double that of the fall. For the ſpace it would deſcribe, ſuppoſing it went on with an accelerated motion, would be, as we proved before, as the times multiplied by the velocities; ſo [135] that by this it would have moved through three times as much ſpace at the end of its continued motion, as it did at the end of the fall. But in the preſent caſe, though the time increaſes, the velocity does not increaſe, ſo that we are to mul⯑tiply the whole time of the body's mo⯑tion, by that part of the velocity only, which it had at the end of the fall, and the product will be the ſpace deſcribed by the unaccelerated motion continued after the fall, and it will be found juſt double the ſpace deſcribed in the fall.

AS the motion of bodies falling from a ſtate of reſt, is uniformly accelerated, ſo likewiſe the motion of bodies thrown upward is uniformly retarded; for the ſame force of gravity which conſpires with the motion of deſcending bodies, acts in direct oppoſition to ſuch as aſcend, retarding thoſe that riſe, as much as it accelerates thoſe that fall. If therefore, I ſhould deſire to throw a bullet up to the top of the tower in Weſtminſter, I muſt give it as much velocity with my hand to [136] make it riſe, as it would acquire by the force of gravity if it fell from that height. The action of gravity is conſtant and uniform, and in whatever time it gene⯑rates any velocity in a falling body, in the ſame time muſt it deſtroy that velocity in a riſing body.

THESE are the celebrated diſcoveries of Huygens, and have been employed to very uſeful purpoſes, in ſeveral of the practical parts of mechaniſm. They ſerve alſo to explain many of the phae⯑nomena of meteors. A hailſtone falling from the clouds, if uninterrupted in its deſcent, would ſtrike us with more than the force of ſwan ſhot from a gun. But in proportion as the rapidity of its deſcent is increaſed, the reſiſtance it meets with from the air is increaſed alſo; ſo that at laſt, the acquired ve⯑locity and the increaſed reſiſtance come to act with equal power; after which, the deſcending body can fall no faſter, but continues the ſame uniform pro⯑greſs till in comes to the ground.

CHAP. XI. Of Bodies deſcending down inclined Planes, and of Pendulums.

HAVING explained the deſcent of bodies falling freely by the force of gravity, it will be eaſy to eſtimate the force with which they will deſcend down an inclined plane, (fig. 12.) in which the direction of the fall is altered, but the abſolute weight remains the ſame.

WHEN a body is withheld from obey⯑ing the impulſe of gravity which always acts upon it, it is evident that it is prevented by ſome obſtacle which reſiſts its natural tendency to deſcend. For all bodies endeavour to fall by the ſhorteſt courſe, that is to ſay, perpendicularly to the earth. When bodies therefore fall down inclined planes, we muſt regard them as obeying the uſual laws of gra⯑vity, as deſcending with an uniformly accelerated motion, but acted upon by [138] new forces, only taking up ſo much more time to deſcend, as the ſpace is lengthened, over which they are obliged to fall. The more the ſpace is in⯑creaſed, that is, the longer the inclined plane is, the more time will the body take in travelling it down. Thus ſup⯑poſe the inclined plane to be twice as long as its perpendicular height, then the body will be twice as long in falling, as it would if it fell from its top per⯑pendicularly.

TO ſhew this by an experiment; let us diſpoſe the cords of (fig. 13.) in ſuch a manner, as that they ſhall form an in⯑clined plane A B, which is twice as long as it is high, and then let the pendulum be ſo adjuſted, that while an ivory ball is falling from A to P, it may make one vibration. If the weight G begins to ſlide the ſame inſtant the ball is let to fall perpendicularly, it will not arrive at B till the end of the ſecond vibration, which ſhews that the time of its deſcent [139] is to that of the ivory ball, as the length of the inclined plane is to its height; and if the inclined plane were three times as long, its fall would be thrice as ſlow.

AS the time of a body's fall is thus lengthened, in moving down an inclined plane, ſo alſo will its velocity be dimi⯑niſhed; for that quantity of force which the body has received from gravity to make it fall a certain perpendicular height, is here employed in making it deſcribe a ſpace, which, by the experi⯑ment, is twice the length of the perpen⯑dicular; therefore the body will move but with half the force that it would down the perpendicular, and conſe⯑quently, with but half the velocity. As the time of a body's fall is thus lengthened in proportion to the inclina⯑tion of the plane, we muſt now go on to obſerve, that a body will take as much time in falling obliquely down the ſhort cord of a circle M N, as it would in falling [140] leſs obliquely down the longer cord M L, or in falling perpendicularly through the diameter M P. I repeat it, that a body will take as much time to fall down the ſhorter cord of a circle, as the longeſt. For bodies falling down the cord of a circle, may be conſidered as moving down inclined planes, as A B, A C; but all bodies moving down an inclined plane are, as we obſerved, actuated by two forces; and all bodies thus actuated, move in the diagonal of a ſquare or parallelogram. But all the diagonals thus deſcribed, by the united action of two forces, are always performed in equal times, and therefore all the cords of a circle are ſo too. Thus for inſtance, the body takes no longer time in moving down the cord A B than it does down the cord A C, for both are diagonals de⯑ſcribed by two forces that continue the ſame.

BUT though velocity is diminiſh⯑ed down an inclined plane, yet if [141] two bodies fall from equal heights, the one perpendicularly, the other down the moſt inclined plane whatſoever, the ve⯑locity acquired at the end of the fall in both will be the ſame. For as gravity is the ſame in both, and is alike uniformly accelerated in either, all the increments of velocity either body receives during the fall, will be ſummed up in each at the end; but thoſe increments are equal, as they are produced by the ſame cauſe, which is gravity, and therefore the velo⯑cities at the end will be equal.

IF, inſtead of one inclined plane, we ſhould ſuppoſe ſeveral united (fig. 14.) and the body moving down them one after the other, its velocity, at the end of the laſt plane, will be as great as it would if it fell perpendicularly from the top of the higheſt plane. For the velocity the body acquires at the bottom of each of theſe planes ſingly, is in pro⯑portion to its reſpective height, and con⯑ſequently the ſum of the velocities of all [142] taken together, is in proportion to the ſum of all their heights.

NOW if, inſtead of ſeveral inclined planes thus united, we ſhould ſuppoſe the body moving in the curve of a circle, from A to B (fig. 15.) as all curves may be looked upon as a number of planes inclining one to another, the velocity a body acquires at the end of the deſcent, is equal to the velocity which would be acquired by falling down the perpen⯑dicular height.

FROM hence we may therefore lay it down, that if, by any contrivance, a body is made to deſcend through the arch of a circle, as from C and A, (fig. 18.) and with the velocity acquired by the deſcent, to aſcend along the arch A D of the ſame circle; the arch A D which it deſcribes in its aſcent, will be equal to the arch C A deſcribed in the deſcent, and the times in which thoſe arches are deſcribed will be equal; and this is the caſe of the pendulum, which is an heavy body, as A, hanging by a ſmall cord or wire B A, and moveable about the [144] point B; the weight being raiſed as high as C and thence let fall, it deſcends by its own gravity to A, and then aſcends by its acquired velocity to D, where, loſing all velocity, it will be turned back by its gravity, and deſcending through the arch D A will, upon its arrival at A, acquire the ſame velocity as before, with which it will aſcend to C; and thus it will continue, and if uninterrupted by external obſtacles, would for ever con⯑tinue a vibratory and equal motion.

THIS is that well known inſtrument in common uſe for meaſuring of time, as nothing yet found out divides it into portions ſo exactly equal; nor does the inequality of the arches, it may be made to deſcribe, make an inequality in the time of the vibration. For the vibrations of the ſame pendulum are performed very nearly in equal times; let it ſwing never ſo violently, or move never ſo feebly, yet it performs both in equal times. We have already proved that all the cords [145] of a circle are deſcribed in equal times, and if the cords are thus deſcribed, ſo will ſmall arches, which may be conſi⯑dered as little differing from their reſpec⯑tive cords. Thus if a body (fig. 19.) be as long a time falling down the dotted cord E A, as it is falling the longer dotted cord C A, ſo will it be as long falling in the circle from E to A as it is from C to A; the long and the ſhort arch will be fallen through in the ſame time, and they alſo riſe on the oppoſite ſide to⯑wards D, in the ſame proportion.

THE diſproportion in the length of two pendulums it is, which creates the great difference of time in their vibra⯑tions; the longer the pendulum the ſlower are its vibrations. The cord of any pen⯑dulum is to be conſidered as proportion⯑able to the diameter of a circle, which the weight at the end deſcribes; therefore, if a body is let fall from the top of this diameter as B, (fig. 20.) and if it takes a ſecond in falling, it will continue a ſimilar [146] time, as we have ſhewn, in half its vi⯑bration C A, and another ſecond to com⯑pleat its vibration in riſing up to A D; now if we ſhould lengthen the pendulum, we ſhould lengthen the diameter of the circle, and as conſequently the body will be a longer time falling down a longer diameter than a ſhort one, ſo will it be a longer time in deſcribing its reſpective arches.

AS I know that the time of half a vibration is equal to that of a body fall⯑ing down the diameter of its reſpective circle; if now I would deſire to know, from what height an accelerated body would fall, during the time of one com⯑plete vibration, the ſolution is eaſy. For as the two half vibrations are exactly equal, ſuppoſing in the firſt half vibration the body fell a ſpace of ſixteen feet, in the ſecond half vibration, if the body moved equally, it would deſcribe a ſpace exactly equal; but the ſpaces deſcribed by fall⯑ing bodies are increaſed by odd numbers, [147] 1, 3, 5, and 7, ſo that the body will deſcribe 3 times ſixteen, that is 48 feet, which added to 16, makes 64 feet, the whole time of the fall during one com⯑plete vibration.

SUCH are the moſt important proper⯑ties of the pendulum, an inſtrument which has been converted to the moſt uſeful purpoſes, either in meaſuring time, and in ſcientific affairs in giving its nicer diviſions. By this inſtrument alſo, we can meaſure the diſtance of a ſhip, by meaſuring the interval between the fire and the ſound of the gun; we can alſo meaſure the diſtance of a cloud by numbering the ſeconds between the lightening and the thunder; but in both theſe laſt caſes we muſt know the exact time the ſound takes in travelling through a certain ſpace, which we ſhall hereafter explain. Galileo had no ſooner found out theſe properties in the pendulum, than he turned them to the advantage of philoſophy; by thoſe he meaſured, with [148] ſome exactneſs, his aſtronomical obſer⯑vations, and the pleaſure thus reſulting from their uſe, in ſome meaſure, recom⯑penced the pain of inveſtigating their properties. However, the pendulum he made uſe of could only meaſure time, for he had no inſtrument like our clock, which might ſum up its vibrations. It was rather, in his hands, the inſtrument of a philoſopher, than a thing that could be rendered univerſally uſeful.

WHAT was begun by Galileo was, in ſome meaſure, improved by the in⯑duſtry of Huygens, a man who added the acuteſt penetration to the moſt indefa⯑tigable induſtry. It was he, who made uſe of them in regulating the movement of clocks; and this happy combination has ſince been univerſally adopted. To have an idea of the manner in which a pendulum regulates the motions of a clock, it is to be obſerved, that all clocks are put into motion either by weights or ſprings: but the wheels, if guided by [149] theſe alone, would never turn equably, therefore the pendulum has two palates, as they are called, which at equal inter⯑vals riſe and fall, and let the teeth of the wheels paſs under them in equable ſucceſſion, ſo that the time is marked with great exactneſs. But this ſuc⯑ceſſion is, undoubtedly, the neareſt an equality of any thing we yet know of; however, there are ſome cauſes which deſtroy the regularity of the motion in all clocks. We ſaid, that all equal pen⯑dulums, vibrating in ſmall arches, are performed in times nearly equal; how⯑ever, we muſt now obſerve, that theſe times are not entirely ſo, for thoſe which deſcribe the greateſt ſpace, are longeſt in performing it. This difference of time indeed, is not immediately perceivable by the ſenſes, and in ſhort durations may be neglected; but in a ſucceſſion of vibrations ſummed up together, it may come to a conſiderable amount. In fact, it has been found by experience, that the beſt regulated pendulum clocks, wherein the [150] greateſt care has been taken to make the pendulums vibrate in equal arches, have notwithſtanding varied in a courſe of time, ſo as to ſtand in need of a new re⯑gulation. And it is almoſt impoſſible to make the pendulum conſtantly deſcribe ſimilar circular arches, and conſequently to make its vibrations preciſely equal; for if the wheels, on account of the thickening of the oil by froſty weather, or any other cauſe, grow more ſluggiſh, this will diminiſh alſo the ſwing of the pendulum, and therefore the length of its arches, and conſequently the portions of time that it is made to meaſure, ſo that the clock goes too faſt. On the contrary, when the oil is thinned by heat, and the wheels thus grow more ſlippery, or from their conſtant friction become more ſmooth, ſo as more freely to obey to the moving power, the pendulum will of courſe be acted upon more forcibly, and cauſed to vibrate in larger arches, by which means, the time of each ſwing is enlarged, and of courſe the clock goes too [151] ſlow. This ſource of inequality did not eſcape the penetration of Huygens: to re⯑medy theſe inconveniences, he thought of another method of adapting pendulums to clocks, in which it would be abſolutely indifferent whether the pendulum moved in larger or ſmaller arches; he found that if they vibrated between two curves of a geometrical figure, called a cycloid, the irregularities ariſing from the altera⯑tions upon the pendulum, could produce no irregularity in the vibration.

A CYCLOID is a figure deſcribed by the revolution of a point in a circle, while that circle is rolling upon an even plane. Thus a nail in a chariot wheel deſcribes cycloids as the chariot moves along. Huygens demonſtrated, that how⯑ever unequal the arches were, which a body falling in this curve might deſcribe, they would all be performed in equal times; for the nature of this curve is ſuch, that a body falling down it ac⯑quires by velocity in the beginning, [152] more than it loſes in time at the end. To explain this, let us ſuppoſe the fourth part of a circle A E D (fig. 21.) divided into four parts by right lines, and a body falling down them, as down ſo many inclined planes. If the velocity were not accelerated, it is evident that the body would be a much ſhorter time in rolling almoſt perpendicularly from A to B, than obliquely from C to D. But the body goes with an accelerated mo⯑tion, and while it goes from C to D, though the plane be moſt inclined, yet it performs it with the velocity which it has acquired by falling from A to C. Now it is evident, that if the planes A, B, E, were more perpendicular, the velocity through C D would be greater. The line F G H, which is the curve of a cycloid, is juſt ſuch a figure; the upper part of its curve F G D is more perpendi⯑cular than the arch of the circle I E D, as is obvious to the eye; and therefore the velocity acquired by the body at D, will be greater by falling from the cycloid F, [153] than if it fell from the curve I. Nay what is more extraordinary, by the ſame reaſons, the time in which the body falls from F to H, will be leſs than if it fell down the right line I H, though it is evidently the ſhorteſt way. Upon this was founded the famous problem which Bernouilli propoſed to the geometricians of Europe. He demanded in what line a body, falling obliquely, would fall ſooneſt to the earth? This was not a right line, though the ſhorteſt that could be drawn, but the curve of a cycloid, which was afterwards called by the hard name of a Brachyſtochrone, or the line of quickeſt deſcent.

IT was between two of theſe curves that Huygens ſuſpended a pendulum, as between the curve of the cycloid C A and the curve F B, (fig. 22.) might be ſuſpended the pendulum C V, in ſuch a manner, that the ſtrings which hold the pendulum, as often as it moves from the perpendicular towards either ſide, might [154] bend round either curve, and by this alſo the pendulum would deſcribe another curve of a cycloid A V B. By theſe means he ſuppoſed that the curve A V B being ſimilar to the other two curves, would deſcribe all its vibrations in equal times, and thus communicate a perfect regu⯑larity in clocks. However, experi⯑ence and theory have evinced the contrary.

WHAT ſeems moſt remarkable in the error of Huygens is, that the learned of Europe perſiſted in the error for more than thirty years, notwithſtanding the irregularities that this produced in the movements of clocks. One while they attributed it to the inaccuracy or igno⯑rance of the artiſt; another time to the obſtruction of ſome phyſical cauſes; Mr. Sully was the firſt who undeceived them. He ſhewed that the regularity of cycloidal pendulums was obſtructed upon a very ſufficient account; namely, the flexibility of the rod or ſtring of the pendulum, which [155] it muſt have had to bend along the curve on either ſide, and which altered the weight of the pendulum upon the work to be regulated. Another ſufficient reaſon againſt cycloidal pendulums is, the moiſture which the ſilken ſtrings im⯑bibe from the air; whereas in other pendulums a ſteel rod is made uſe of, which is not ſubject to equal variations. In ſhort, theſe kind of pendulums are now entirely out of uſe; however, it is poſſible they may again be brought into faſhion, ſince a late improvement in one of the movements of a clock by Le Roy, in which the cycloidal pen⯑dulum may be uſed with advantage.

SUCH are the aſſiſtances which geome⯑tricians have brought to regulate the vi⯑bration of pendulums, and to make all the arches they deſcribe equal; but there are other natural cauſes of irregularity, which are entirely irremediable by calculation. As the rod of the pendulum, like all other bodies, contracts with cold, and dilates [156] with heat; ſo it muſt in cold wea⯑ther be conſiderably ſhorter than in hot weather, and conſequently its vibrations muſt be ſwifter in winter when it is coldeſt than in the heats of ſummer. It was a ſuſpicion of this kind that induced ſome to think, that as the pendulum at the equator was found to move much ſlower than the ſame pendulum towards the poles, this might proceed from its being lengthened by the heat of the cli⯑mate. In this however they were de⯑ceived, for its ſlowneſs there (as we ob⯑ſerved before) proceeds from its having a greater centrifugal force, which thus makes the force of gravity leſs at the equator, than towards the poles. I ſay, they were deceived in this; for it has ap⯑peared by the moſt careful experiments, that the lengthening of the pendulum in the hotteſt weather, bears no ſort of pro⯑portion to the ſlowneſs with which the pendulum at the equator is found to move. Mr. Mairan's pendulum at Paris required to be 3 French feet, 8 lines and an half, to vibrate ſeconds. This pendu⯑lum, [157] by every experiment that has been tried to make it vibrate ſeconds at the equator, muſt be 2 lines ſhorter. Now if the air at Paris were as hot as boiling water, yet it could not require the pen⯑dulum to be made the third of a line ſhorter, ſo that the heat at the equator is not the only reaſon that makes it too long to vibrate ſeconds there, ſince the heat alone could not increaſe its length above a third part of what we find it.

THE lengthening of the rod of a pen⯑dulum by heat, and its contraction by cold, are inconveniences however which ſome mechanics have attempted to ob⯑viate, by employing another piece of metal in the movements of the machine, which ſhall counteract the lengthening or ſhortening of the pendulum, by its own dilatation or contraction. Mr. Har⯑riſon's machine is made upon this princi⯑ple, Le Roy and Caſſini have publiſhed treatiſes upon this ſubject: it is our duty in ſo ample a ſubject, to excite curioſity rather than to gratify it.

CHAP. XII. Of Projectiles, or that Motion cauſed by a ſingle Impulſe, and at laſt deſtroyed by Gravity.

[160]NOW inſtead of throwing the body perpendicularly upward, let us ſuppoſe it to be ſhot directly forward, and ſtill ſuppoſing the force to go uniformly for⯑ward, let us divide the whole of its way F G (Fig. 24.) into four equal parts. If the ball F, during the firſt ſecond, falls 1 a by its force of gravity, during the next ſecond, the cauſe increaſing by odd numbers, will make it fall 3 times as low, to 2 c; in the third ſecond it will fall 5 times as much, to 3 c, and in the fourth ſecond it will fall 7 times as much, to 4 g. By this means we ſhall have a ſucceſſion of points, F a c e g, which together form a curve, which geometricians call a Parabola. And in this curve all pro⯑jected bodies will move, in whatſo⯑ever direction they are thrown, except directly upward, or perpendicularly downward.

NOW ſhould it be aſked in what manner a cannon ſhould be planted in order to drive a ball to the greateſt poſſible diſtance, [161] the ſolution will be obvious. For if we ſuppoſe it raiſed perpendicularly as B, (fig. 25.) it is evident that the ball ſhot from its mouth will fall perpen⯑dicularly back again, to the ſame ſpot from whence it was driven. And if we ſuppoſe the cannon laid level with the ſurface of the earth at A, it is evident that the ball can be ſhot to but a very ſhort diſtance; for as it deſcribes the curve of a parabola, and conſequently is every moment deſcending, ſtrictly ſpeaking, it would reach the ground the moment of the exploſion. To give therefore a ball the greateſt amplitude, and to drive it to the greateſt random diſtance, we muſt point the cannon exactly between the horizontal direction A, and the perpen⯑dicular direction B; that is, we muſt elevate it to about forty five degrees of a circle, or the half of its quadrant C; and every day's experience in gunnery confirms the truth of this theory.

ALL the Balliſtic art, or that part of engineering which conſiſts in meaſuring [162] with exactneſs the force of a cannon ball, or a bomb, and ſuch like, conſiſts in a due knowledge of the weight of the body to be driven, and the projectile force that drives it. The weight of the body is eaſily meaſured; the force of the pow⯑der requires much more aſſiduity to underſtand, and can after all be only found by experience. Upon underſtand⯑ing the quality of this, and the quantity that can be employed with effect, de⯑pends almoſt the whole of the gunner's art. I ſay, that can be employed with effect; for only a certain quantity of the powder is always conſumed, which is put into the piece; the reſt is diſcharged entire without ever taking fire, or at moſt is not kindled till the ball is paſt the ſphere of its force.

EXPERIENCE, therefore, is the beſt guide in the doctrine of either throwing bombs or ſhooting balls; for the theory, of which we have given here but a ſmall part, can carry the young engineer but [163] a ſhort way, and indeed it is clogged with ſo many exceptions, that it is rather an object of amuſement than utility. For firſt, the reſiſtance of the air conſider⯑ably alters the former calculations. Mr. Robins, who ſome years ſince publiſhed a work entitled New Principles of Gun⯑nery, even aſſerts that the figure the body deſcribes is not a parabola; others, later than him, who appeal to experience as well as he, affirm the contrary. Future experiments muſt determine the diſpute; for in natural things, the experimenter ſhould ever lead the geometrician ^*. What we have here ſaid with reſpect to the pro⯑jection of bodies, and of their deſcribing parabolas, muſt be conſidered as their motion is ſeen by us ſituated on the earth; but by a ſpectator, removed at a diſtance from its ſurface, and not par⯑taking [164] of its motion, bodies thrown forward would be ſeen to deſcribe very different curves from what an inhabitant of the earth conceives. For in reality, a body thrown upward, beſide the two forces already mentioned, is urged alſo by the rotation of the earth upon its axis. Some ſay, a body thrown upwards will, to ſuch a ſpectator, appear to deſcribe the curve of a parabola as before; others are for reſtricting this aſſertion. Hap⯑pily for mankind, and for philoſophy too, the queſtion is merely ſpeculative: the figure is very difficult to determine, but it is eaſy to determine that all en⯑quiry is to be diſcontinued where it ceaſes to be uſeful.

CHAP. XIII. Of the Communication of Motion.

NATURAL philoſophy, ſtrictly ſpeaking, is little elſe but the mea⯑ſuring of ſuch motions as are obvious, or accounting for ſuch as proceed from an hidden cauſe. We have already ac⯑counted for and meaſured the motions of bodies, that to the vulgar ſeem to put themſelves into action, or, that put into action by us, go on without communi⯑cating their motion to any others: of the firſt ſort, were bodies attracting each other; of the laſt were projected bodies, that were ſuppoſed to meet with no ob⯑ſtruction in their way.

WE now come to conſider that mo⯑tion, which is communicated from one body to another, without conſidering the firſt cauſe which gave that motion to either. If upon ſeeing two bodies in motion, I apply my ſtrength to ſtop [166] either, I will naturally and juſtly con⯑clude that body to have had moſt force, which required moſt of my force to ſtop it. Now there are two things by which a body acquires this ſuperior force; it either moves very ſwiftly, or the body moving is very heavy: in either caſe it requires very great force to ſtop it, but moſt of all, if it is at once both ſwift and heavy. A tennis ball, though it moves very ſwiftly, will give but a moderate blow; a leaden bullet, moving with equal ſwiftneſs, would be fatal. The force therefore, with which a body moves, is in proportion to its ſwiftneſs and weight: or, to expreſs the ſame thing in harder words, the momentum (for ſo is the force uſually called) is compounded of the quantity of matter in a body and velocity united. If then at any time we deſire to know the force with which a body moves, it is but multiplying the velocity by the weight, or the weight by the velocity, and the product is the force ſought for. So that by this we ſee that [167] two bodies may go on with very different degrees of ſwiftneſs, and yet both move with the very ſame force, provided the difference of their weights balances this exceſs. Thus, ſuppoſe a bomb to weigh 40 pounds, and to move 2 miles in a minute; and a cannon ball to weigh 4 pounds, and move 20 miles in the ſame time. If I would know which will ſtrike down a parapet with greater force, I multiply 40 pounds, which is the weight of the bomb, by 2, which is its ſwift⯑neſs, and that makes its force 80. Then I do the ſame by the cannon ball, and 20 multiplied by 4, gives 80; ſo that the force in both is equal, and either would level the parapet with equal force. Once again therefore, I repeat it, that the force or momentum of any moving body is found, by multiplying its velocity by its weight.

TO prove this another way: if it ſhould be ſaid that bodies, which move with equal ſwiftneſs, will alſo move with [168] equal force; ſuppoſe I threw any body forward, and by the time it got to ſome diſtance it ſhould divide into four dif⯑ferent parts, theſe would ſtill move to the end of the caſt with as much ſwift⯑neſs as the body would if it had remained entire; but it would be abſurd to ſay that theſe parts move each with as much force, ſince if ſo, the force in the four parts would be four times greater than what was at firſt impreſſed upon the body, ſo that to put it into motion, the effect would be greater than the cauſe.

ALL this is apparent, and was well known to Archimedes; but notwithſtand⯑ing, obvious as it is, Leibnitz and his followers inſiſt that the force of a body is to be eſtimated, not by multiplying the weight by the velocity, but by the ſquares of the velocity. Thus Archi⯑medes would ſay, that a ball which weighs 2 and moves 2, would go on with a force 4; but Leibnitz contradicts him, and ſays that a ball which weighs [169] 2 and moves 2, will go on with a force 2, multiplied by the ſquare of the velo⯑city 2, which is 8.

THE queſtion in diſpute therefore is, whether the force of a moving body becomes double or becomes quadruple, when the ſwiftneſs is only doubled? Now were the force employed in deſtroy⯑ing its motion, allowed as a proper meaſure to eſtimate the force, with which the moving body went forward, the queſtion would ſoon be at an end, and the followers of Leibnitz muſt ſubmit; for to deſtroy the motion of any body what⯑ſoever, we have only to oppoſe to it an equal weight to its own, multiplied by an equal velocity. Suppoſe a ball of 2 pounds moves forward with a ſwiftneſs of 2 yards in a minute; if I deſire to ſtop it with another ball which weighs 2 pounds, this I can effectually perform if I give the laſt ball, which has already as much weight, as much ſwiftneſs as the former. This ſhews that if the [170] force deſtroyed in one body, be equal to that deſtroying in the other, the moving force muſt originally have been as the weights multiplied ſimply by the velocity, and not as the ſquares.

THE ſtrength of this objection Leibnitz was aware of, and therefore anſwered it by making a diſtinction. The force ſufficient, ſays he, in one body to de⯑ſtroy another body's motion, I grant, is rightly meaſured by the weight multi⯑plied by the velocity; but the force with which a body ſurmounts obſtacles, is to be eſtimated differently from that in which it is overcome by them. A body moving forward, becomes in a manner animated on its way, and when once put forward, overcomes obſtacles that would have been inſurmountable to its force at the very inſtant it began; as a man will overcome difficulties, when in his heat, that in his cool moments would be inſurmountable. Suppoſe, for inſtance, a body, with a certain degree of [171] weight and ſwiftneſs, is able to coil up a watch ſpring; if I double the weight alone it will coil up but two watch ſprings, but if on the contrary I double the velocity alone, it will coil up four. Thus then, continues Leibnitz, we have two kinds of forces; dead forces, which are as the weight multiplied by the velocity; and animated forces, which are as the weight multiplied by the ſquares of the velocity. The dormant force which a body poſſeſſes while counter⯑acted by ſome other, is the dead force; that of a body actually put into motion, the animated. An arrow drawn to the head and juſt ſtarting from the bow, is a dead force withheld by the archer's hand, with a power that would, upon computation, appear to be equal to a certain weight multiplied by a certain velocity; but when the arrow is once ſhot forward, then the animated force begins, and with a power, made up of the ar⯑row's weight and the ſquare of its velocity. Whatever totally deſtroys the [172] animated force, turns it into a dead one, and it therefore yields to an inſurmount⯑able obſtacle in the ſame manner as a dead force would do. But it is other⯑wiſe when ſlight obſtacles are overcome; for ſuch are paſt over with a force, as the ſquares of the velocities multiplied by the weight of the body in motion. We muſt not therefore, concludes Leibnitz, eſtimate the force of a body in motion, by com⯑puting the force which would be ſuffi⯑cient to deſtroy that motion; ſince a moving body ſurmounts obſtacles with a much greater force, than that by which its force is deſtroyed by inſurmountable ones.

SUCH is the doctrine of Leibnitz upon the forces of bodies which impell each other; by which we ſee that he was of opinion that a body, whoſe ſwiftneſs was twofold, would have four times the force of one which only went forward with a ſingle velocity. But however reſpectable the name of Leibnitz may be, there are [173] among his adverſaries, names ſtill more reſpectable, for Newton and Clarke are of the number. We grant, ſaid they, that four watch ſprings will be coiled up by a body with a double velocity, and nine ſprings by a triple, and ſo on; but as you diſtinguiſhed once, ſo now muſt we. Between the firſt in⯑ſtant that the body begins to coil the ſpring, and the laſt, in which the work is completely performed, however quick it may appear to ſenſe, yet there paſſes ſome time. Now if we conſider the effect of the coiling body at the end of the time, it will certainly produce a force as the ſquares of the velocities, and Leibnitz is in this reſpect right; but if, on the contrary, we could eſtimate the force, at the commencement of the coil, it would be ſimply as the velocity multiplied by the quantity of matter.

THIS diſpute, which is not even yet perfectly determined, has for more than ſixty years divided the learned of Europe, and ſharpened ſome even into animoſity; [174] however, it is only a debate merely ſpe⯑culative, and may be reduced to this frivolous queſtion; namely, Whether the obſtacle, a moving force ſurmounts, reſiſts in ſucceſſion its parts oppoſing, one after the other; or whether its reſiſtance is inſtantaneous, all its parts oppoſing together? Which ever of theſe happens, the effect is to be meaſured in the ſame manner, only one takes in the time of ſucceſſion, the other not.

NOTWITHSTANDING this diſpute therefore, we may ſtill continue to meaſure the quantity of force in moving bodies, by their weight multiplied by their velocity; we go on therefore to ob⯑ſerve, that whatever be the action of a body thus moving upon another, that other exerts an equal re-action upon it. If the moving body takes three degrees of force, to drive forward a body at reſt, this quieſcent body employs three degrees of force, to keep the other back. If I preſs a ſtone with my finger downward, the ſtone preſſes my finger equally up⯑ward. [175] If a horſe draws a load forward, as much as he promotes the progreſs of the load, ſo much is he retarded, or in other words drawn back; and whatever motion he communicates to the load, he loſes ſo much of his own. In a word, the re-action of any body whatſoever, is equal to the action employed in put⯑ting it into motion.

AS action and re-action are thus equal, it is manifeſt that in the ſtroke one body makes upon another, the motions of both muſt be equally affected by the blow; and whatever additional motion the one receives, the other muſt loſe ſo much that gave it; whatever the one imparts, ſo much muſt the other be a gainer.

FROM theſe two principles united, namely, that the force of bodies is made up of their ſwiftneſs and weight mul⯑tiplied by each other, and that action and reaction are equal, depends the laws [176] of the communication of motion; laws which ancient philoſophy had never ſup⯑poſed to exiſt, and in which more mo⯑dern philoſophers were for a long time miſtaken.

HOW one body becomes poſſeſſed of a power of granting its motion to another, how matter, which is itſelf inert, ſhould be capable, when moved, of communi⯑cating its activity; theſe are queſtions which we may aſk, but can never re⯑ſolve; perhaps our wiſeſt anſwer will be, with Malbranche, to ſay, that God has willed it to be ſo. But though we are ignorant of the cauſe of its motion, yet, by certain laws, we can readily tell the preciſe quantity of motion (or let us call it force) which one body communicates to another, provided we know the weights of the two bodies, and their ſwiftneſs before they impinged.

IF we could ſuppoſe all bodies perfectly hard, it is manifeſt, that if thus circum⯑ſtanced, [177] any two of them ſhould ſtrike againſt each other in an even direction, they would never ſeparate after the ſtroke, but either remain together im⯑moveable, or go forward together with one common and equal ſwiftneſs. For what is it that could ſeparate them? They cannot recoil from each other, for this would imply that their parts gave way, which they cannot do, as the bodies are ſuppoſed to be perfectly hard, and there⯑fore unyielding. They cannot be ſepa⯑rated by the air, or any other external reſiſtance, for theſe, in the preſent caſe, are ſuppoſed to be removed. If two per⯑fectly hard bodies therefore ſtrike againſt each other, if they move after the ſtroke, they both move together the ſame way.

ALL bodies perfectly hard may be called non-elaſtic bodies; theſe, after the ſtroke, never ſeparate from each other, but either remain together immoveable, or go on with one common velocity. [178] The quantity of force they communicate or receive from each other, may be deter⯑mined in the manner following. If two non-elaſtic bodies meet in oppoſite directions, the exceſs of force in one of them, before they ſtrike, will be all that is left in both after, and this being diſtributed between them, in proportion to their weights, will tell us the force with which each moves after the ſtroke. For all the reſt was deſtroyed by their contrary and equal actions upon each other.

If one body in motion purſues and ſtrikes another, which is either at reſt or in motion, both bodies, after the ſtroke, will have all the force they had before, but then diſtributed between each, in proportion to their weights. For in this caſe there is no contrary agent to deſtroy their con⯑ſpiring forces; and as they both move to⯑gether with equal ſwiftneſs, from their want of elaſticity, the force of either muſt be computed by its reſpective weight, their velocity being the ſame.

[179]THESE are the great laws found out by Sir Chriſtopher Wren, for meaſuring the quantity of force communicated or deſtroyed by the mutual percuſſion of non-elaſtic bodies; and we can, with great eaſe, apply thoſe rules to any par⯑ticular caſes that may be ſtated; as when one body is only in motion at the time of the ſtroke, or when both move in the ſame direction; when they move in op⯑poſite directions, and this with equal or unequal force, or unequal weight. Any of theſe caſes, I ſay, may be very eaſily ſolved, by applying to the rules above mentioned. I ſhall only therefore take any one of them as an example at a ven⯑ture, for as it is a buſineſs rather of calcu⯑lation than curioſity, ſuch learners as are delighted with ſtudies of this nature, will very eaſily ſolve the reſt themſelves. Let us ſuppoſe then two bodies of un⯑equal weight, both moving, and the one overtaking the other. Let us ſuppoſe the weight of the preceding body to be one pound, and let it have three degrees of [180] velocity, ſo that its force will be three. Again, let us ſuppoſe the purſuing body to weigh two pound, and to have a velocity of ſix degrees, ſo that its force will be twelve. Now I deſire to know with what degree of force theſe two bodies will proceed after one has ſtruck the other? Firſt then, according to my rule, I find the force in both bodies before the ſtroke, which is three, and twelve, and that makes fifteen. Now this I diſtribute between the two bodies, after the ſtroke, giving to each in propor⯑tion to its weight. The firſt weighs one, the laſt two; therefore the force in the firſt body, after the ſtroke, will be five, and the force in the laſt body, after the ſtroke, will be ten. Now if I deſire to know what force was communicated by the ſtriking body to the ſmaller; the force of the ſmaller body before the ſtroke was three, and after the ſtroke five; therefore the motion it received by com⯑munication was two.

[181]AND what is thus found exact in theo⯑ry, will be found nearly true in experi⯑ment. I ſay only nearly true, for in the whole circle of nature there is not to be found a body perfectly non-elaſtic, and the philoſopher in this caſe, is obliged to be content with employing in his experi⯑ments, ſuch bodies as are moſt void of elaſticity. If bodies were perfectly hard, they would be perfectly non-elaſtic, as their parts, upon preſſure, would never give way; but as in nature thoſe ſubſtances we meet with that have hardneſs, have great elaſticity alſo; the natural philoſopher, in his experiments upon non-elaſtic bodies, inſtead of uſing unyielding hard bodies, as they are not to be met with, is obliged to have recourſe to ſoft bodies that are non-elaſtic from a different principle; they yield to preſſure, but do not recover themſelves with a ſpringy or elaſtic force.

THE ſubſtances, uſually employed in experiments upon non-elaſticity, are balls [182] made of moiſt clay, and ſuſpended by fine ſtrings, as we uſually ſee pendulums. Theſe are let fall from certain heights, and the time they take to paſs through theſe heights is conſidered as their velo⯑city. With theſe the experiments are found to anſwer nearly to the theory; their ſtill having a ſmall degree of elaſtic force, and the reſiſtance given by the air, cauſes the deviation.

BY theſe we can experimentally be convinced, that bodies, when they hold a certain proportion, are moved, and remove each other in equal proportion. But it is otherwiſe if the difference of the two bodies be very great; if I ſtrike a clay ball againſt the wall of an houſe, the wall remains unmoved as before, or the motion is ſo infinitely ſmall, that ſenſe is not capable of diſcerning it. And this may ſerve to refute the noted opinion of the Epicurean ſects, that no motion was ever loſt in the world, but that what was once begun, though it [183] ceaſed in the firſt body that received it, yet it was only by its being tranſmitted to another, but not actually deſtroyed. It is true, they may reply, that though motion be infinitely diminiſhed, yet this is not equivalent to its being actually de⯑ſtroyed. Much might be ſaid upon this queſtion, but we will paſs it over, as a diſ⯑cuſſion of it would be a matter of uſe to none, and a matter of curioſity only to metaphyſicians.

CHAP. XIV. Of Elaſticity, and Elaſtic Bodies.

AS there are no bodies in nature that are perfectly non-elaſtic, ſo none are endued with perfect elaſticity. By elaſticity, I mean that ſpring or power with which we find many bodies, when preſſed, reſtore themſelves, as ſoon as that preſſure which bent their parts to⯑gether is taken away. Thus a watch ſpring, which, when coiled up, unfurls itſelf as ſoon as at liberty, may be called elaſtic; marble, which, when ſtruck againſt the pavement, rebounds to ſome height, may be called elaſtic. No body on earth, even water, as we ſhall ſee in its proper place, is entirely without this power, and yet no body in nature has this power in perfection. To be per⯑fectly elaſtic, the body muſt reſtore itſelf with a force exactly equal to the preſſure made upon it. The marble, if dropt from an height of three feet, to be perfectly [185] elaſtic, muſt riſe to the height of three feet. It falls to the pavement, is preſſed inwards by the fall; if it recovered from that preſſure with equal force, it would riſe as high as it fell. But no body is found to do this completely; an ivory ball is the moſt elaſtic body that we know of, and ſuch are uſed in all the ex⯑periments upon this ſubject. But before we begin to meaſure the efforts of this elaſtic power, it will not be amiſs to en⯑quire from whence the power itſelf proceeds.

SUPPOSE I hold, by one end, a bit of catgut moiſtened, between my fingers, and lengthen it by pulling at the other; this, when let free, will again ſhorten itſelf as before it was drawn. Now it is required to explain what power it is, which thus ſhortens the ſtring which I had lengthened? A common obſerver would ſay, that it ſhortens itſelf, that the fibres of the ſtring which were lengthened by force, when that force is removed, again [186] reſume their natural ſtate. But what is the natural ſtate of its fibres? Mere matter is intirely inert and paſſive, and the fibres in one ſituation, are as natu⯑rally placed as in any other. There muſt therefore be ſome other power, that thus impells thoſe fibres again to contract; and what that power is, is what philoſo⯑phers enquire.

TO ſolve this queſtion, a Carteſian will ſay, that by lengthening the ſtring we leſſen its pores, and thus ſqueeze a cer⯑tain ſubtile fluid, ſuppoſed to be in all bodies, into a narrower compaſs, which by its endeavouring to fly out, will pro⯑duce an endeavour in the body to reſume its form. This ſolution, is a more incom⯑prehenſible difficulty, than that which it is brought to explain.

OTHER philoſophers, at the head of whom is Malebranche, ſuppoſe that all bodies are filled with little vortexes, which, like watch ſprings coiled, give [187] way to preſſure, but reſtore themſelves upon its removal. This is only ſuppoſ⯑ing one kind of elaſticity that we do not ſee, to prove another that we do ſee.

THE followers of Newton ſay, that this power is nothing elſe but that of attraction. When the ſtring is length⯑ened, ſay they, its parts are not however drawn out of the ſphere of each other's attraction, by which they were held toge⯑ther; and as ſoon as the power that lengthens the ſtring is removed, and the attracting parts are permitted to reſume their functions, they again attract and contract the parts to their former ſitu⯑ations, and the ſtring ſhortens as in the beginning. A ſingle queſtion will ſerve to invalidate this ſolution. Why then are not heavy bodies, which have moſt parts, and ſhould have conſequently moſt attraction, the moſt endowed with elaſticity?

WHAT the cauſe is therefore, that a body, when thus lengthened, recovers [188] its former ſhortneſs when the length⯑ening force is taken away, as yet appears inſcrutable. All that we know is, the actual exiſtence of the experiment; and perhaps this is as much as is worth our knowing. Now methodically to ſhew that a ſtring may be lengthened, and yet recover its former ſhortneſs, the follow⯑ing experiment will ſerve. If the ſtring of a fiddle or an harpſichord, (fig. 26.) be ſtretched between two fixed points, G, H, and let it be ſtruck upon by a ſolid body, ſufficient to bend it from the point from I to K; it is evident that this ſtroke will lengthen the ſtring, for the line G K H, is obviouſly longer than the ſtreight ſtring G H. The ſtring there⯑fore is lengthened by the ſtroke, and were it perfectly void of elaſticity, it would continue lengthened.

NATURE however has endued the ſtring with an elaſtic power, a power which will induce it to ſhorten, and re⯑ſtore [189] itſelf with nearly as much force, as that of the body that gave the ſtroke. So that therefore being lengthened to K, as I ſaid before, it will, by its elaſticity, return back to I. Now the velocity which it acquired by coming from K, being in proportion to the elaſtic force which acts continually, will be continually accele⯑rated, and will drive the ſtring in the oppoſite direction to L. The elaſtic power may in this caſe be reſembled to the gravitating power which we formerly deſcribed in the pendulum; where we ſhewed, that whatever heights the vibra⯑ting body falls from on one ſide, ſo much will it riſe on the other. In this manner will the elaſtic ſtring continue to vibrate from one ſide to the other for ſome time, and if perfectly elaſtic, and not reſiſted externally, would continue to vibrate for ever. And what is re⯑markable enough, each of its little vibra⯑tions, like thoſe of a pendulum, will be performed in times exactly equal to each other.

[190]THE very ſame thing that is here de⯑monſtrated concerning ſtrings, will be found true of all other elaſtic bodies whatſoever; like theſe, their parts give way, recover, and put themſelves into a vibratory motion. Let us, for inſtance, take a ſmall bell or drinking glaſs, and ring them at the edge with the finger; the ſtroke of the finger preſſes the edge of the glaſs, and for that inſtant alters its form; from a circle it becomes an ellipſe, in form of the dotted circle A B, (fig. 27.) but upon the preſſure being removed, it inſtantly recovers its former figure, and the reſtitutive force acting upon it conſtantly, it will acquire ſuch an ac⯑celerated velocity, as to drive it into the oppoſite ellipſe C D. Thus will it continue to vibrate backward and forward, from one ellipſe into the other, till the reſiſt⯑ances it hath to encounter, from its non-elaſticity, and from the external air, en⯑tirely deſtroy its motion.

IN the ſame manner will other elaſtic bodies change their figure, making allow⯑ances [191] for the ſtiffneſs and uncompliancy of their matter or figure. The parch⯑ment of a drum becomes alternately con⯑cave and convex; an ivory billiard ball, let fall upon earth-ſtone, becomes an ellipſoide by the fall, but ſoon alters its figure again.

BUT perhaps it may be thus objected: How do we know, that an ivory ball, which to all appearance is compoſed of parts ſtiff and uncomplying, does thus yield to the impreſſion, and then recover its former figure? An experiment will prove that it yields. Let a ſmooth mar⯑ble hearth-ſtone, or ſuch like, be ſmeared ſlightly over with oil, and then let an ivory ball be dropped upon it, and it will leave a pretty broad ſpot upon the ſtone. Now it will be owned, that this ball upon the fall would touch the marble only in a ſingle point if it were inflexible, but by yielding, it levels a part of its ſurface to the preſſure it receives from the ſurface of marble, and marks it with the im⯑preſſion as before.

[192]FROM hence we may gather, that all elaſtic bodies, how different ſoever their figure, yet exert this force in the ſame manner; that an elaſtic ſtring and an elaſtic ball reſiſt preſſure juſt alike, and take the ſame methods to recover their former ſhapes. And from hence we may infer, that an elaſtic ſtring or body, when lengthened or dilated, recovers its former tenſion with an accelerated velocity: thus the ſtring in returning from K, was uniformly accelerated till it came to I: thus in the figure repreſenting a bow ſtring, the arrow would not quit the bow till the ſtring arrived at the middle point, where it acquired its greateſt velocity.

HAVING thus ſhewn the manner in which an elaſtic body reſiſts preſſure, it is now time to meaſure the quantity of motion received and communicated by elaſtic bodies that ſtrike each other; and as it is impoſſible to throw that degree of perſpicuity into this ſubject which I could wiſh in the compaſs to which I have [193] confined myſelf, I ſhall adopt Helſham's manner, which, though ſome may think difficult, is allowed to be the beſt and plaineſt yet publiſhed. In eſtabliſh⯑ing the theory of which we muſt ſuppoſe the bodies perfectly elaſtic, and all ex⯑ternal reſiſtance from the air taken away. In the ſhock of elaſtic bodies, nature follows the very ſame laws as in that of non-elaſtic bodies, but with this differ⯑ence, that elaſtic bodies fly off after the ſhock with as much force as that with which they came together, whereas if they were non-elaſtic, they would deſtroy each other's motion entirely. The rule for determining the quantity of force in elaſtic bodies, after the ſtroke, is this.

Let the two ſtriking bodies be firſt con⯑ſidered as non-elaſtic, and let the force of each body after the ſtroke be found, as alſo the force communicated from the one to the other. Then as they are elaſtic, let this force be ſubducted from that of the ſtriking body after the ſtroke, and added to [194] that of the body which received the ſtroke, and the reſidue will be the force of the ſtriking body, and the ſum the force of the other body after ſeparation.

THIS is demonſtrable; for with whatever force the bodies ſtruck each other, by virtue of their weights and ſwiftneſs, they will recede as much by virtue of their elaſticity, and throw one another contrary ways, each with a quan⯑tity of force equal to that which the ſtrik⯑ing body communicates to the other; for which reaſon, if that force be ſubducted from the force remaining in the ſtriking body after the ſtroke, as being contrary thereto, and added to the force of the other body after the ſtroke, as conſpiring therewith, the reſidue and ſum will give the forces of the bodies after ſepa⯑ration.

THESE general expreſſions will be better underſtood, by making particular applications. If two equal bodies meet [195] one another with equal forces, they will be reflected back with the ſame forces and the ſame velocities wherewith they approached. For if non-elaſtic, they would upon the ſtroke deſtroy each other's force; but by the rule each of them muſt, on account of elaſticity, re⯑ceive as much as they gave; and the forces which are thus received by the bo⯑dies being equal, muſt carry the bodies backward with the ſame equal force wherewith they approached.

IF a body, perfectly elaſtic, ſtrikes another of equal magnitude at reſt, the ſtriking body will communicate all its force to the other, and remain at reſt itſelf. For if they were non-elaſtic, the ſtriking body would upon the ſtroke communicate half its force, (as may be eaſily calculated;) and by the rule now laid down, a quantity of force, equal to that communicated, muſt be ſubducted from the ſtriking body, and added to the motion of the body which receives the ſtroke, by which means [196] the ſtriking body will have no force left; but the other will have a quantity of force equal to what the ſtriking body had before the ſhock.

IF two elaſtic balls be unequal; for inſtance, if one be double the other, and if the greater have nine degrees of velocity and the leſſer be at reſt, they will both move forward after the ſtroke; the ſtriking body with one third of the force which it had before the ſtroke, and the other with two thirds; and the velocity of the ſtriking body will be three, and of the other twelve. For ſince the ſtriking body is to the quieſcent as two to one, if non-elaſtic, it would communicate one third of its force; and being elaſtic, a quantity of force equal to what is communicated, muſt be taken from the force remaining in the ſtriking body, and added to the force of the other; conſequently the ſtriking body will retain one third only of its force, the other two thirds being communicated [197] to the body which receives the ſtroke; wherefore, ſince the ſtriking body weighs double, or is two, and its velocity nine, its force muſt be eighteen, one third of which, to wit, ſix, it will retain after the reflection, and the other two thirds, to wit, twelve, will be the motion of the other body; and theſe motions being divided by the bodies, will give three and twelve for the quotients; which quotients are as the velocities of the bodies after reflection.

ON the other hand, if a ſmall elaſtic ball ſtrikes a larger at reſt, let us ſuppoſe the ſmaller ball to have nine degrees of velocity, and weigh one pound, the larger, which is at reſt, to weigh two pound. The force of the ſmaller will be nine, and it would, if non-elaſtic, com⯑municate two thirds of this force upon the ſtroke to the greater, and only one third remain in it which is the ſtriking ball. Now on account of the elaſticity, [198] we muſt ſubduct from this remainder, as much force as was communicated, namely, two thirds; but upon ſubduct⯑ing two thirds from one third, there will remain one third negative, which ſhews that the ſtriking ball will be reflected with one third of the force it had at the time of the ſtroke, ſo as to aſcend backward with a velocity of three. But the greater ball, to which two thirds of the ſtriking ball's motion was communicated by the ſtroke, will likewiſe, on account of the elaſticity, receive two thirds more, ſo as to be carried forward with a force equal to what the ſtriking ball had at the time of the ſtroke, and one third more; that is to ſay, with a motion which is as twelve, which being divided by two, the weight of the ball, gives ſix for the velocity with which the ball will recoil.

IF two equal elaſtic bodies move in the ſame direction, and in ſuch a manner as that one may overtake and ſtrike the other, upon the ſtroke, they will ex⯑change [199] their quantities of force with each other. For inſtance, if the force of the ſubſequent body before the ſtroke be double the force of the preceding body, then will the preceding body after the ſtroke, have double the force of the ſub⯑ſequent body after the ſtroke; and the preceding body after the ſtroke, will move with the ſame velocity the ſubſe⯑quent body moved before the ſtroke; and the ſubſequent body will, after the ſtroke, be carried with the velocity of the preceding body before the ſtroke: ſo that upon the ſtroke the bodies will exchange their forces; but as the weights of the bodies are the ſame, we may in other words ſay, they will exchange their velocities. For let us ſuppoſe the ſum of the forces to be three, and as the bodies are equal, the force of each after the ſtroke, if they were non-elaſtic, would be one and an half, and the force communi⯑cated would be one and an half; and ſo likewiſe will the force ariſing from elaſti⯑city, which being deducted from the [200] force which remains in the ſtriking body after the ſtroke, and added to that of the preceding body, leaves the force of the former as one, and the latter as two, ſo that after the ſtroke the forces will be exchanged.

IF the bodies be unequal, and move the ſame way, their forces and velocities after the ſtroke, may in like manner be diſcovered by the help of the rule. For inſtance, if the ſubſequent be two pound, and have twelve degrees of force, and the preceding be one pound, and have three degrees of force; the force of the ſubſequent body after the ſtroke will be eight, and that of the preceding body ſeven; and the velocity of the former will be as four, and that of the latter as ſeven. For the ſum of the two forces before the ſtroke being fifteen, and the bodies being as one and two, the force of the leſſer body after the ſtroke, if non-elaſtic, would be five, and that of the greater ten. But the force of the leſſer [201] body, before the ſtroke, was three, con⯑ſequently the communicated motion is two. Now adding ſo much, on account of elaſticity, to the motion of the leſſer body, and ſubducting as much from that of the greater body, we ſhall have eight for the motion of the greater, which being divided by two, the quantity of matter in the greater, gives four for its velocity; and we ſhall have ſeven for the motion of the leſſer body, which, be⯑cauſe the weight in the leſſer is one, will likewiſe expreſs the velocity.

IF two bodies meet each other with unequal forces, if their weights be equal, they will both be reflected, and each of them will recede with the force and velocity wherewith the other approached; that is, they will exchange their forces and velocities. For let us ſuppoſe the motions of the two bodies to be as ſix and three; if they were non-elaſtic, the body which has the ſmalleſt quantity of force, would upon the ſtroke be turned [202] back, and the two bodies would be car⯑ried with the difference of their forces divided equally between them; that is, the force of each would be as one and an half, and the force communicated would be as four and an half. But a quan⯑tity of force, equal to what is communi⯑cated, muſt be ſubducted from the force remaining in the ſtriking or greater body, and added to the force of the other; that is, four and an half muſt be ſubducted from one and an half, and like⯑wiſe added thereto, whereby there will be three negative for the force of the ſtriking or greater body; which ſhews that it will be carried back with a force as three; and there will be ſix poſitive for the force of the other body, which ſhews that it will be carried with a force which is as ſix, in the direction of the ſtriking body before the ſtroke, that is, it will be reflected; ſo that each of them will be carried back with the motion wherewith the other approached.

[203]IF the balls be unequal and meet each other with unequal forces, their forces after the ſtroke may in like man⯑ner be determined by the rule. For inſtance, if two bodies, one weighing two pound, and with ſix degrees of velocity, the other weighing one pound with three degrees of velocity, and theſe ſtrike each other in oppoſite directions; in this caſe, the greater ball will upon the ſtroke loſe all its force, and the ſmaller will be reflected with the dif⯑ference of their forces. For ſuppoſing them non-elaſtic, the force in the larger, which is two, multiplied by ſix, makes twelve; the force of the leſſer, which is one, multiplied by three, makes three. The difference therefore of their motions is nine, and this being divided between the bodies, in proportion to their quan⯑tities of matter, gives ſix for the motion of the larger, and three for that of the ſmaller; now by reaſon of their elaſticity, a force equal to what is communicated by the ſtriking or larger body to the other, [204] which in this caſe is ſix, muſt be taken from the force of the greater body and added to that of the ſmaller, which two forces being ſix and three, the remain⯑der, after ſubduction, which expreſſes the force of the greater body, will be nothing, and the ſum ariſing from the addition, which expreſſes the motion of the ſmaller ball, will be nine.

ALL that has been aſſerted here from theory, will, upon experiment, be found to anſwer pretty nearly. The bodies made uſe of in ſuch admeaſure⯑ments are ivory balls, which diſcover the greateſt elaſticity. They are hung upon ſtrings like pendulums, and then let fall from determined heights, which heights are adjuſted by a ſcale. The height from which the body falls repre⯑ſents its velocity, the weight and height together repreſents the body's force.

THE force will be thus communicated if the balls are equal; but if the ſtriking ball be leſs than the balls at reſt, and if theſe increaſe in weight one above the other in proper order, the force in the laſt ball that flies off, will be conſider⯑ably greater than that of the ball which firſt made the ſtroke; and this force may be increaſed to any degree whatſoever. For let us ſuppoſe but two balls only, the ſmaller ball muſt upon the ſtroke, if it were non-elaſtic, communicate more than half its force to the greater ball, and there muſt likewiſe be, on account of elaſticity, as much more ſubducted from the ſmaller ball, and added to the larger; wherefore, ſince two equal quantities of force, each of which exceeds half the ſmaller ball's force, are to be ſubducted from the ſmaller ball, and given to the larger, it is plain that the ſmaller muſt loſe all its motion and ſomething more, that [207] is, it muſt recoil back, and the greater ball muſt go forward with more force than was in the ſmaller at the time of the ſtroke, that is, its force will be augmented. Now therefore, if a force be communi⯑cated from a ſmaller elaſtic body to a larger, by means of ſeveral intermediate bodies each larger than the other, the motion will be augmented in each of them, and the motion of the laſt will greatly exceed that of the firſt; and this force will be conveyed with leaſt diminu⯑tion, if the weights of the bodies riſe above each other ſo that the laſt be as much greater than the former, as that is exceeded by the foregoing. As an inſtance how prodigiouſly force may be augmented by being ſucceſſively com⯑municated through a range of bodies, increaſing in this progreſſion: If twenty elaſtic bodies be placed one after another, each ſucceeding body being twenty times greater than that next it, and if a force be impreſſed upon the ſmalleſt body, the laſt body will fly off with a [208] force two hundred thouſand times greater than that with which the ſmalleſt body firſt ſtruck the range. If we ſhould ſuppoſe a cannon ball, ſhot from its culverin, to be elaſtic, and ſtriking with all its force a range of balls, in⯑creaſing in the proportion above men⯑tioned; what an amazing effect would it not have. But ſuch a ſwiftneſs would quickly deſtroy itſelf; the ball, from the reſiſtance of the air to its paſſage, would fly into a thouſand pieces; for no ſtroke that we have an idea of, could equal that with which the air, however yield⯑ing it may appear to us, would act upon a body thus violently carried againſt it.

CHAP. XV. Of Mechanic Powers.

THE power which man thus finds that one body has of communi⯑cating its motion to another, has taught him to make uſe of ſome bodies to re⯑move others which he finds neceſſary or proper to be removed. A weight greater than what his natural ſtrength could manage, without ſome ſuch contriv⯑ance, could never be lifted from the earth; he finds himſelf therefore obliged to call in the force of inanimate nature, in making ſuch alterations as his plea⯑ſures or neceſſities may require. By means of levers he lifts weights much greater than his ſtrength could over⯑come; with the axle and wheel he can lift them to greater heights; with the pulley to greater ſtill; the ſcrew, if it could move without friction, would give him greater force than any of the reſt; but a machine compoſed of all theſe united, would increaſe his ſtrength to a degree [210] ſurpaſſing credit. Biſhop Wilkins, in a work of his called Mechanic Magic, aſſerts that he could pull up an oak by the roots with a ſingle horſe hair; and ſo indeed he could, if the parts of the machine did not rub againſt each other, and thus retard the motion. However, even as it is, we ſee ſuch weights re⯑moved and raiſed to conſiderable heights, as would, to an unexperienced ſavage, appear the work of enchantment. Nor were the ancients without a great knowledge in this art, of increaſing human ſtrength by machinery. The ſtones which we ſee laid upon the tops of the pyramids of Egypt, each of which is as big as a ſmall houſe, create even the wonder of a modern machiniſt, and teach him to reverence the ſuperior arts of antiquity.

WE come now therefore to explain the manner in which human ſtrength is thus aſſiſted, and the inſtruments made uſe of for that purpoſe. Theſe are called [211] mechanic powers, and are ſaid to be ſix in number; namely, the lever, the axle and wheel, the pulley, the ſcrew, the wedge, and the inclined plane. Such is the number uſually reckoned; ſome however mention the balance among the mechanic powers, and omit the inclined plane; a Frenchman among the moderns adds another mechanic power, which he calls La Machine Funiculaire. It mat⯑ters little what number of mechanic powers we make, it is ſufficient if we deſcribe them all. Were whatever in⯑ſtrument encreaſed human force in moving or raiſing bodies by machinery, to be reckoned among the number of mechanic powers, we might add ſtill another, namely, ſuch a machine as would convey a range of elaſtic bodies increaſing in the progreſſion, which has been explained in the former chapter; this and others ſtill might be added, differing in principles from thoſe we are ſhortly to explain. But no matter for the names, let us deſcribe the things.

[212]THE balance, as we ſaid, is reckoned by ſome among the mechanic powers; and though it does not tend to increaſe human force, yet it will be the propereſt to be deſcribed firſt, as it will ſerve to explain the reſt, which are ſomewhat upon ſimilar principles. Suppoſe I take any thing that is next my hand, a walk⯑ing cane for inſtance, and attempt to balance it acroſs my finger; I ſhall at laſt find ſome one particular part in it which being ſupported, neither of the ends will preponderate. The very part of it that reſts upon my finger is the center of its weight, which being ſup⯑ported, the whole cane is ſupported. It is called by mechaniſt the center of gra⯑vity. If I ſhould remove my finger from this center of gravity, which I have thus found out, towards either of the extre⯑mities of the cane, though but of the ſmalleſt diſtance; that ſide would ſink towards the earth which had the center of gravity in it. Thus no body at free⯑dom will be ſupported, unleſs the [213] greateſt part of its weight be ſupported, and whatever ſupports that, muſt ſup⯑port the center of gravity alſo.

BUT though I have thus balanced the [...]ne with ſome ſmall difficulty, yet all bodies whatſoever that are at reſt, are ba⯑lanced in the ſame manner; their centers of gravity are ſupported upon ſome baſe or prop, which keeps them firm, and the wider the baſe is on which the body is ſupported, the more difficulty will that body be overturned. For in order to this, I muſt firſt puſh the center of gravity, or in other words, the greateſt half of the body's weight, from off the baſe or prop, before the body can become top heavy; and it is plain, that it will be harder to lift the half of the body's weight over a large baſe than a ſmall one. If a caſk be placed upon one of its ends, for inſtance, it may require great ſtrength to overturn it, becauſe I muſt puſh the center of gravity beyond its baſe, which is broad; but if the caſk lies [214] on one ſide, I can roll it over with eaſe, becauſe the narrow baſe touches the ground but almoſt in a point, and therefore the centre of gravity may eaſily be puſhed beyond it. For this reaſon it is that a cylinder, or body ſhaped like a rolling ſtone, makes many turns as it deſcends down an inclined plane, for the center of its gravity falls continually beyond the narrowneſs of the baſe; while on the contrary, if the ſame body were made ſquare, and con⯑ſequently with a large baſe, it would either not deſcend at all, or it would ſlide down without being once over⯑turned in the way.

MAN himſelf may be conſidered as a body thus balanced: if his center of gravity reſts upon his feet he can ſtand; but if it is thrown beyond this ſupport, he muſt inevitably fall. A man with a burthen at his back muſt lean forward, for ſhould he attempt to retain his uſual rectitude of figure, his center of [215] gravity would be altered, and he muſt conſequently fall backward. With a burthen on his breaſt, he in the ſame manner counter-balances the weight by altering his figure in the oppoſite poſi⯑tion. Almoſt in every inſtance of his motions he is obliged to make uſe of theſe balancing arts to keep himſelf up⯑right; and it is uſually the ſtudy of a fine painter to known how far the human figure may be bent, without its abſolutely loſing the center of its gravity. Da Vinci, one of the firſt painters after the revival of the art, has laid down rules upon this ſubject; ſucceeding painters have improved upon his plan: Dom⯑ponius Gaurie, an Italian ſculptor, who wrote a Latin treatiſe upon this ſubject, thus admirably expreſſes himſelf: Omne corpus, niſi extrema ſeſe undique conti⯑neant, librenturque ad centrum, collabatur ruatque, neceſſe eſt. "Every body muſt neceſſarily fall, unleſs it unites together in the center of all its extremes, and theſe are balanced againſt each other." What⯑ever [216] weight, ſaith Watelet, the human figure is repreſented as lifting, we are by no means to eſtimate it by its ſize, and ſo, to make it appear more ponderous, to draw it more large; no, we are to throw the whole effect of its weight into the figure that is ſuppoſed to lift it, and diſtort the animal form as much from the natural poſition, as the weight is ſuppoſed to be heavy.

IN general the human body, and every other whatſoever, will ſtand moſt firmly where the baſe is broadeſt, and bears every part of the weight moſt equally; or in other words, where the center of gravity lies moſt exactly over the middle of the baſe. For this reaſon, a man when he wreſtles, generally widens his legs in order to widen his baſe, and thus prevent his antagoniſt's ſtrength from overturning the center of his gravity.

THUS we ſee man and all other bodies balanced upon their centers; the bodies [217] which have the largeſt baſes, and bear the incumbent weight moſt equally, are moſt firmly fixed; on the contrary, thoſe which have the ſmalleſt baſes, or whoſe bodies are ſupported but upon a point, are leaſt firmly placed, and may be overturned with the leaſt ſenſible alteration. Now ſuppoſe we ſhould place a wooden beam, with its center of gravity reſting upon the point of an upright needle, this would not fall; for as the center of gravity is ſupported, ſo likewiſe would the whole of the beam be. Again, ſuppoſe the beam, thus wavering at every touch but ſtill balanced upon the point, to be twice as long on one ſide as on the other; that is, ſuppoſe it one yard long on one ſide of the ſupporting point, (fig. 29.) and two yards long on the other. To it, thus balanced as it is, let us hang equal weights at either end, a pound at one end, and a pound at the other. The balance will now entirely be deſtroyed; the weight at the longer end, which is two yards, will inſtantly [218] preponderate, and appear to be much heavier than the other. Why? The uſual ſolution is this. Suppoſe the weight at the longer end B, deſcends to C, it will deſcribe a ſpace equal to B C, while the weight at the ſhorteſt end A, will at the ſame time riſe only to D, and deſcribe a ſhorter ſpace equal to A D. The weight B therefore, which deſcribes the largeſt ſpace, will have the greateſt velocity. But the force of all bodies is compoſed of the velocity and weight; and as B hath as much weight as A, and a much greater velocity, it will have therefore a greater force, and conſequently out-ba⯑lance its antagoniſt.

UPON this eaſy principle, continue they, the whole of mechanics depends; ſo that if two bodies are ſuſpended at each end of a beam, or any machine whatſoever, if the one be as much ſuperior in its velocity, as the other ex⯑ceeds it in weight, the bodies will balance each other; if the velocity be greater in [219] proportion, that ſide will ſink; on the other hand, if the weight be greater in proportion, that will preponderate. As for example: If the ſide or arm A of the beam be one yard to the prop F, while the ſide or arm B is two yards; as B has thus twice the velocity of A, I muſt make A twice the weight to counterpoiſe B. If B be one pound, I muſt make A two pounds, to keep the balance equal. So that univerſally to make a lighter body out-weigh an heavy one, it is but to make up the defects of its weight by increaſing its velocity. Thus one pound, if it has twice as much velocity, or in other words, be twice as diſtant from the prop, it will balance a body that is twice as heavy as itſelf. A weight of one pound, if it be twelve degrees diſtant from the prop, will balance a weight of twelve pounds that is but one degree diſtant.

A COMMON pair of ſcales is a beam ſuſpended upon a point or axle, and its [220] arms are equally long, and equally heavy; ſo that the velocity on both ſides is the ſame, and alſo the weight is the ſame; and conſequently all bodies of equal weights put into either ſcale, will balance each other. But this, as I ſaid before, will not happen, if one arm of the inſtrument were longer than the other; for then that at the longeſt end having greater velocity will prepon⯑derate.

THE ſteelyard is an inſtrument of this kind, contrived for weighing bodies by a ſingle weight, whoſe velocity or diſ⯑tance from the prop, we increaſe in pro⯑portion to the weight to be known. For if a ſcale hangs at A, the extremity of the ſhorter arm, and is of ſuch a weight as will exactly counterpoiſe the longer arm C; if this arm be divided into as many parts as it will contain, each equal to A B, the ſingle weight P, which we may ſuppoſe to be one pound, will ſerve for weighing any thing as heavy as itſelf, [221] or as many times heavier than itſelf, as there are diviſions in the arm B C. Thus we ſee that one pound, at the diſtance of twelve, balances againſt twelve pound at the diſtance of one.

SUCH is the manner in which me⯑chaniſts have uſually explained this ſub⯑ject; and it muſt be owned that in practice it anſwers pretty exactly. Not⯑withſtanding this, Newton, ſagacious in all things, was ſenſible that the theory ſhewn here, was obſcure and unſup⯑ported; he therefore gave a theory much more difficult, though much more ſatisfac⯑tory. Mr. Varignon and Mr. D'Alembert are equally diſpleaſed with the former the⯑ory. We have not, ſays the latter, a ſingle work on mechanics, in which the theory is proved with the exactitude it requires. In fact, to eſtabliſh the former theory, we are obliged to ſuppoſe two bodies equally at reſt to have ſuperior velocity one above the other; though, when we are aſked what velocity means, it only [222] ſignifies their going through more ſpace in the ſame time. Now is it not evident that at the beginning of the time, neither has gone through any ſpace at all, and therefore their velocities muſt be equal. So that ſuperior velocity cannot be brought to prove why one body firſt begins to preponderate againſt its antagoniſt of equal weight, yet this is what we deſire to know. The theory therefore muſt be built upon another foundation; perhaps it may be eſtabliſhed by the method following.

WHAT I deſire to know is, why a beam, with one arm longer than the other, and which being placed upon a point or prop, is exactly balanced; why, I ſay, when thus balanced, if I hang equal weights at either end, the beam ſhall no longer continue in balance, but the longer arm ſhall preponderate? To explain why this is ſo, it muſt again be repeated, what was ſaid of the center of gravity, that all bodies ſtood moſt firm when the [223] baſe was largeſt, and the center of gravity was placed moſt exactly over the middle of the baſe. The nearer the edge of the baſe the center of gravity fell, as was ſaid then, the readier would the body be to fall. If the center of gravity fell juſt without the baſe, the body would effectually tumble, though only with ſo much velocity, as the reſiſtance of the baſe, which tends to keep it upright, is exceeded by the power that cauſes it to deſcend. Thus the body may be ſup⯑poſed as acted upon by two contrary forces, and the velocity muſt be in pro⯑portion to the exceſs of one force above the other; but ſmall, becauſe the differ⯑ence between the gravity and the reſiſt⯑ance is ſuppoſed to be juſt begun. Now if the center of gravity fell ſtill farther beyond the baſe, the reſiſtance of the baſe to the body's deſcent would be ſtill leſs; for as we ſaid, the baſe gives moſt reſiſt⯑ance when the center of gravity is in the middle, and therefore the farther the center of gravity is removed from [224] its middle, the leſs reſiſtance will it give; and therefore the body will be more acted upon by the power which cauſes it to deſcend, and it will tumble with greater velocity. So that in general we may conclude, the farther the center of gravity falls beyond the ſupporting baſe, the ſwifter will be its deſcent.

ALL this being premiſed, if I now inquire why a ſmaller weight C, pre⯑ponderates in the balance, though op⯑poſed by a great one A; I anſwer, be⯑cauſe the center of gravity in the beam, falls to a greater diſtance on the pre⯑ponderating ſide C, than A. For let us ſuppoſe the beam F, without its weights, but balanced upon its baſe, which is but a point. Now if I ſhould hang a pound at A, this would throw the center of gravity, which was before at F, nearer to A, and far beyond the baſe, ſo that A would preponderate. In order to oppoſe this therefore, I muſt hang an equal weight of a pound at an [225] equal diſtance from the baſe on the oppoſite ſide at E, which will throw the center of gravity as much beyond the baſe that way, ſo that the center in this caſe, actuated by two equal forces, will ſtill remain ſuſpended over the middle of its point or baſe F. But again, if we place this equal weight at more than an equal diſtance, ſtill farther to B, it is evident that it will overcome its antagoniſt, and remove the center of gravity at a greater diſtance from its baſe, and that therefore the body muſt fall that way; and conſequently, as we ſaid above, with the greater velocity. We may therefore conclude univerſally, that if two equal bodies be balanced upon a point, and each equally diſtant from it, if one of them be removed at a ſtill greater diſtance, it will endeavour to deſcend with greater velocity, the farther its center of gravity falls beyond the baſe or point on which it reſts. In other words, the baſe or point is thus rendered more diſtant, and conſequently [226] leſs capable of contributing to the body's ſupport.

FROM all that has been here ſaid, we at length perceive the weakneſs of the former theory, and we now ſee that a ſmall weight out-balances a greater, not becauſe it has a greater velocity, but becauſe the prop, which in ſome meaſure ſupports both, ſuſtains a greater part of the large weight that is near, than of the ſmall weight that is farther off. That the body placed at the longer end, when put into motion, hath more velocity, is moſt certain; but this velocity was nothing when the bodies were in equilibrium, and therefore could never deſtroy that equilibrium: velocity is the conſequence of motion, not the cauſe. If it be ſaid, that the body had a poten⯑tial, or, as Leibnitz expreſſes it, a virtual velocity, though not yet exerted; this is only ſaying in a dark and unintelli⯑gible manner, what we have endeavoured to throw into greater ſun-ſhine.

[227]THIS theory may, with great eaſe, be applied to the ſolution of ſeveral more complex propoſitions. As for inſtance, if a man, ſtanding in one ſcale of a large pair of ſcales, and balanced by weights in the oppoſite, ſhould extend his arm, and preſs the beam upward with his hand, towards the middle, this preſſure would take effect, although his feet ſeem to preſs downward as much as his hand upward; this preſſure upward, I ſay, would raiſe the ſcale in which he ſtands. For (to diſpatch it in a few words) by extending his arm nearer the prop, he brings the general centre of gravity more within the baſe. It is partly owing to this, and partly to the elaſticity of the muſcles employed in the preſſure above, while the muſcles below have leſs employment, and conſequently leſs elaſticity.

THIS theory will ſerve to explain the proportions that muſt be obſerved in a balance, where one or both the arms [228] are crooked. All the mechanic powers may be reduced to the balance, this theory may therefore, by ſome attention in the ſtudents, be applied to them; it is enough here to explain the principle; ſuch as are fonder of calculations than I am, may make the application.

THE mechanic power moſt allied to the balance, and in fact, ſcarce differing from it, is the Lever. A lever is a bar of iron or wood, one part of which being ſupported by a prop, all other parts turn upon that prop as their center of motion. This inſtrument is of two kinds. Firſt, the common ſort, where the weight we deſire to raiſe, reſts at at one end of it, our ſtrength is ap⯑plied at the other end, and the prop is between both. When I ſtir up my fire with the poker, I make uſe of this lever; the poker is the lever, it reſts upon one of the bars of the grate as a prop, the incumbent fire is the weight to be overcome, and the other [229] end I hold in my hand, which is the ſtrength or power. In this, as in all the reſt, we have only to increaſe the diſtance between the ſtrength and prop, to give the man that works the inſtru⯑ment greater power: the reaſon has been already explained at large.

THE lever of the ſecond kind, has the prop at one end, the ſtrength is applied to the other, and the weight to be raiſed reſts between them. Thus in raiſing the water plug in the ſtreets, the workman puts his iron lever through the hole of the plug till he reaches the ground on the other ſide, and making that his prop, lifts the plug with his ſtrength at the other end of the lever. In this lever alſo, the greater the diſtance of the prop from the ſtrength, the greater is the workman's power.

THESE inſtruments, as we ſee, aſſiſt the ſtrength; but ſometimes a workman is obliged to act at a diſadvantage, in [230] raiſing either a piece of timber or a ladder upon one end. We cannot, with grammatical propriety, call this a lever, ſince ſuch a piece of timber in fact no way contributes to raiſe the weight. In this caſe, the man, who is the ſtrength or power, is in the middle, the part of the beam already raiſed is the weight, the part yet at the ground is the prop, on which the beam turns or reſts. Here the man's ſtrength will be diminiſhed, in proportion to the weight it ſuſtains. The weight will be greater the farther it is from the prop, therefore the man will bear the greater weight the nearer he is to the prop.

THE ſecond mechanic power is the axle in the wheel, in which the ſtrength is applied to the circumference of the wheel, and the weight to be raiſed is faſtened to one end of a rope, whoſe other end winds round an axle, that turns with the wheel. (Fig. 30.) This inſtrument is more commonly uſed with [231] an handle: thus, to wind up a jack I turn the handle, which coils the cord round the axle in the middle: to wind a bucket from a well, I do the ſame thing; to wind up my watch, the ſame: the handle in all theſe is in the place of a wheel, and the farther this handle is from the center, the axle, on which the whole weight is ſuſtained, the more powerful will it be. Or if it be a wheel, the more its diameter exceeds the diameter of the axle, the greater will be its power. Thus, if the wheel be eight times as wide as the axle is thick, it will have eight times the power; and a man, who by his natural ſtrength, could only lift an hundred weight, by this machine will be enabled to lift eight hundred.

ONE circumſtance with regard to this machine I muſt not omit: workmen uni⯑verſally affirm, that in raiſing weights to conſiderable heights, (to an houſe-top, for inſtance) with an axle and wheel, they find the weight moſt heavy when [232] they firſt begin to wind, and that it grows lighter and lighter as it approaches the axle. The reaſon of this ſeems to be, that the weight appended at the cord, when longeſt, is apt to ſwing; and if we reſolve the whole machine into a common lever, we ſhall find that the weight to be raiſed in this caſe, will, by ſwinging, either fall at a great diſtance from the prop, or it will fall nearer the prop, or it will fall between the prop and the power. In the firſt and laſt caſe, its ſeeming weight will be augmented, in the middle caſe it will be leſſened. So that when the weight ſwings, there are two to one that the weight will appear augmented to the labourer; and the greater the ſwing, the greater will this augmentation be.

A FIXED pulley that only turns on its axis and riſes not with the weight, can only ſerve to change the direction of the moving power, which is in all caſes exceedingly convenient. For inſtance, if the weight W, is to be raiſed to A, and the man cannot readily get to it, or exert his ſtrength when he gets there, he has then only to throw the cord B round the pulley fixed at A; and ſtand⯑ing upon the ground, and exerting his ſtrength at D, he can move the weight [234] W, to the height A intended. But though this be convenient, yet it gives him no additional power, for it is only as the beam of a balance, whoſe arms are of equal length and weight. Thus, if the equal weights W and P, hang by the cord B B upon the pulley A, they will counterpoiſe each other, juſt in the ſame manner as if the cord was ſtreight⯑ened into an inflexible iron bar, and the two weights left to balance each other with the pulley for a prop.

BUT in the moveable pulley it is otherwiſe; for if a weight W hang at the lower end of the moveable pulley D, and the cord G F go under the pulley, and is fixed at the top of the hook H on one ſide, and nailed to the block C on the other; it is evident that H and C be⯑tween them ſupport the whole weight W; H ſupports one half, and C the other half. Now ſuppoſe I take the ſupport of one of their halves upon myſelf, but merely change the direction of my power, and inſtead of holding up the [235] cord at C, throw it over the immoveable pulley fixed there, and exert my ſtrength below at P; it will be evident that I ſupport one half of the weight W, and the hook H ſupports the other. If therefore I draw the cord at P, the weight W will continue to riſe, but wherever it riſes, I continue to ſupport but half its weight, while H ſupports the other. Thus, one ſingle moveable pulley diminiſhes one half of the weight to be raiſed; if we ſhould add another, it would diminiſh the half of that which remained, and ſo on. For inſtance, if a weight of eight hundred pounds is to be raiſed, I uſe one moveable pulley, and that will leſſen the weight one half, to four hundred; I add another moveable pulley, and that will leſſen the remaining four by one half, which is two hundred; if I ſtill add a third, that will leſſen the remaining two by one half, which is one; ſo that if I uſe three moveable pullies in raiſing eight hundred weight, I ſhall be able to raiſe it with as much eaſe, as one hundred without them.

[236]AS a ſyſtem of pullies have no great weight, and lie in a ſmall compaſs, they are eaſily carried, and can be uſed in many caſes where more cumbrous engines cannot. They have much friction however, becauſe the diameter of their axis bears a very conſiderable pro⯑portion to their own diameter, becauſe they are apt to rub againſt each other, or againſt the ſides of the block, and be⯑cauſe the rope that goes round them is never perfectly pliant.

THE mechanic power that comes next is the ſcrew, with which moſt people are ſo well acquainted, that it needs no deſcription. With this inſtrument our preſſes are uſually driven cloſe together with ſurprizing force, and held during pleaſure in that poſition. It cannot pro⯑perly be called a ſimple machine, becauſe it calls in the aſſiſtance of the lever to increaſe its force, which is uſually ap⯑plied in the manner of an handle, to turn its ſocket upon it. (Fig. 33.) To eſtimate the force of this machine, let us [240] ſuppoſe that I deſire to ſcrew down the preſs G upon B; every turn I make once round with both handles, I ſhall drive the preſs only one ſpiral nearer to B; ſo that if there be eleven ſpirals, I muſt make eleven turns of the handles F L, before I come to the bottom. In preſſing down the ſcrew therefore, I act with a force as much ſuperior to the reſiſtance of the body I deſire to preſs, as the circumference of the circle, which my hands deſcribe in turning the machine, exceeds the diſtance between two little ſpirals of the ſcrew. For inſtance, ſup⯑poſe the diſtance between the two ſpirals to be half an inch, and the length of both handles 12 inches. My hands placed upon them in going round will deſcribe a circle, which upon calculation will be found to be 76 inches nearly, and conſequently this will be an hundred and fifty two times greater than half an inch, which was the diſtance between two of the ſpirals. Thus, if a body is to be preſſed down with this machine, [241] one man will preſs it with this aſſiſtance, as much as an hundred and fifty two men without it. Or if the ſcrew were ſo contrived as to raiſe the weight inſtead of preſſing it, which it ſometimes is, the human force would be aſſiſted in the ſame proportion with the ſame inſtru⯑ment. But we here only talk as if the handles of the ſcrew were but twelve inches acroſs, and the ſpirals a whole half inch diſtant from each other; what if we ſuppoſed the handles five times as long, and the ſpirals five times as cloſe! the increaſe of the human force then would be aſtoniſhing!

TO theſe, which uſually go by the name of mechanic powers, and of which alone all complicated machines whatſo⯑ever are ſuppoſed to be made up, and each of which act but with one power on the weight at a time; to theſe, I ſay, Mr. Varignon has added one more, which he calls La Machine Funiculaire. This is a compoſition of cords, many [242] of which different powers act upon one or more weights at the ſame time; and by which, from their conſpiring with each other, a greater force is exerted than would ariſe from the ſum of all the cords, ſingly applied to the weight to be removed. They who have ſeen the common ludicrous method of placing three ſpoons upon a table each ſupporting and ſupported, will have ſome idea of a machine of this nature.

SOME add to theſe powers alſo the inclined plane, and indeed not without reaſon, if diminiſhing the weight of a body laid upon it can entitle it to the name. The properties of the inclined plane we have conſidered already; we ſhall only here ſay, that the more the plane is inclined, the eaſier a body may be rolled or forced up its ſurface; or in other words, the advantage we gain by it ſo much exceeds the abſolute weight to be raiſed, as the length of the plane exceeds its height. Suppoſe CD (fig. 34.) [243] be an inclined plane, and ſuppoſe its whole length be three times as great as its perpendicular height F G; in this caſe the roller E will be ſupported upon the plane, and kept from rolling down by a power equal to a third part of the roller's weight. A weight there⯑fore may be rolled up this plane, with three times greater eaſe than it could be lifted up directly from the perpendicular G to F.

BY one or more of theſe ſimple powers, all great weights are raiſed to conſiderable heights; but in them all, the more they diminiſh the weight, the more ſlow they are in their operations, and conſequently the more do they retard the workman's diſpatch; and univerſally the more ſimple they are, the more ex⯑peditious. Beſides this, their friction or rubbing againſt each other, greatly diminiſhes their power. The friction in the balance is leaſt, it is more in the lever, increaſed in the axle and wheel, [244] yet more in the pulley, but moſt of all in the ſcrew. In general, in combined engines, upon account of this friction, they will require a third part more of power to move them, than the theory allows. For this reaſon therefore, it will for ever be impoſſible to fulfil the boaſt of Wilkins, who vaunted that he could pull up an oak by the roots with a ſingle horſe-hair; for the force requi⯑ſite to work the machine in pulling it up, would nearly amount to a third part of the force which the machine exerts. The large capſtan and pulley, uſed in launching a man of war, would in theory do it moſt effectually. A ſimple lever, drawn a proper length by the imagination, would do it as well; it would even fulfil the great boaſt of Archimedes, it would remove the earth itſelf. The learned often amuſe them⯑ſelves with fancies like theſe; and it was for this that Cicero, who was per⯑haps the wiſeſt man, called Archimedes a trifler.

CHAP. XVI. Of Man, conſidered as an artificial Machine.

MAN has been conſidered by anatomiſts, as a ſyſtem of all the artificial machines united in the human fabric; they have found the lever, the pul⯑ley, the axle in the wheel, the wedge, and even the ſcrew, or at leaſt ſomething re⯑ſembling each of them, in his perſon: thus, his arms have been likened to levers, his head turning upon its axle, the digaſtric muſcle that aſſiſts his ſwallowing, to a rope running over its pulley, the glands as lifting up their fluids in the manner of an artificial water ſcrew, and his teeth have been compared to wedges. But ſome have not ſtopt here, they have gone on not only to pleaſe themſelves with the reſemblance, but to eſtimate the force of man through all his vital and in⯑voluntary motions, ſuch as the running of the blood through his veins, the [246] drawing his breath, and ſuch like, by the inflexible laws of mechaniſm. They have even applied geometrical rules to meaſure objects conſtantly in change, and built theories upon proportions they were unable to diſcover. Thus when Borelli once got the hint of comparing the muſcles or fleſhy parts to cords, he then readily built this theory, and calculated the human force, by conſidering the thickneſs of the cords, and the length of the lever. Thus, when another found the ſimilitude between the blood running through its channels, and water ſpouting through pipes, he purſued the ſpecu⯑lation, till he at laſt was taught to believe that vomits would cure a ſpitting of blood, and bathing in warm water would be a remedy for the dropſy; happy how⯑ever, had his theory never been put into practice.

IT is as impoſſible to determine the muſcular force of any man, by the bare inſpection or admeaſurement of his [247] muſcles, as it is to meaſure the ſwiftneſs of the circulation of his fluids, by the ſpouting of his blood from a vein. Neither can be done, though Cheyne has pretended to demonſtrate, that if we compare the muſcular ſtrength of two animals, that animal whoſe fluids circulate twice as ſwift, will be ſix times as ſtrong. Friend and Wainright adopted his demonſtration, for he called it a demonſtration, and indeed it was drawn up with a ſufficient degree of mathematical parade. Martin however, in a treatiſe entitled de ſimilibus animalibus, has demonſtrated that Cheyne's demonſtration was falſe; but it was in order to eſtabliſh another demonſtration of his own. He aſſerted, that the force in ſimilar animals, was as the cube roots of the fourth powers of the limb put into motion. The learner will not perhaps underſtand the preciſe meaning of theſe words, but it is no matter, for his de⯑monſtration is as falſe as the former.

FROM the mere dimenſions of the muſcles in two ſimilar animals, it is im⯑poſſible [248] to determine their force. The ſtrength of the muſcle is generally more in proportion to the exerciſe it has been employed in, than to its ſize; the legs of a chairman are ſtronger, the arms of a ſmith; in ſhort, to uſe the words of a bully, in a Spaniſh comedy, who miſtook his man and was beaten, we can never know the ſtrength of the muſcles, till we experience their effects.

BUT though we cannot determine with any preciſion, of two men which are ſtrongeſt, yet in the ſame man, we can compare the force of his muſcles with rather more preciſion: this at leaſt can be ſaid with great certainty, that thoſe muſcles which are inſerted into the bone, neareſt to the place where it moves upon another, overcome the greateſt reſiſtance, and conſequently act with the greateſt force. But to a learner this wants explanation.

[249]ALL our fleſh is compoſed of muſcles, which (if I may uſe a vulgar ſimilitude) are like red ribbands, and almoſt all have one of their ends fixed into one bone, and another of their ends into ſome other bone. Thus, if we feel the great ham-ſtring, which is made up of many muſcles, we ſhall find that at one end it is fixed into the bones of the leg, juſt under the knee, and at the other end it runs upwards, partly to be fixed in the great bone of the thigh. The muſcles being thus ſtretched from one bone to another, have a wonderful power of contracting and ſhortening them⯑ſelves at pleaſure; and when we chuſe to put them into action, they ſwell in the middle, ſomewhat into the ſhape of a ninepin. As theſe muſcles thus contract, they muſt neceſſarily draw the two bones, into which they are inſerted, their own way; the ham-ſtring, when it contracts, for inſtance, draws the leg backward toward the thigh; when we want to make the limb ſtraight, there are muſcles [250] inſerted under the fore part of the knee, that contracting, anſwer this pur⯑poſe; while, in the mean time, the ham-ſtring ſuffers itſelf to be relaxed, in order to let the oppoſing muſcles take effect. This being underſtood, it will follow, that if we conſider any one of the bones, the arm bone for inſtance, as a beam, and the muſcles that raiſe it and put it into motion, as the power that agitates and works the inſtrument, the whole will give us the idea of the third kind of lever, where the prop is at one end, the weight to be ſuſtained at the other, and the ſtrength is applied between them both. Thus for inſtance, if I ſtretch out my arm, the prop is in the joint of my ſhoulder, the weight is my hand, and the raiſing power is the muſcles, which are fixed into the arm bone near the ſhoulder, and go from thence to be inſerted into the bones of the trunk of my body. Now the nearer the ſhoulder theſe muſcles are inſerted into the arm bone, it is evident that the longer will [251] be the lever, againſt which they are to act, and conſequently the greater will ap⯑pear the weight which they are to ſuſtain. To make this quite plain, ſuppoſe a ladder were laid flat on the ground; and ſup⯑poſe that I ſtanding at one end, take the neareſt round of the ladder in both my hands, and thus pulling back attempt to raiſe the fartheſt end, keeping the neareſt end ſtill ſteady to the ground. Would not this require immenſe ſtrength to effect? Pretty ſimilar is the force that the muſcles of the arm exert in raiſing the whole length of the arm, and the weight of the hand beſide. They are inſerted into the bone cloſe to the ſhoulder, and ſupport the whole length of the arm in the deſired direction. But what is more, they do not only act upon the lever at ſo diſadvantageous a diſtance, but alſo they act upon it in a direction the moſt oblique, and conſequently at a greater diſadvantage ſtill. Suppoſe I attempt to raiſe the diſtant end of the ladder by pulling the round neareſt me; this, as I [252] ſaid, will be very diſadvantageous: but ſuppoſe yet farther, that I ſhould firſt lie upon my back, and then by drawing the next round to me of the ladder, I ſhould attempt to raiſe the diſtant end; the force that would be capable of effect⯑ing this, would be incredible. Yet in this very manner it is that the muſcles of the ſhoulder act, in raiſing the arm. They are not only inſerted at the greateſt diſtance from the weight, but they exert their power the moſt obliquely. The force they exert in keeping the hand and arm extended is great; the force they exert in keeping it extended, while the hand holds a weight of about twenty pounds, is aſtoniſhing. Some ſay that theſe muſcles, upon equal terms, would lift a weight ten thouſand times greater. What has been here ſaid of the muſcles of the arm, is true, in a greater or leſs degree, of all the muſcles of the body; ſo that this natural machine, thus faſhioned by the Great Workman, is infinitely more powerful than any [253] artificial machine that man could form, though it took up four times the ſpace.

THE muſcles, as we ſaid, are ſup⯑ported by bones; theſe make altogether a ſingle pillar or column, which though not perfectly ſtraight, but with about five different curvatures or bendings; yet when perfectly balanced upon itſelf, will actually ſupport weights that would ſurpriſe the inexperienced. La Hire, and Deſaguliers give us ſeveral accounts of the amazing weight ſome people have ſuſtained, when they were able to fix the pillar of their bones directly beneath it. The latter tells of a German who ſhewed ſeveral feats of this kind at London, and who performed before the King and a part of the royal family. This man, being placed in a proper ſituation, with a belt which reſted upon his head and ſhoulders, and which was fixed below to a cannon of four thouſand weight, had the props which ſupported [254] the cannon taken away, and by fixing the pillar of his bones immoveably againſt the weight, ſupported it with ſeeming unconcern. There are few that have not ſeen thoſe men, who, catching a horſe by the tail, and placing them⯑ſelves in direct oppoſition to the animal's motion, have thus ſtopt the horſe, though whipped by his rider to proceed. In all ſuch caſes, the pillar of the bones is placed in direct oppoſition to the weight; they ſupport each other, and are pre⯑vented from rubbing or cracking by elaſtic griſtles fixed between each bone; theſe give way a little upon great preſſure, and reſtore themſelves almoſt inſtantly, when that is removed. Beſides theſe, there is a viſcous or ſlimy liquor that is ſqueezed in, as if from a ſponge, between every joint, and keeps theſe griſtles ſmooth, moiſt, and pliant. By means of this fluid, all the joints move eaſily, and obey the impulſe of the muſcles with greater diſpatch. This fluid, and the griſtles (or cartilages, as [255] anatomiſts call them) contribute not a little to the ſtrength of the animal; they reſiſt the burthen with an elaſtic force, and conform themſelves to the inequality of the preſſure. In old age both are diminiſhed, the griſtles become hard, and this liquor (which anatomiſts call the ſynovia) is ſqueezed out in leſs quantities. The man therefore, in old age, becomes more ſtiff and more weak, chiefly upon this account, though partly becauſe his muſcles become then alſo more rigid, hard, and leſs fleſhy, as it is uſually called; as thoſe who have eaten the fleſh of old animals know. While we are at reſt, this fluid, or ſynovia above mentioned, oozes out between the joints, to fit them for the hour of action; when in exerciſe, the ends of the bones preſs againſt their griſtles, and theſe are ſeparated in ſome meaſure by the ſynovia or fluid; but there is ſtill another liquor of an oily nature, which is preſſed at the ſame time from a ſmall fleſhy ſponge, placed in every joint, and [256] this mixing with the ſynovia, makes all ſupple and fit for buſineſs. I ſaid, that the ſynovia or viſcid liquor oozes out between the joints in the hour of reſt; it is there⯑fore in greateſt quantity between them, in the morning, after we have taken our reſt the preceding night. So great is the quantity uſually ſeparated during ſleep, between the joints of the back bone, that ſome men are an inch taller in the morning than at night, and all men are ſomewhat taller, as may be quickly found by any who chuſe to make the experiment upon themſelves.

FROM what has been ſaid it appears, that in carrying large burdens, the whole art conſiſts in keeping the co⯑lumn of the body as directly under the weight as poſſible, and the body as up⯑right under the weight as we can. For if the center of gravity in the burthen, falls without this column, it will go near to fall; in fact, if the ſupporter were an inanimate machine, it would fall inevi⯑tably; [257] but human power, in ſome mea⯑ſure, catches the center while yet be⯑ginning to deſcend, and reſtores the balance which it had loſt the moment before. A man balancing under a weight, reſembles one of thoſe people whom we uſually ſee walking upon a wire; they totter from ſide to ſide, for a moment loſe the center of gravity, but by throwing forward a limb or diſtorting their bodies they recover it again, to the great amuſe⯑ment of every ſpectator. It is thus, that he who carries a weight is obliged to act; on whatever part of his body the weight is placed, he balances it by throwing as much of his column beneath the load as he can. Could the weight be laid and evenly balanced upon him, ſtanding in his natural poſture, he could, as we obſerved before, ſupport an incredible burthen; and though he could not move under what he could thus ſupport, yet he could carry a much greater load, than if the burthen were laid in any other manner. The weight a man could ſupport, when thus [258] evenly laid upon his ſhoulders, would break the back of the ſtrongeſt horſe in the world. The reaſon is obvious. In a man, the whole column of bones ſup⯑ports the weight directly; in an horſe, the weight is laid upon the column croſs ways. The porters of Conſtan⯑tinople are known to carry each a weight of nine hundred pounds; they lean upon a ſtaff while loaded, and are unloaded in the ſame manner. The por⯑ters of Marſeilles in France are found to carry yet more; their manner is this: four of them carry the burthen between them, each having a ſort of hood that covers the temples and head down to the ſhoulders; to this is faſtened the cords that ſupport the frame or bier, on which the weight is laid. By this contrivance the whole column of the bones acts directly againſt the load, and an immenſe weight is thus ſuſtained.

WE now therefore at length ſee the reaſon why two men carrying a load [259] between them, can ſuſtain a greater weight than what either could ſepa⯑rately carry, if it were divided into two equal parts. The reaſon is, that two men can bear the load each more upright, and with the column of their bones more oppoſed againſt it.

AS man bears a weight the better, the more upright he ſtands againſt it, it muſt follow neceſſarily, that the more bendings he makes in ſupporting weights, the leſs will be his power. There are three principal bendings in the human column; the firſt at the hams, the ſecond at the hips, and the third along the back bone, which reſembles the oſier in pliancy, though it be ſtronger than the oak. A man of ordinary ſtature and ſtrength, upon an average, has been computed to weigh an hundred and ſixty pounds; he can ſupport, as we ſaid before, an immenſe weight if his column acts directly againſt it; if he bends a little at the hams, ſuch a man [260] may raiſe from the ground about an hundred and ſeventy pounds, provided the weights are placed to the greateſt ad⯑vantage. If he bends at the hips and back, he will lift thirty pounds leſs. If a weight be placed upon his head, and he be put between the rounds of a ladder placed horizontally and breaſt high, he can lift thirty pounds by the ſtrength of the muſcles of his ſhoulders and neck alone.

FROM this we ſee, that human ſtrength is not the fourth part as great when the body is bent, as when it is upright. From this alſo we ſee, that if a man draws a load after him, as in that caſe all his muſcles act in an oblique direction, he can exert but very little force, when compared to other animals. Deſagulier pretends to ſay, that an horſe can draw as much, upon an average, as five Engliſh workmen. The French writers ſay, Dr. Barthes in particular, that an horſe can draw as much as ſix Frenchmen, or [261] ſeven Dutchmen; but if the load were to be placed upon the ſhoulders, two men will be found to be as ſtrong as an horſe. A London porter ſhall carry three hundred weight at the rate of three miles an hour; two chairmen carry an hundred and fifty pounds each, and walk at the rate of four miles an hour. Whereas a travelling horſe ſeldom carries above two hundred weight, and a day's journey with ſuch a load, would be apt to diſqualify him from travelling the day following.

MAN's greateſt force therefore, is directly upward; if he draws a load, he muſt act at a diſadvantage. A man how⯑ever, when obliged to draw a load, a rolling ſtone for inſtance, hath two methods of doing this. He may either turn his back to the ſtone, and puſhing the frame with his breaſt, thus go on⯑ward, while the ſtone rolls after; or he may turn his face to the ſtone, and go backward, drawing the ſtone with [262] him. This laſt method may be the moſt inconvenient, but it gives the workman much the greateſt ſhare of power, and that for two reaſons. In the firſt place, by inclining farther back, he can give a greater column of his body to the draft; and in the next place, a greater number of his muſcles come into action; particu⯑larly the two great deltoid muſcles of the arms, the force of which is very great. It is for this reaſon that men who row a boat, more uſually draw the oar to them, than puſh it from them.

CHAP. XVII. Of Wheel Carriages.

BY what we have ſeen of man con⯑ſidered as a machine, it is eaſy to obſerve that his frame is not adapted to drawing carriages; while on the con⯑trary, in that of an animal upon all fours, the column of whoſe bodies, and the ſituation of whoſe muſcles, act almoſt directly upon bodies placed behind them, they are perfectly fitted by nature for this kind of ſervice. Horſes are uſually employed in the draft in England; mules, oxen, ſheep, and other animals are ſometimes uſed in other parts of the world. It might incur ridicule if we pretended to inform the learner that each of theſe will draw a weight or carriage in proportion as they are ſtrong. But notwithſtanding this is generally the caſe, yet we are going to mention what will ſeem a paradox; namely, that two horſes may be found, one ſtronger than the [264] other, and alſo better ſkilled in the draft, yet the weaker ſhall draw a weight, with the very ſame carriage, the ſtronger one could not remove! This will be effected, if the weakeſt horſe be the hea⯑vieſt; if he exceeds his antagoniſt more in weight, than he is exceeded in ſtrength. We have obſerved in a former chapter, that the weight re-acts or pulls back the horſe, as much as the horſe acts upon the weight to pull it forward. Now the horſe has two ſources of power in drawing the weight along; his ſtrength, which gives him velocity, and his weight, which added gives force; and it is evident that the horſe which hath both in the greateſt proportion, will draw the heavieſt weights. If we ſhould ima⯑gine both horſes raiſing an equal weight from a deep pit, and this weight ſtill increaſed, ſo as to overcome their ſtrength, it is plain that the lighteſt horſe would ſooneſt be drawn in. We have ſeveral inſtances in ordinary practice, of the great benefit of increaſing the horſe's [265] weight, to promote his draught; for in many places, horſes employed in turning a mill have a ſmall load laid upon their backs, which, though it takes away ſome⯑thing from their velocity, adds to their weight, and conſequently increaſes their force.

BUT ſuppoſing the ſtrength, ſkill and weight of two horſes to be the ſame, all the difference then in their drawing the ſame weights, will ariſe from the com⯑modiouſneſs of the machine, in which they draw. If the load they are to drag after them be breaſt high, they can draw it with much greater eaſe than if it lay along the ground. They can, for inſtance, draw much greater draughts, if the weights are laid upon a ſledge as high as the horſe's ſhoulders, than if the ſame weights were laid upon a low ſledge on the ground. For in the firſt caſe, the column of their bodies acts directly againſt the weight, in the latter it acts obliquely; and we have ſhewn before, [266] that the more directly this column can act, the greater is its force. Even in either going up hill or down hill, the ſledge breaſt high is more commodious than that laid low. For if the low ſledge is dragged up an hill, it is plain that it will be then lower, with reſpect to the horſes, than it was before, and conſe⯑quently they will be obliged to draw it more obliquely upwards, than when they drew it along the plain. If on the contrary, the low ſledge is drawn down an hill, it will then be higher with reſpect to the horſes than when on the plain, and therefore their power of drawing it will be greater; but in going down an hill, its own gravity conſpires with the draught, and will alſo help the load to deſcend, ſo that the horſes in this caſe are permitted to exert their greateſt power where there is the leaſt neceſſity; they can draw the low ſledge down hill with all their power, when by the natural deſcending of the load, they are not permitted to exert it. [267] This doctrine however, ſimple as it is, is different from what is uſually taught by mechaniſts, upon this ſubject.

SLEDGES were probably the firſt ma⯑chines uſed in carrying loads; we find them thus employed in Homer, I mean in the original, in conveying wood for the funeral pile of Patroclus. There are ſome countries alſo, that preſerve their uſe to this day. However, men early began to find how much more eaſily a machine could be drawn upon a rough road, that run upon wheels, than one that thus went with a ſliding motion. And indeed, if all ſurfaces were ſmooth and even, bodies could be drawn with as much eaſe upon a ſledge as upon wheels; and in Holland, Lap⯑land, and other countries, they uſe ſledges upon the ſmooth ſurface of the ice; for as every ſurface upon which we travel, is uſually rough, wheels have been made uſe of, which rub leſs againſt the inequalities than ſledges would do. [268] In fact, wheels would not turn at all upon ice, if it were perfectly ſmooth, for the cauſe of the wheels turning upon a common road, is the obſtacles it continually meets. For if we ſuppoſe the wheels to be lifted from the ground, and carried along in the air, the wheels in this caſe would not turn at all, for there would be nothing to put any part into motion rather than another; in the ſame manner, if they were carried along upon perfectly ſmooth ice, they would meet nothing to give a beginning to the circulatory mo⯑tion, and all their parts would reſt equally alike. But if we ſuppoſe the wheel drawn along a common road, then the parts will receive unequal obſtructions, for it meets with obſtacles that retard it at bottom, therefore the upper part of the wheel, which is not retarded, will move more ſwiftly than the lower part, which is; but this it cannot do, unleſs the wheel moves round. And thus it is, that the obſtacles in the rough road cauſe this circulatory motion in the wheel.

[269]THIS rotation of the wheels about their axle, very much diminiſhes that friction which always attends the weight's being drawn along upon a ſledge; and this in ſo great a proportion, that ac⯑cording to Helſham, a carriage drawn by four wheels, will be drawn with five times as ſmall an effort as one that ſlides upon the ſame ſurface in a ſledge. Still more to diminiſh the friction in wheel carriages, a countryman of our own hath found out an expedient, whereby the axle, contrary to what is uſual in moſt carriages, is made to turn round, and its gudgeons or ends, inſtead of preſſing againſt the boxes as in common wheels, are made to bear on the circumference of moveable wheels; ſo that by this con⯑trivance, a number of parts are made to roll one over the other, which ſlided before: ſuch wheels, from their thus diminiſhing the friction, are called friction wheels. We ſhall enter no farther into their theory or uſes; the ſingle inſpection of the machine itſelf [270] would throw more light upon the ſubject, than we could do in pages.

THUS we ſee how much a wheel carriage aſſiſts the horſe in drawing, ſuperior to a ſledge or any other machine without wheels. Now if we compare wheel carriages with each other, and we deſire to know whether large or ſmall wheels are beſt in a machine; the anſwer will be, that large wheels are eaſieſt for the horſe, but ſmall wheels ſafeſt for the rider. A large wheel has a double ad⯑vantage over a ſmall one, either in ſur⯑mounting obſtacles, or in depreſſing them. To prove this, let us ſuppoſe two wheels, (fig. 35.) A and B, the one large, the other ſmall. As the circumference of both may be conſidered, like all other circles, as compoſed of a number of right lines; we may ſuppoſe both endeavouring to overcome the obſtacle C, with the ſpoke of either conſidered as levers, the large wheel with a lever equal in length to B g, the ſmaller with [271] a lever equal to F g. But the longer the lever, the greater the moving power is increaſed; it is evident therefore, that the horſe drawing at D B, where the lever is long, will have far greater power to overcome the obſtacle, than if he drew at F E, where the lever is ſhort, and therefore the larger wheel has the advantage. The horſe will draw ſuch a wheel with greater eaſe over the obſtacle, or preſs the obſtacle down into the earth with greater force. As wheels cannot always run upon hard ground, but muſt frequently meet with holes, in which they partly ſink; in this caſe alſo the large wheel will have the advantage over the ſmall, for it preſſes a larger ſurface upon the ſinking earth, and it will not therefore ſink ſo deep; thus a man can eaſily thruſt his finger into ſoft clay, but it will give more reſiſtance, ſhould he attempt to thruſt his fiſt.

LARGE wheels have the advantage of ſmall wheels, in having leſs friction [272] round their axles; for if the ſmall one turns an hundred times in going over a certain piece of road, the larger wheel will not turn by any means ſo often to travel the ſame length, and the leſs the wheel turns, the leſs will the friction be. And this frequency of turning required in ſmall wheels, as alſo the greater obſta⯑cles they continually meet with, is the reaſon why they are more frequently out of order, and ſtand in need of repair much oftener than the large.

LASTLY, large wheels have the ad⯑vantage of ſmall wheels, by better directing the load againſt the column of the horſe's body, either in going up or down hill. If the horſe draws the load up hill, the wheels being large, raiſe the weight, more directly to be acted upon by the column of his body; if the horſe goes down hill, the wheels being large, raiſe the weight high above the horſe's power, and conſequently thus diminiſh his power; but then it is at [273] a time when he hath leaſt occaſion to make uſe of it, for the load in ſome meaſure will then deſcend of itſelf^*.

THUS in almoſt every inſtance, with reſpect to the draught, large wheels are preferable to the ſmall, and therefore we neceſſarily expect to find all our coaches, waggons, and other four wheel car⯑riages, have the fore wheels as large as the hinder. If a waggoner is aſked the reaſon why this is not ſo, his anſwer is, that by making the foremoſt leaſt, the hinder wheels thus drive on the firſt. This however is by no means the true reaſon; the fore wheels are made thus ſmaller than the hinder, both for the conveniency of turning with greater eaſe, and becauſe the carriage being thus ſup⯑ported [274] upon unequal wheels, it will be in leſs danger of overturning. They thus alſo avoid cutting the braces or ſtraps, by which the horſes draw. In heavy waggons however, where the neceſſity of turning is but ſeldom, and the danger of overturning ſcarce any, and the braces are removed at a diſtance, if the fore wheels were made as high as the hinder ones, it would be ſo much the better. As it is however, waggoners ſhould lay the load equally upon all the wheels; but on the contrary, they are univer⯑ſally found to lay the greateſt part of the load upon the two fore wheels, which not only makes the friction greateſt, where it ought to be leaſt, but alſo preſſes the fore wheels deeper into the ground than the hinder ones, which we obſerved before, were moſt apt to ſink, without this additional diſadvantage. The only danger that might reſult from the waggon's being evenly loaded would be, that in drawing up ſteep hills, the load might be apt to fall backward, and [275] thus tilt up the fore wheels of the carriage. This might eaſily be remedied, by a ma⯑chine placed under the fore part of the waggon, which, upon the carriage's going up hill, might be ſo contrived, as to let ſink the foremoſt end of the load, and thus keep the whole ſtill even.

IT now only remains to ſay ſome⯑thing with reſpect to the breadth of the wheels. Some have inſiſted that broad wheels are beſt for the draught, and build their aſſertions upon theory and experiment; others, on the contrary, and the whole body of carriers in particular, taught by experience, give the preference to the narrow. The determination of this diſpute muſt be left to others, more ſkilful in waggons and broad wheels than I can pretend to be; a word or two will ſuffice. If we ſuppoſe the broad wheel to have three times the breadth of the narrow wheel, it will meet with three times as many obſtacles by the way, but the narrow wheel will ſink three times as deep; the queſtion therefore is, whether [276] three times the obſtacles at the ſurface of the ground, is greater or leſs than three times the obſtacle beneath the ſur⯑face? The anſwer will be, that the three obſtacles at the ſurface will be much eaſier removed than the three beneath it; for they lie lighter, and are ſooner thruſt out of the way. But however this may be in theory, in experience it is otherwiſe; for the narrow wheel does not ſink three times as deep as the broad, becauſe the earth hardens by the preſſure under it, as it deſcends; on the contrary, the broad actually encounters three times as many obſtacles. However, though the latter may not be ſo good for the carriers, yet they are certainly good for the roads, and therefore for the public in general. Private diſadvantage muſt ever be poſtponed to public utility.

THUS much will ſuffice upon the principles of mechaniſm in general; to enter upon a deſcription of particular artificial machines, would be both unin⯑ſtructing, and indeed foreign from the [277] purport of a ſcience, that pretends only to explain the wonders of nature. To give any idea of machines, plates would be requiſite, and even ſuch would make but an obſcure impreſſion. The beſt way to underſtand the arts of machinery is, to view them as they really exiſt, to viſit the ſhops of artificers, or the yards where great works are carried on. To be a good mechaniſt would take up a whole life, and the art is rather perfected by practice than theory. For inſtance, theoriſts have long debated what is the proper angle of obliquity, by which the ſails of a wind-mill are to be regulated and fixed, and whether they are to be elliptical, or on the con⯑trary oblong: practice at preſent ſeems to follow the opinions of neither ſide; the ſail is made to boſom upon the wind, like the ſail of a ſhip. In ſhort, the principles of mechaniſm may be learned in books, the art muſt be acquired by experience. Several volumes have been written upon the ſubject; ſhould we, upon the preſent [278] occaſion, enter into a deſcription of but a few machines, we muſt neceſſarily ſay either too little, or too much: too little to give the learner an adequate idea of any of them; too much for an elementary treatiſe upon natural philoſophy.

CHAP. XVIII. Of Friction and the Reſiſtance of Fluids.

THROUGH the whole former theory of motion, we have ſup⯑poſed that machines did not rub againſt each other, and ſo interrupt their mutual workings. We ſuppoſed that all the planes on which they moved were even, all the levers inflexible, and that the air gave no reſiſtance: but in nature this is not the caſe; for all theſe are impediments which it is impoſſible wholly to overcome. As we have eſtabliſhed the theory how⯑ever, it will now be eaſy to conſider the nature of theſe reſiſtances, how far they diminiſh motion, and to make an abate⯑ment in proportion, in the working of any machine, or in the colliſion of one body againſt another.

HOWEVER plane and ſmooth bodies may appear to our ſight, yet if we exa⯑mine their ſurfaces through a micro⯑ſcope, [280] we ſhall diſcover numberleſs inequalities. Theſe inequalities are the cauſes of friction in two bodies, that move in contact with each other; the little riſings in one body ſtick themſelves into the ſmall cavities of the other, in the ſame manner as the hairs of a bruſh run into the inequalities of the coat, while it is bruſhing. If the bodies ſlide one over the other, the little riſings in one body in ſome meaſure tear, or are torn by the oppoſite depreſſions into which they had been driven, ſo that ſliding bodies move with difficulty. If, on the contrary, they roll over each other, then the ſmall riſings fall perpendicularly each into its ſocket, and are lifted out of it again, without any rupture in the ſurface of either body whatſoever.

IT is no eaſy taſk to meaſure preciſely the quantity of motion that any two bodies will loſe by thus rubbing one over the other, even though we knew that the workman had poliſhed both the [281] ſurfaces to the higheſt pitch of his art; though we knew the dimenſions of each ſurface, and ſtill more, though we knew the exact preſſure in each body; it is almoſt impoſſible, I ſay, in this caſe, preciſely to tell how much the friction between theſe two bodies will alter any former theory. Thus for inſtance, ſup⯑poſe I throw a ſmooth cord over a fixed pulley, and hang a pound at one end of the cord; then if I have a mind to out-balance this, I hang a pound and a grain at the other end of the ſame; but though in theory, this pound and grain would out-balance the other, yet in fact it will not; it will not ſtir the former, becauſe the friction of the cord is yet to be overcome. If I then aſk what is the preciſe additional weight requiſite for overcoming this friction, all the anſwer a philoſopher can make is, that he has no general rule for this, and that he cannot tell what weight will ſuffice, till he tries the particular caſe. It is true, he may gueſs pretty nearly, but ſtill it will be but gueſſing.

[282]IF I am to gueſs at the quantity of motion that is loſt in any machine, by the rubbing of two bodies one againſt the other; I muſt firſt conſider the roughneſs or ſmoothneſs of the ſurface; I muſt next conſider how great the force is, that preſſes the two rubbing bodies together; I muſt then find out with what ſwiftneſs they move one over the other; and laſtly, I muſt take into my account the largeneſs of the two ſurfaces that are thus rubbed together.

WITH regard to the ſmoothneſs of the two rubbing bodies, it is very evident that the ſmoother they are, the leſs will be the friction, and for this reaſon; in all machines where there is much friction of the parts, ſuch as in the nave of a wheel, in the axle of a pulley, and ſuch like, they are greaſed with oil to fill up the cavities and riſings, and thus to facilitate their ſliding with eaſe, ſurface over ſurface.

[283]WITH regard to the preſſure of the ſurfaces againſt each other, all philoſo⯑phers allow, that where the ſurfaces are preſſed hardeſt together, their friction will be greateſt; the friction, for inſtance, in the nave of a waggon wheel, where the preſſure is proportioned to the load, will be greater than the friction in the wheel of an ordinary poſt-chaiſe, that carries much leſs weight, and the ſurface will require to be ſmeared oftener. Now ſuppoſe it ſhould be aſked, if we dou⯑ble the preſſure, whether we ſtill increaſe the friction alſo in the ſame proportion? It is not eaſy to anſwer this. Amontons of the academy of ſciences of Paris, and Deſaguliers our countryman, think in the affirmative, and ſay, that friction conſtantly increaſes with preſſure, and that double preſſure will cauſe a third part more friction. Thus for inſtance, if there be a machine, in which to over⯑come its friction, will require two mens ſtrength, if we double this load, it will, they ſay, require three men to overcome [284] the friction; if we double that again, it will require ſix men; and ſo forth. To ſupport this aſſertion, they bring ſeveral experiments, tolerably exact, and very plauſible.—Moſt philoſophers had come into their ſentiments, till Muſchenbrook of Leyden, and Camus, by contrary experi⯑ments, induced them to ſuſpend their aſſent. They have ſhewn, by more accurate preparations, that by the ſame preſſure, ſome bodies have greater fric⯑tion than others, that the friction will be very different if the ſurfaces are ſmeared with oil, or if with tallow, or with water. Thus the experiments of theſe two latter philoſophers differ greatly from the preceding; but unfortunately, they differ as much from each other. All therefore that we can generally con⯑clude from the experiments of each of them is, that friction is increaſed the more the ſurfaces are preſſed together; but we cannot exactly tell, if by increaſ⯑ing the preſſure, the friction increaſes in a ſimilar proportion.

[285]TO bring our conjectures nearer to certainty, in meaſuring the quantity of motion loſt by friction, we muſt next conſider the ſwiftneſs with which the two ſurfaces are rubbed together. Muſ⯑chenbrook aſſures us, that from ſeveral experiments he has made (though he does not tell us what thoſe experi⯑ments are) the friction increaſes in proportion to the ſwiftneſs with which the ſurfaces glide over each other; Nolet is of the ſame opinion; they only differ in this, that the former thinks increaſing the ſwiftneſs to a great degree, will ſtill increaſe the friction the more; the latter ſuppoſes, that the friction hath its bounds, and after the ſur⯑faces come to a certain degree of ſwiftneſs, though their velocity be then increaſed never ſo much, yet there will be no increaſe of friction. Should we aſk the opinion of a common carrier of common underſtanding upon this ſubject, he would affirm the very contrary of what the two laſt mentioned philoſophers [286] have aſſerted. He would ſay, that if his wheels were well greaſed, the ſwifter they went, the eaſier they were upon the horſe, and the leſs would be their friction: Euler of Berlin is of the very ſame opinion. In fact, let us compare the inequalities of one ſurface going ſwiftly over the depreſſions of the other, to a chariot wheel, drawn violently over the inequalities of a ſtony road; we have often ſeen that before it well could get to the bottom, in deſcending from the top of one ſtone, it is drawn up to the top of another, ſo that in fact, it had thus a leſs obſtacle to encounter, than if drawn ſlowly along; for thus it ſcarce had time to ſink between the two obſta⯑cles, with the whole force of its gravity. It is juſt thus in the caſe under conſider⯑ation; the ſwifter the ſurfaces move, the more their mutual preſſure is dimi⯑niſhed, and conſequently, the leſs deep will the inequalities of one ſurface inſert themſelves into the depreſſions in the other. The truth of this theory Euler [287] has confirmed by experiment, as may be ſeen in the Memoirs of the Berlin Aca⯑demy for the year 1748, that upon the whole, the ſwiftneſs rather diminiſhes than increaſes friction.

LASTLY, in eſtimating how much a machine is retarded in its workings by friction, we are to conſider the largeneſs of the two ſurfaces that rub each other; and to firſt thoughts it would ſeem, that as the inequalities of the ſurfaces are the principal cauſe of friction, if we aug⯑mented the extent of theſe inequalities, we ſhould alſo augment the friction; ſo that if the ſurfaces were doubled, the friction would be doubled in the ſame manner; if the ſurfaces were made three times as great, the friction would be made three times as great alſo. How⯑ever, this is by no means the caſe, the increaſe of friction bears no degree of equality to the increaſe of the ſurface; ſo that I may often make the ſurfaces ten times as large, and yet the friction ſhall [288] not for all this become four times as great. Deſaguliers and Amontons are of opinion, that we may increaſe the ſur⯑faces to what degree we pleaſe, and yet their friction would ſtill remain the ſame. For, ſaid they, to make the inequalities of a large ſurface, ſink into the depreſ⯑ſions of the oppoſite ſurface, will require a force of preſſure, in proportion to the number of the inequalities. The number of inequalities is greateſt in the largeſt ſurface, and therefore, if the preſſure in the large ſurface, be no greater than in a ſmall ſurface, the inequalities of the large ſurface will be preſſed in with leſs force, and ſo not ſink ſo deep as they will in the ſmall. In two bodies there⯑fore, preſſing each other in large ſurfaces, though the preſſure is more diffuſed, yet it is not ſo deep; and conſequently, con⯑tinue they, the reſiſtance they give to each other's motion will not be increaſed by merely increaſing the ſurface only. This theory, as we may eaſily conceive, would have but few partizans, if it were unſup⯑ported [289] by experiments. Feeble experi⯑ments were produced, to ſupport a feeble theory; but both gained ſtrength when united, and convinced many, whom either, ſingly, could not perſuade. Muſchenbrook was the firſt who oppoſed this erroneous theory, and that with an experiment that was inconteſtible. He aſſerted, that by increaſing the ſurfaces of two bodies ſliding over each other, the friction was alſo increaſed. For, continued he, if we take two ſmall pieces of a deal board ſmoothed and poliſhed, one piece a foot long and an inch broad, the other a foot long and two inches broad, and if we lay the ſame loads upon both, taking into conſideration the weight of the boards themſelves, the largeſt, he aſſures us, will be always found to move with greateſt difficulty; a proof of its receiving greater obſtacles from friction. Thus it appears, that increaſing the ſurface will increaſe the friction, how⯑ever in no very conſiderable degree; for it often happens that the friction is not [290] thus increaſed a fifth part greater, when the ſurface becomes twice as great.

IN a word therefore, in eſtimating the beſt manner of diminiſhing the friction in any machine, if we ſuppoſe all the parts ſmooth and well oiled, it will be found, that the leſs the preſſure is upon the rubbing ſurfaces, or in other words, the leſs the load lies upon the parts that move, the leſs will the force of the machine be retarded by friction; the leſs extenſive the rubbing ſurfaces are, the leſs alſo will be the friction. But then this conſideration of the ſurfaces, is by no means equal to that of the preſſure: for if we double the preſſure, we ſhall go near to double the friction; on the other hand, if we double the ſurface, this will give but a very inconſiderable addition to the friction, ſo that we may reſt aſſured, that a doubled preſſure pro⯑duces more friction than a doubled ſur⯑face. Laſtly, the ſwifter the bodies move over each other, the leſs will they [291] rub, and therefore friction will be more diminiſhed in a machine that goes faſt, than in one that moves ſlow.

FRICTION is to be taken into conſider⯑ation in the working of every one of the mechanic powers, and as it is incom⯑modious in ſome, ſo it is beneficial and convenient in others; the lever, the pulley, and the axle in the wheel, are retarded by this; while, on the contrary, our operations by the wedge and ſcrew, would be impoſſible to be performed without it. For in the wedge, when it is driven into the cleft by the force of the hammer, if it were not kept in the cleft by the power of friction, it would be driven back again by the reſiſting power of the timber. In the ſcrew, when we had preſſed down a reſiſting body, by the exceſs of power we had over it, this body, upon our preſſure being removed, were it not for the force of friction, would drive the ſcrew back again, and we ſhould ſee the ſcrew [292] turning up again, with much greater velocity than that with which it was forced down.

THE theory of friction, if perfectly underſtood, would be of infinite ſervice to ſociety; for then we might calculate with the greateſt exactneſs, the force with which any machine would move, and the number of hands it would re⯑quire to work it. Beſides this, geome⯑tricians might make their calculations on ſeveral mathematical problems with greater preciſion, as in Brachyſto⯑chrones, Iſochrones, and ſuch like; this would be a great pleaſure to them, though of little advantage to ſociety. Some of our own countrymen have taken pains, to aſcertain how much friction ſome woods have more than other woods, and ſome metals more than others. The friction is found to be greater between ſmall deal boards, than oak; it is much greater between plates of lead, than plates of braſs. [293] It were indeed to be wiſhed, that if poſ⯑ſible, this part of natural philoſophy were cultivated with more aſſiduity; and as we have tables for ſhewing the different denſities of bodies, ſo we might have tables for ſhewing their different frictions alſo. It muſt be owned however, that a work of this kind would require aſſiduity in the experimenter, and great accuracy in the meaſuring inſtrument. Inſtruments have already been contrived for this purpoſe, but moſt of them too faulty to be built upon. Muſchenbrook's inſtrument for meaſuring friction, is reckoned the beſt; to him we refer the reader for its deſcription. He calls it a Tribometre, a name compounded un⯑grammatically enough, but it means a meaſurer of friction. The great defect of this inſtrument is, that a part of the force employed in turning the diſk, is ſpent in twiſting the cord that holds it.

BESIDES the obſtructions all machines [294] find from friction againſt each other, there is another by no means to be diſregarded, which they receive from the air. That the air gives great reſiſt⯑ance to bodies paſſing through it, every one muſt have experienced; and that this reſiſtance is increaſed, the ſwifter the body is moved, and the larger the ſurface is expanded, which is carried through it. Who does not know, that if I ſpread a fan, and move it too and fro, it will find more oppoſition from the air, than if I furled it up, and only brandiſhed the ſticks. A man on horſe-back, if he goes in a calm day, with an eaſy gentle motion, will perceive no wind; but if he puts the horſe upon a full gallop, it will appear to him as if he rode in a ſtorm; for he paſſes ſucceſſively from one body of air to the other, and whether he daſhes againſt the air with violence, or the air daſhes with violence againſt him, as in an high wind, it will, with reſpect to his ſenſations, have the ſame effect.

[295]NOW ſhould I deſire to know the exact reſiſtance of the ſame air, upon two bodies of exactly the ſame kind, but different weights; ſuppoſe, for inſtance, how much a leaden bullet of two pounds, would be reſiſted more than a leaden bullet of one. This queſtion can⯑not be reſolved exactly, without the geo⯑meter's help. I may anſwer in general indeed, that the bullet of two pounds will meet as much more reſiſtance from the air, as its ſurface is greater than the ſurface of the other. But to determine this is not ſo eaſy, as ſome may at firſt imagine. For to calculate exactly how much reſiſtance the air will give to a body oppoſed to it, we muſt know exactly how much is the tenacity of the air itſelf, that is, how much its parts ſtick together, how far its parts are elaſtic, how far its parts cloſe round the body that paſſes through them, and laſtly, what part of its ſurface the moving body preſents to oppoſe it. We know not enough of the air to determine [296] theſe points with any preciſion; the diſ⯑cuſſion of each particular makes the moſt abſtruſe parts of ſpeculative geometry. Huygens diſcovered by experiment, that in bodies moving through a fluid, if the body moved twice as faſt, it met with four times as much reſiſtance as before; if it moved four times as faſt, it met with eight times as much reſiſtance, and ſo on. This experiment he attempted to prove by theory, (for theory moſt uſually follows experience) but finding himſelf unequal to the taſk, he left it for Newton to perform. Newton's demonſtrations are too abſtruſe to be inſerted here, and indeed they do not ſeem eſtabliſhed upon a baſis equally firm, with the reſt of his diſcoveries; for this reaſon they have been controverted by ſome of the greateſt geometricians of the age. Pemberton has undertaken to explain the doctrine of Newton upon this difficult ſubject, as follows; though we muſt obſerve that the reader will by no means ſee Newton himſelf through the medium of this [297] explanation. "The principal reſiſtance which moſt fluids give to bodies, ariſes from the inactivity of the parts of the fluids, and this depends upon the velo⯑city with which the body moves, on a double account. In the firſt place, the quantity of the fluid moved out of the place by the moving body in any deter⯑minate ſpace of time, is proportionable to the velocity with which the body moves; and in the next place, the velo⯑city, with which each particle of the fluid is moved, will alſo be proportional to the velocity of the body: therefore, ſince the reſiſtance which any body makes againſt being put into motion, is pro⯑portional both to the quantity of matter moved, and the velocity it is moved with; the reſiſtance which a fluid gives on this account, will be doubly increaſed, with the increaſe of the velocity in the moving body; that is, the reſiſtance will be in a two-fold or duplicate pro⯑portion of the velocity wherewith the body moves through the fluid." That, [298] as we ſaid above, if the body moves twice as ſwift, it will meet four times the reſiſtance. Such will be the caſe of a body moving through a non-elaſ⯑tic fluid; but the air is elaſtic (as we ſhall ſee when we come to treat of its properties) and therefore it muſt reſiſt in a different manner. "If the elaſtic power of the fluid," continues Pem⯑berton, "were to be varied, ſo as always thus doubly to reſiſt the velocity of the moving body, it is then ſhewn (by Newton) that the reſiſtance derived from elaſticity would increaſe in the ſame proportion, inſomuch that the whole reſiſtance would be in that pro⯑portion, excepting only that ſmall part which ariſes from the friction between the body and the parts of the fluid. From whence it follows, that becauſe the elaſtic power of the ſame fluid does in truth continue the ſame, if the velocity of the moving body be dimi⯑niſhed, the reſiſtance from the elaſti⯑city, and therefore the whole reſiſt⯑ance [299] will decreaſe in a leſs proportion than the duplicate of the velocity; and if the velocity be increaſed, the reſiſtance from the elaſticity will increaſe in a leſs proportion than the duplicate of the velocity; that is, in a leſs proportion than the reſiſtance made by the power of inactivity of the parts of the fluid." Upon the whole, as this is a ſubject that more particularly belongs to mathematicians, with them we ſhall leave it; only ob⯑ſerving, that by a train of reaſoning, Newton has proved that a globe moving through a fluid, ſuch as air, that cloſes behind the body as it moves, ſuffers but half the reſiſtance which a cylinder will do of equal diameter, if it moves endways; and in general, let the ſhape of the bodies be ever ſo different, yet if the ſurfaces with which they cut the air be equal, the bodies will be equally reſiſted. Thus, in the motion of an arrow, if the ſurface, with which it cleaves the air end foremoſt, be as ſmall [300] as that with which a bullet cleaves the ſame, it will meet with no greater reſiſtance.

WE have now ſeen, though obſcurely enough, that if a body moves twice as faſt, it will meet nearly four times as much reſiſtance from the air, and that ſome ſorts of ſurfaces are more reſiſted than others. But this difference of ſurface however, cauſes but very little alteration in the air's reſiſtance; ſo that phyſically, though not geometrically ſpeaking, we may ſay, that the greater the ſurface of a body oppoſed to the air, the greater will be the reſiſtance. A body which has twice the ſurface of another, when moved along, will ſtrike twice as many columns of air in its way, and conſe⯑quently will meet with twice the reſiſt⯑ance. Bodies however that have a great deal of weight under a ſmall ſur⯑face, will meet with a very trifling reſiſt⯑ance, compared to the force with which they move. For to make this very plain, [301] ſuppoſe an hollow paſte-board globe were ſhot from the mouth of a cannon, the reſiſtance it would meet from the air, would be in proportion to its ſurface, as we ſaid before. But now ſuppoſe it to be filled with an hundred leaden bullets, each as heavy as the globe itſelf, and ſhot forward; the reſiſtance it would meet from the air, would be no greater than before; but there would be an hundred bullets within it, that met with no reſiſtance from the air what⯑ſoever, therefore the whole of the globe would move forward with all its parts, an hundred times leſs reſiſted than when it was hollow. Thus, though light and heavy bodies meet a reſiſtance great or little, as their ſurfaces are large or ſmall, yet the power that heavy bodies have of overcoming this reſiſtance, is much greater than that of the light. The force that has driven the heavy body forward, was impreſſed upon all its parts, the force of the air that reſiſts it, is merely impreſ⯑ſed upon the parts of the ſurface alone.

[302]FROM all this therefore it appears, that the ſmalleſt bodies having the greateſt ſurfaces in proportion to their weights, are moſt reſiſted in their pro⯑greſs through the air. From this it appears, that a body reduced to powder can be thrown but to a very ſmall diſtance, the reſiſtance being great, be⯑cauſe the bodies in motion are but ſmall A fowler who ſhoots with ſmall ſhot, is ſenſible that the charge can carry it but a ſhort way, if compared to the diſtance to which a bullet would go. Should the ſurfaces of all the grains be united under one general ſurface, and the whole be melted down into a ſingle ball, this would proportionably diminiſh the ſurface, this would diminiſh the air's reſiſtance, and this would carry the charge to a more diſtant mark. From this it appears, that a body thrown from the hand will go fartheſt if it does not divide by the way; for its diviſion multiplies the ſurfaces, and the ſurfaces increaſed, ſo alſo is the air's reſiſtance.

[303]THUS far we have ſpeculated, as if the body to be moved was only in motion, and the air was quite ſtill and motionleſs. This however it ſeldom is; we always perceive ſome wind, and there is almoſt ever enough to point the weather-cock. In this caſe therefore, a body moving againſt the wind has a double reſiſtance to overcome, its own inertneſs to motion, and alſo the motion of the air. For this reaſon, the motion of the body will be retarded in proportion as both theſe reſiſtances are increaſed: if a race-horſe ſhould carry his rider with as much rapi⯑dity againſt a ſtrong wind as he does in a calm, the jockey would not be able to endure its impulſe; but this he is unable to do.

FROM all that has been ſaid of friction, and a fluid's reſiſtance, we ſee how vain it is to expect that a body will move for ever; ſince if we could ſuppoſe an infinite force to put it into motion, we here ſee a reſiſtance continued infinitely [304] to controll it; and where two forces are equally infinite, they will deſtroy each other. We might perhaps, upon the principles of mechaniſm, contrive ſuch a machine as would move, if unreſiſted by external preſſure; this we muſt ſup⯑poſe, if we allow the firſt principles of philoſophy, which take it for granted, that all motion if once begun, would, if uncontrolled, continue for ever. A pendulum, if its machine never required winding up, would in this ſenſe be a perpetual motion; but ſuch machines for pendulums have never been hitherto diſcovered, and they might anſwer but few uſeful purpoſes upon the diſcovery. In fact, the perpetual motion is now ſcarce ſought for by any; we even hear the name now little uſed, except in the mouths of thoſe half witted people, who are ſaid by the vulgar to have gone mad with too much learning.

CHAP. XIX. Of Water.

AMONG fluids, water ſeems to claim the firſt place; its proper⯑ties are more obvious than thoſe of air, for even the ignorant allow water to be a fluid ſubſtance, but few of them will grant air, which they do not ſee, to have any ſubſtance whatever. Its ſervices to mankind alſo give it the preference to other liquids, and are well known; but it is not our buſineſs to declaim upon its uſes; let us as far as we can explain its nature.

HOWEVER fluid water may ſeem, and unreſiſting to the touch, yet few bodies can be found, the parts of which are more hard. If it be put into a globe of metal, and the hole be then ſoldered up with care, no art, no power nor force on earth can preſs it into a ſmaller compaſs than it occupied before. We [306] can condenſe metals into a ſmaller compaſs, hard as they appear, but water cannot be condenſed. If our attempts be proſecuted with violence, the metal, and not the water, will give way; for the fluid will drive through the pores of the globe, and ſtand like dew upon its ſurface.

NOR is the hardneſs of the parts of water leſs proved, by the pain it gives upon ſtriking its ſurface pretty ſmartly with the palm of the hand. Many alſo who have leaped into water, from the battlements of high bridges, have been cruelly undeceived with regard to the unreſiſting qualities of this fluid; the ſhock the body ſuſtains in this rude ex⯑periment, is inexpreſſibly violent. But it is no way extraordinary that the body ſhould feel pain in the conflict; for if a leaden bullet itſelf be diſcharged from a gun, into the water, this ſeemingly unreſiſting fluid will actually flatten the ball.

[307]BUT whatever force water may have while its parts remain together, is nothing, if compared to the almoſt in⯑credible power with which its parts are endued, when they are reduced to vapour by heat. Thoſe ſteams which we ſee riſing from the ſurface of boiling water, and which to us appear ſo feeble, yet, if properly conducted, acquire im⯑menſe force. In the ſame manner as gunpowder has but ſmall effect, if ſuf⯑fered to expand at large, ſo the ſteam iſſuing from water is impotent, when it is permitted to evaporate into the air; but when confined in a narrow com⯑paſs, as, for inſtance, when it riſes in an iron tube ſhut up on every ſide, it then exerts all the wonders of its ſtrength. Muſchenbrook has proved by experiment, that the force of gunpowder is feeble, when compared to that of riſing ſteam. An hundred and forty pounds of gunpowder blew up a weight of thirty thouſand pounds; but on the other hand, an hundred and forty [308] pounds of water, converted by heat into ſteam, lifted a weight of ſeventy-ſeven thouſand pound, and would ſtill lift a much greater, if there were means of giving the ſteam greater heat with ſafety; for the hotter the ſteam, the greater is its force.

UPON this principle of the irreſiſtible force in the ſteam of boiling water, one of the moſt forceful and noble machines has been completed in our days, that ever appeared among the inventions of mechaniſm. It is called the ſteam engine, a machine by which the force of ſteam is made to anſwer all the purpoſes of the united ſtrength of hundreds. The force of ſteam may thus be applied to the working of exceſſively large machines, which would require a moſt expenſive ſhare of bodily labour to manage. The ſame force may be applied to the raiſing immenſe weights, to the fatigue of which, animal ſtrength would be un⯑equal; in ſhort, wherever great force [309] and perſeverance are wanted, theſe en⯑gines can effectually lend their aſſiſtance. The moſt uſual purpoſes however, to which the force of ſteam has been ap⯑plied, are in working pumps to clear the water from mines, or raiſing it to proper heights for the ſupply of cities. Philoſophers were long acquainted with the great force of ſteam, and Papin actually contrived an inſtrument, ſome⯑what reſembling the ſteam engine now in uſe, but in miniature. But yet this in⯑ſtrument of Papin's contrivance, was only a ſubject of ſpeculation to the curious; though long before him the marquis of Worceſter had aſſerted the uſes to which the force of ſteam might be converted, in a machine for raiſing water. Still however neither the principle nor its utility were generally known, ſo that the honour of the compleat diſcovery and uſe of this machine, which is incon⯑teſtably the greateſt production of the preſent age, was reſerved for two ob⯑ſcure but ſenſible citizens of plain under⯑ſtanding, [310] which is ever the beſt. Mr. Newcomen an ironmonger, and Mr. John Cowley a glazier, inhabitants of Dart⯑mouth, are the perſons to whom we are indebted for this ſurprizing engine, which has been of more ſervice to man⯑kind than the invention of algebra. The principle on which it is founded is only this: Inſtead of working an enor⯑mous water pump with bodily labour, the ſteam may be ſo applied as to drive up the arm of a pump rod, and the power of ſuction will ſerve to draw it down again; ſo that the arm, thus alter⯑nately raiſed and depreſſed, lifts the water in the pump, which flows out at top, at the rate of above three hundred and twenty hogſheads in an hour.

BUT to give the learner a ſuperficial idea of this machine, let us imagine a common pump prepared, ſuch as we every day ſee, and that we want to move the handle of this pump upward, by the force of ſteam only. In the firſt place, [311] let us ſuppoſe matters may be contrived ſo as that the handle, or ſomething joining to it, may go into the barrel of a gun, or ſome ſuch hollow tube, ſet upright over a cauldron containing boiling water. Next let us ſuppoſe, that the ſteam may be let into the tube at plea⯑ſure, through the touch-hole; now as the fire begins to dilate the ſteam, a part of it will enter the tube at the touch-hole, and this will preſs up the pump handle which fills the tube very exactly, and would drive it quite out at the mouth, but that by the time it gets near the mouth of the barrel, there is a contriv⯑ance by which a little cold water is ſpouted into it, and this effectually de⯑ſtroys the ſteam at once; and thus it ſinks to the bottom of the barrel and leaves it perfectly empty. The air there⯑fore without will now come into play, and preſs down the handle again into the empty tube, into which no ſteam is permitted to enter, by a contrivance that ſtops up the touch-hole below; [312] but when the handle is thus preſſed down, the touch-hole below is again opened, and new ſteam entering again, preſſes the handle upward; when the handle comes toward the top, the ſteam is again cooled and deſtroyed as before, and the handle again is preſſed down by the external air; and thus it is alter⯑nately preſſed up and down, and works the pump with unwearied aſſiduity.

SUCH is the force of vapour, and a part of the uſe to which it may be ap⯑plied. But although the ſtronger the fire, the greater the force of the vapour, and the greater its quantity alſo, yet no fire how fierce ſoever can give water above a certain degree of heat; for as ſoon as it boils, we may increaſe the fire in the moſt vehement manner imaginable, yet the water will not get one whit hotter than before. The greateſt heat water is capable of receiving, being meaſured by the themometer, juſt amounts to two hundred and twelve degrees; at that pitch [313] it begins to boil, and increaſing the fire afterwards ſerves to promote its evapo⯑ration, but not to increaſe its heat. However, though it becomes no hotter, yet its power of diſſolving the texture of ſubſtances thrown into it, is increaſed by increaſing the heat beneath; for by this means, the parts of the water ſtrike with more force upon the parts of the body, and thus ſooner deſtroy their arrangement.

AS water begins to boil, it is uſually ſeen to bubble; the leſs it is preſſed by the atmoſphere above, the more it bubbles, and in the void it bubbles very readily: if the ſurface of boiling water be therefore covered with a fluid, which preſſes like the atmoſphere upon it, the bubbling, or as it is uſually called, the boiling over of the water will be thus prevented. The more tenacious or gluey any fluid is, the more in this manner it is apt to boil over; however, if any lighter fluid is thrown in which will [314] preſs down the bubbling ſurface, and thus make an artificial atmoſphere, if I may ſo expreſs it, this will prevent the dangerous effects of the overflowing fluid. Boiling ſugar thus is apt to run over; but this is prevented by throwing in a piece of butter, or ſome ſuch like ſubſtance, which ſpreading, floats upon the ſurface, and keeps the other fluid from riſing.

THE cauſe of this ebullition in boiling water, the cauſe of the ſurprizing force of its vapours when driven off by heat, the cauſe of the yielding fluidity of its parts; theſe are utterly unknown, and in this reſpect we muſt be contented like geographers, to give the map of a coun⯑try, without knowing its real produc⯑tions. Some aſcribe the bubbles in boiling water to the air endeavouring to get free, and thus aſſuming a ſphe⯑rical figure. Others aſcribe them to the parts of the water itſelf, reduced into thin plates by the interpoſition of the [315] parts of the fire. For the firſt, waters purged of their air by former boiling, bubble as much as thoſe which have all their air ſtill remaining; as to the ſecond, the denſeſt liquors bubble leaſt, ſuch as mercury, yet theſe admit of a much greater proportion of fire be⯑tween their parts to reduce them to thin plates, than lighter fluids. Theſe, and ſeveral other phaenomena of this fluid, are all equally inexplicable. Thus we know that water extinguiſhes fire. Why? Muſchenbrook will tell us, that the fire conſumes and feeds upon bodies, only becauſe they contain a quantity of oil: That this oil, when ſet on fire, has an heat of ſix hundred degrees, that the greateſt heat of water is only two hun⯑dred and twelve degrees, ſo that water muſt cool the oil, and ſo extinguiſh the flame. This would be a very plauſible ſolution, did we not find that water often makes a fire burn with ſtill greater force, when thrown in ſmall quantities upon it; ſo that in ſuch a caſe, water, mixed [316] with this imaginary oil, makes it burn fiercer.

WATER, like every other ſubſtance with which mankind are acquainted, is never found ſimple and unmixed; though it be diſtilled never ſo often, yet it will have an earthy ſediment at the bottom of the veſſel, in which the proceſs is performed. We have an account of the different ſubſtances with which it is uſually mixed, in Boerhaave; but one more accurate ſtill, has lately been given us by Margraff, a German chymiſt. A hundred German meaſures, or about fifty Engliſh quarts of rain water, gave, upon diſtillation, an hundred grains of a yellowiſh white earth, a few grains of nitre, and ſome of common ſalt. The greateſt care was taken to have the water pure and unpolluted, yet ſtill it exhibited this heterogeneous mixture. Theſe ſalts were evident demonſtrations that the ſame water alſo contained oil, and there⯑fore if ſo, it muſt have been upon that [317] account ſubject to putrefaction. For this purpoſe, Margraff expoſed it for ſome time to the weather, and at about the end of one month, he perceived a kind of internal fermentation, and a greeniſh ſubſtance began to ſtick to the bottom and ſides of the glaſs, reſembling the mantle of a ſtanding pool; its ſmell was diſagreeable, but it was near three months before it was perfectly putrefied; a proof that the oil it contained was in much leſs quantity, than in the gene⯑rality of other ſubſtances, which rot much ſooner. Snow water exhibited the very ſame appearances, but upon the diſtillation, rather furniſhed more earth, and leſs nitre; a pretty evident proof that nitre is not the cauſe of the congela⯑tion of water into ſnow, as ſome have imagined. In ſhort, in this naturaliſt's experiments, ſnow water ſeemed equally foul with that of rain water; contrary to the experiments of Boerhaave, and many of our own countrymen, who have taught us to regard ſnow water as more pure than any other.

[318]SPRING water is generally pure or polluted, in proportion as the earth through which it happens to ſtream, is impregnated with minerals or ſalts, which it is capable of diſſolving. Thoſe waters which come through or over beds of ſalt, or layers of ore, take a ſtrong tincture from either, from whence we have ſpaw waters of different kinds. Thoſe that are ſtrained through a ſandy ſoil, free from ſaline or metallic ſub⯑ſtances are much more pure.

RIVERS in general furniſh pure water in proportion to the purity of the foun⯑tains by which they are fed, or the nature of the ſoil through which they flow. The largeſt rivers have in general the moſt unpolluted ſtreams; the Indus, the Rhine, and the Thames, all produce the ſofteſt and pureſt waters, moſt pleaſing to the diſtinguiſhing palate, and leaſt liable to putrefaction.

AS water, when thus mixed with weighty ſaline and metallic principles, [319] muſt be neceſſarily more heavy than when perfectly pure; ſo in many caſes, the weight of water will ſerve to diſtinguiſh its purity. The moſt pure water will in general be the lighteſt; but we muſt not depend upon this as a rule, for often a putreſcent oil is mixed in⯑timately with the fluid, particularly when it flows over fat and unctuous beds of earth; this in a ſmall quantity mixes with its ſubſtance, diminiſhing its weight at the ſame time that it increaſes its tendency to putrefaction.

OF all kinds of water, that in ſtagnant pools is the moſt impure and noxious to the conſtitution. Water ſerves as a diſſolvent to almoſt every ſubſtance that is thrown into it; in this manner ſalts, metals, plants, ordures of every kind, are all generally mixed together in theſe places, and make one maſs of corruption, equally diſpleaſing to the ſenſe, and in⯑jurious to the health.

[320]THIS water however, may be uſed in caſes of neceſſity: but there is ſtill a larger ſtore of this fluid, which nature ſeems not to have allotted for the uſe of man, I mean the ſalt waters of the ſea. Theſe, as we well know, contain ſalt in very great quantities, together with a bitumen, perceivable both to our taſte and ſmell; theſe ſalts being much heavier than water, and being diſſolved in it, give the contents of the ocean that ſuperior ſtrength and weight which freſh water cannot equal. Where freſh water ſupports a body of a thouſand pounds, ſea water will ſupport, all other circumſtances the ſame, one of a thou⯑ſand and thirty pounds.

HERE again new queſtions ariſe, for which philoſophy has not yet found a ſatisfactory ſolution; Whence is it that the ſea water is charged with ſaltneſs, while that of rivers is mild, freſh, and fit for human purpoſes? Some, inſtead of giving a cauſe for its ſaltneſs, have [321] offered reaſons to ſhew that it is fit the ſea ſhould be ſalt. Wanting, ſay they, the motion which rivers have, it would be apt to putrefy by its natural ſtagna⯑tion, but ſalt preſerves all ſubſtances from putrefaction, and therefore it pre⯑ſerves the waters of the ſea alſo. This is falſe: the ſea is prevented from ſtag⯑nating by many cauſes, as for inſtance, the tempeſts and tides give it continual motion; and when ſea water actually ſtagnates, it putrefies like freſh.

Halley rejecting ſuch a pucrility, ſub⯑ſtitutes one of his own: he thinks that rivers waſh down all this ſalt from the earth into the ocean; and that at firſt, the ſea water was as freſh as that of the rivers themſelves. This is not true: the ocean is ten times as large as the earth; ſalt makes a fortieth part of the ocean. If the earth ſupplied this fortieth part, a fourth part of its ſub⯑ſtance muſt thus have been ſolid ſalt; but common earth does not furniſh a [322] grain of ſea ſalt from an hundred pounds of it. Buffon aſcribes the ſaltneſs of the ſea, to beds of ſalt at the bottom of the ocean. An experiment is againſt him; ſea water is ſalter at top than at bottom. We muſt at laſt therefore be compelled to unite theſe two cauſes, and this will bring the matter ſomething nearer to probability; let us then ſuppoſe that the ſea is ſalt, from the rivers which continually bring in a ſtore of this mineral with their waters, and from beds of ſalt lying at the bottom of the ocean, which its waters are diſſolving and carrying away.

CHAP. XX. Of Springs and Rivers.

WERE water always at reſt, un⯑diſturbed either by the winds or other external preſſure, it would corrupt and putrefy. We have already taken notice of its putrefaction in the veſſels of the chymiſt, who expoſed it for that purpoſe, and the ſame thing conſtantly happens to thoſe who ſtore up water for long voyages. It loſes its tranſparence, generally becomes firſt brown, then greeniſh, and at laſt turns red; in fact, it always putrefies: but the waters of different rivers have various appearances in each ſtate of their putre⯑faction, each putrefying leſs offenſively, in proportion as it furniſhes a fluid the leaſt polluted with heterogeneous mixtures.

THIS putrefaction is prevented in the natural ſtate of things, by the motion of [324] the fluid; for we ſeldom ſee water running in ſprings, rivers, or ſeas, ſuffer theſe changes. By conſtantly rolling onward, it is probable that the fluid ſtill preſents new ſurfaces to the ambient air, and either imbibes a freſh⯑ening principle from the atmoſphere, or depoſits its feculent parts upon air, which, like a ſponge, is fitted to attract them. However this be, certain it is that running ſtreams and rivers are more pure than ſuch waters as ſtagnate; ſo that though we may be ignorant how motion thus contributes to the ſweetneſs and tranſparence of water, yet we are certain that motion produces theſe happy effects. The manner how water freſhens as it flows, may be hidden from human penetration; the conſequences of this motion are obvious to the ſlighteſt ſearch.

BUT now it becomes an enquiry equally intereſting and curious, to in⯑veſtigate how this ſalutary motion in [325] waters has been originally produced; how this circulation of the fluid, which we ſee carried round our globe, is con⯑tinued; from whence do ſprings derive their ſtores, to furniſh rivers with a con⯑ſtant ſupply; in what manner do rivers flow conſtantly towards the ſea; or how does the ſea itſelf daily ſwell and ſink in tide and ebb, with unremitted alter⯑nation?

TO begin with the firſt natural agent in this extenſive circulation, we muſt obſerve, that the atmoſphere has a power of raiſing waters up into itſelf in large quantities. We have ſeen capillary tubes lift water much above its level; we have ſeen a loaf of ſugar, wet at the bottom, ſuck up the moiſture to the very top. In this manner probably it is, that the bottom of the atmoſphere reſting upon a large ſurface of water, attracts it up into itſelf, and becomes loaded with the vapours of the ſubjacent fluid. This evaporation alſo is not a little forwarded [326] by the beams either of the ſun, or the heat which we know to be encloſed within the boſom of the earth; theſe dilate and increaſe the ſurface of the fluid, and conſequently promote its aſcent. Winds alſo in the ſame manner promote this evaporation; they raiſe the water into waves, and we need not be taught, that the ſurface of a pond when uneven and wavy is greater than when it is perfectly ſmooth. All theſe cauſes therefore concurring, water is raiſed in great quantities into the air. If then we ſuppoſe this body of water continually raiſed and riſing in the atmoſphere, and again falling upon earth; if we ſuppoſe thoſe immenſe ſtores of fluid, ſucked up from the ocean, to be condenſed into rain, ſnows, and dews, and to depoſite their ſtores upon land, here will be a fund ſufficient, for the production of ſprings, and rivers.

LET us now then carry our imagina⯑tion to the courſe which a body of [327] theſe vapours may be ſuppoſed to take in the air. A ſheet of vapour riſing from the ſea, and wafted by the winds to land, is carried over the low grounds with an even flight, till it daſhes againſt the ſides of mountains, or is lifted up by the riſing air to their tops. Here the air, which was at firſt capable of buoying the vapours up, ſoon becomes too light to ſuſtain them, and alſo the vapours being condenſed into larger drops, by the cold of thoſe upper regions, they ſink like rain upon the mountains ſide, and trickle downwards into the chinky bed of the hills: here entering into their caverns, they gather in thoſe natural baſons, overflow, and at laſt force themſelves a paſſage, and thus ſingle ſprings are formed; many of theſe running down by the vallies between the ridges of the hills, and coming to unite, form little rivulets or brooks; many of theſe again, meeting in one common valley, and arriving at the plain, become a river, the magnitude [328] of which is generally in proportion to the greatneſs of the mountain from whence its waters deſcend. The largeſt rivers flow from the greateſt mountains. The Andes of America, ſend forth their Marannon; the African mountains of the moon, their Nile and their Niger; the Alps, their Danube and their Rhine.

BUT perhaps it may be thought that evaporation alone, is a cauſe too ſlight and inſufficient to produce thoſe im⯑menſe torrents of water, which we have juſt enumerated. To this Doctor Halley replies, (for the preſent theory is taken from him) that the quantity of water raiſed by evaporation, is more than ſuffi⯑cient to effect all theſe purpoſes. He has attempted to prove, by evaporating a determined quantity of water, with the natural heat it generally ſuſtains, that every ten inches ſquare of water, loſes one inch in a day, by evaporation; and therefore, knowing the number of ſquare miles in the ſurface of the Mediterranean [329] ſea, he calculated that it would loſe by evaporation, every ſummer day, fifty⯑two thouſand and eighty millions of tons. This quantity he ſuppoſes to be two thirds more than it gains, by the nine great rivers which flow into it. The water of its evaporation alone, would be therefore ſufficient to fill three times as many rivers as empty them⯑ſelves there; and what is true of the Mediterranean, may be applied with equal force to every other great reſervoir of waters. What they gain by rivers, is not equal to half of what they loſe by evaporation; however, if the ocean fur⯑niſhes in this manner more than enough, it may be ſuppoſed to fall back in rains upon its own boſom.

IT would he in ſome meaſure unkind to diſenchant the beauties of the proſpect which this theory preſents us. A romantic imagination can form nothing more ſtrik⯑ing than this unceaſing rotation of waters; clouds riſe from the ocean, travel till they daſh againſt the tops of the higheſt moun⯑tains, [330] deſcend feebly in little ſtreams down their ſides, enter the ſubterranean caverns of the earth, overflow, burſt forth in ſprings, and at length they all aſſemble into rivers, that carry the united torrent again to its parent ocean. Such ſpecula⯑tions are amuſing; but as ſpeculations however may be driven too far, ſo here ſuch a quantity of evaporated water has been contrived in ſupport of this theory, as would, if it fell, drown our earth, inſtead of refreſhing it. Almoſt every calculator ſeems to admit, that near one third more water is raiſed by evaporation, than falls in rain: now what becomes of the ſurplus, which we muſt ſuppoſe not to fall, is no eaſy matter to deter⯑mine. In one part of this theory alſo, Halley aſſigns as a reaſon for the Medi⯑terranean's conſtantly receiving a ſtrong current from the Atlantic ocean, that the Mediterranean loſes ſo much of its water every day by evaporation, and conſe⯑quently requires this ſupply. But how can this be the cauſe of the current in [331] queſtion, ſince the Atlantic ocean loſes as much water by evaporation, as the Mediterranean itſelf. The ſame influ⯑ence acts equally upon both, and ſo will cauſe no difference on either.

WHEN numberleſs rivulets unite, they form a river, and in every country there ſeems ſome region higher than the reſt, from whence its rivers ſeem detached on every ſide to the ſea. Varenius the geo⯑grapher has made an aſſertion that at firſt ſeems extremely improbable, when he gives it as his opinion, that all rivers were originally formed by human toil and induſtry; that at firſt they might have been but ſmall canals, but being widened by degrees by the current, they at length have ſwolen into a Wolga or a Po. Wherever, continues this geogra⯑pher, we ſee a flood of water burſt from the earth, the water forms no channel, makes no progreſs towards the ſea, but overflows the adjacent country; there forming a lake, which is either con⯑ſtantly [332] ſupplied, or ſoon dried up by evaporation; he alſo mentions ſeveral rivers that have had their channels evidently made by human labour. His obſervation is curious, though his reaſoning be falſe; and indeed it is ex⯑traordinary, that though natural hiſtory informs us of many new lakes, that are naturally formed by the burſt of waters, it can furniſh us with no accounts of rivers made in the ſame manner.

BUT leaving Varenius and his opi⯑nions, we muſt obſerve, that it is moſt probable rivers have originally formed their own channels. If the ground over which they flow be very ſteep, the water muſt acquire proportionable ſwiftneſs; it muſt thus level the grounds which nature has oppoſed in their way, the water will by its weight ſink itſelf a bed; and wherever the ſtreams are directed with greateſt rapidity, there they will wear the earth moſt, and become wideſt or deepeſt.

[333]WHEN a river has thus levelled itſelf a bed, it will then flow more horizon⯑tally along, and of conſequence will wear its channel more ſlowly; by this means the bottom will at length be in a ſtate of permanence; whatever it loſes by the continual bruſhing of the water over it, it will gain by the ſediment the water naturally depoſites wherever it flows. The ſteepy deſcent of rivers, when they firſt begin their courſe, is generally very great, for it is this which gives them ſtrength to force a paſſage to the ſea; as they flow onward, their deſcent is leſs precipitate, they go onward more gently, and their fall is uſually very little as they approach the ſea. From hence we may conceive a general picture of the windings of a river. When the waters towards their ſource are rapid and head⯑long, they move directly forward in a ſtraight channel; but as their deſcent leſſens, their windings increaſe; and ever, as they approach the ſea, aſſume greater meanders. By this rule, Mr. Fabry, [334] when travelling through deſolate and uninhabited countries, was always en⯑abled to form a probable conjecture of his diſtance from the ocean; the fewer the ſinuoſities of the rivers, the farther was he removed from the ſea.

THE rapidity of a river's current ariſes from two cauſes, the declivity of its channel, and the quantity of its waters; therefore it ſometimes happens, that thoſe rivers which have the greateſt declivity, are not ſo rapid as thoſe whoſe declivity is much leſs, but whoſe waters are more abundant. Thus the Rhone is by no means ſo rapid as the Danube, and yet its channel is more ſteepy; for they both ariſe from the ſame mountain, but the Rhone falls by a ſhorter, and conſequently a more preci⯑pitate courſe into the ſea.

IT is not my deſign to give in this place a geometrical theory of motion of water in rivers; that depends upon prin⯑ciples [335] not yet explained; though in fact, there is nothing in the writers on this ſubject, upon which we can depend with certainty. Thus they obſerve, that the bed of a river may be compared to an inclined plane, and the water as moving down it with an increaſing velocity, and conſequently the greateſt ſwiftneſs will be at the river's mouth. But then, ſay they, in proportion as the velocity is increaſed by the deſcent, it is retarded by attrition againſt the bottom and ſides of the canal, and this more than coun⯑terbalances the former celerity.

THOSE parts of the ſtream that are moſt in the middle are ever the ſwifteſt, becauſe they receive the leaſt obſtruction from the bottom and ſides to their pro⯑greſſive motion. For this reaſon, the union of two rivers muſt encreaſe their celerity, as it diminiſhes the number of obſtacles which they would meet with if their courſes were ſeparate. This alſo will give the reaſon why great rivers with [336] a ſmall declivity, are yet more rapid than ſmall rivers whoſe declivity is very great. The waters of the former meet with leſs obſtruction, and go forward with all their communicated force, while thoſe of the latter continually ſuffer delay from the ſides and bottom of their canals.

WHATEVER diminiſhes the channel of a river, increaſes the rapidity of the ſtream; for the force which drives the water forward ſtill remains the ſame, and we all know that the ſame force impreſſed upon any body, drives it for⯑ward with greater velocity, in proportion as the body is leſs. Thus we ſee waters going with great rapidity under the arches of a bridge, becauſe the channel is leſſened through which they paſs.

WE are not to acquieſce in ſuppoſitions of geometrical writers upon this ſubject, that the ſurface of a river is quite even and plane from one bank to the other. [337] On the contrary, upon a ſudden inun⯑dation, or when the middle of the cur⯑rent is extremely rapid, the middle part riſes above the other parts of the ſur⯑face, ſometimes, as it has been found by admeaſurement, three feet, though in a ſmall river. The ſwiftneſs with which the middle of the current is driven, in ſome meaſure deſtroys its gravity, and thus it riſes moſt, where its preſſure from gravity is leaſt. When a river has a backward ſtream, as in the caſe of tides flowing up its channel, then the water is higheſt towards each bank, and loweſt in the middle; in the former caſe, the water of the river reſembled a ridge, in this it is hollowed like a furrow.

THE water at the ſurface of a river, and that at its bottom, are often found to have very different rapidities: if for inſtance, we dam the ſurface of a river, by a bridge of boats thrown acroſs it, while the rapidity above is thus dimi⯑niſhed, the rapidity of the water running [338] under the boats, is greatly increaſed. Thoſe therefore who ſwim in ſtreams, interrupted in this manner by boats or timber, ſhould not truſt to the ſmooth appearance of the ſurface, for very fre⯑quently, a ſtrong and a fatal current lurks beneath.

WITH regard to the overflowing of rivers, the inundation is generally greater near the ſource, than the mouth of the ſtream; for wherever the force is greateſt, there will be the moſt likelihood of the waters burſting their banks, or overflowing them. But we have before obſerved, that the declivity of the ſtream is greateſt towards the ſource, and con⯑ſequently the force of the ſtream againſt its banks, muſt be greateſt there alſo.

THESE hints may ſuffice upon this ſub⯑ject; but it muſt not be ſuppoſed, that general rules can give us any certain infor⯑mation; a huſbandman who, conducted by geometry alone, ſhould attempt to alter [339] the courſe of a river, or ſtop its inunda⯑tions, would be ſoon taught, that un⯑taught experience alone, was in this inſtance a much better inſtructor. In ſhort, the natural hiſtorian is a much better guide on this ſubject than the ma⯑thematician.

CHAP. XXI. Of Tides.

IT has been the fortune of philoſophy to ſucceed beſt in accounting for the greater operations of nature, while it is evidently feeble in the minute. In the ſame manner as we have a ſatis⯑factory idea of the planetary ſyſtem, we have but an obſcure account of the changes wrought in our own at⯑moſphere. Thus alſo, the theory of the flowing of a ſpring is but uncertain; the theory of the tides of the ocean is nearly demonſtrative.

AS rivers flow and ſwell, ſo alſo does the ſea; like theſe it hath its currents, that agitate its waters, and preſerve them from putrefaction. This great motion of the ſea is called its tides. The waters of the ocean have been obſerved regularly from all antiquity, to ſwell twice in about four and twenty hours, and as [341] often to ſubſide again. This ſwelling of the ſea is moſt obſervable upon ſhelving ſhores, where the waters retire for near ſix hours, and leave them quite dry, but ſoon return again and overflow the ſands; and thus the alternate ebb and flow is twice perceived, in the ſpace of ſomething more than four and twenty hours.

IT was an obſervation alſo, in the earlieſt ages of mankind, that this ebb and flow had a conſtant correſpondence with the moon, and that the ſea's motions ſeemed to be guided by the moon's motions. They obſerved, that whenever the moon came over our heads, one of theſe ſwellings of the ſea was ſeen alſo. They remarked, that whenever it was either new or full moon, the tides were greateſt; and on the contrary, whenever the moon was between the new and the full, and ſhewed us but half its face, that then the tides were leaſt. There are ſeaſons of the year [342] when, as aſtronomy ſhews, the moon is nearer the earth than at other times; they knew that at thoſe ſeaſons the tides roſe higheſt in proportion. They remarked with equal ſagacity, that the ſun, in ſome meaſure, joined his influ⯑ence to that of the moon; that when the ſun and moon were on the ſame ſide of the heavens, then the tide roſe on that ſide higheſt; on the contrary, when theſe two luminaries were on oppoſite ſides, that the tides then obeying a divided influence, roſe leſs high than before. The ſun and moon, as aſtronomy ſhews, are more near the earth in autumn and ſpring than at other times, and therefore the tides obeying their influence, were ſeen to be greater at thoſe ſeaſons. All this was diſcovered by the ancients, and Pliny has given us a chapter upon the in⯑fluence of theſe two luminaries upon the waters of the ocean.

BUT this was only an obſcure con⯑ception of theſe wonderful appearances: [343] they knew neither the cauſe of this ſwelling, nor the manner in which the waters obeyed the lunar influence. The moon came over their heads but once in twenty-four hours forty-nine minutes, whereas they ſaw the tides actually riſe twice in that ſpace, ſo that here they were perfectly at a loſs, ſince the tides roſe twice as often as the cauſe that pro⯑duced them. The thorough inveſtigation of theſe appearances, was left for the ſagacity of Newton.

WE have often laid it down that attrac⯑tion prevails throughout all nature; the earth attracts the moon, and the moon at⯑tracts the earth towards itſelf, each in pro⯑portion to the quantity of matter contain⯑ed in either. This being acknowledged, let us ſee what will happen, when the moon comes directly over any part of the ocean. We have allowed that this planet continually draws the whole earth in ſome meaſure towards it; but it will particularly act upon the waters, which [344] are more at liberty to obey its influence than the ſolid parts of the earth; ſo that the waters immediately underneath it, will be attracted up in a heap. Thus we may conceive that part of the ocean as one immenſe mountain, with its ſummit pointing towards the moon. But now let us ſee what will in the mean time be doing on the oppoſite ſide of our globe? We ſaid that the waters on the ſide next the moon, will be more violently at⯑tracted, than any other part of the globe, becauſe they are neareſt the moon; then of conſequence, the waters on the op⯑poſite ſide will be leſs attracted than any other part of the globe, becauſe they are fartheſt off from the moon. If they be but feebly attracted, they will be very light, as we know all bodies feebly at⯑tracted are; if they be very light they will riſe, and all the neighbouring waters will flow to that place; in ſhort, ſwell into an heap or mountain of waters, whoſe ſummit points to the oppoſite part of the heavens, as the ſummit on the [345] other ſide pointed to the moon. Thus does the moon, in once going round the earth in twenty-four hours, produce two tides or ſwells, and conſequently as many ebbs: one tide, when ſhe comes to the meridian, nearly over our heads; another tide, when ſhe is over the heads of our antipodes, on the other ſide of the globe. Theſe tides muſt flow from eaſt to weſt, for they muſt neceſſarily follow the moon's motion, which is from eaſt to weſt. We readily ſee now, that this double power, acting conti⯑nually upon oppoſite parts of the ocean, muſt agitate its whole maſs, and ſpread the motion not only to the ſhores of the ſea, but drive its waters a conſiderable way up the rivers alſo.

BUT all this time, we have made no mention of the ſhare the ſun has in theſe operations. Were this great luminary as near the earth as the moon is, without doubt its influence would be much greater than that of the moon; but this [346] is not the caſe; the ſun is placed at an immenſe diſtance from us, and though its power over the waters of the ocean is very ſenſibly perceived, yet it is greatly inferior to that of the moon, which though ſo much leſs, is ſo much nearer. Whatever power the moon hath, the ſun has a ſimilar power, but in a ſmaller degree. If the power of both the moon and the ſun conſpire in raiſing the tides, they will then have their greateſt ſwell; if both act in ſuch a manner as to leſſen each other's in⯑fluence, the tides will not then be ſo high. Thus, for inſtance, when it is new moon, aſtronomy ſhews us that the ſun and moon are on the ſame ſide of the heavens; they will therefore attract the ocean with united force, and we ſhall have high tides. If again it be full moon, the moon will draw the waters in one direction, the ſun will draw them directly oppoſite, and this we know is the ſame, as if they both drew the ſame way, ſo that this alſo will make the tides [347] riſe high. But now if it be half moon, then the moon makes different tides from the ſun, and the ocean obeying a double impulſe, ſwells but in a ſmall degree under either. To have a more thorough knowledge of this ſubject, it is neceſſary to underſtand aſtronomy; we will only therefore ſlightly obſerve, that the tides arrive each day later by forty-nine minutes, becauſe a lunar day is ſo much longer than a ſolar day: and let us add, that the greateſt ſwell is not ſeen while the moon is directly in the meridian of the place, but about three hours after ſhe hath paſt; in the ſame manner as we ſee the waves of a lake have their greateſt ſwell, a ſhort time after the tempeſt is allayed. Again, when the moon riſes directly over the earth's equator, the tides are equally high on both ſides of it; but as the moon declines towards either pole, the tides will riſe on either ſide in proportion to her proximity. Towards the poles however the tides are much leſs than near the [348] equator, for the moon acts upon the ſeas of thoſe countries with more remote influence; and beſides, the polar oceans being almoſt continually ſtiffened into ice, they leſs readily obey the lunar impulſe.

WE ſaid above, that the tides purſued the moon's motion to the weſt; for this reaſon therefore the eaſtern coaſts will have high tides, before thoſe that lie more weſterly. This is the general law which prevails over all the globe; the navigation of ſhips to the weſt, is much more ſpeedy than their return, for they thus in a manner go with the tide.

BUT we muſt not expect to find this law prevailing in narrow ſeas, clogged with iſlands, or altered by contrary currents. The tides are variouſly affected in their paſſage through different ſhoals and channels, and retarded by winding round capes and promontories, that jut out into the ocean. Thus the tide in [349] the German ocean, takes twelve hours to come to London bridge, where it ar⯑rives juſt as a new tide is raiſed in the ocean; ſo that we have the higheſt tides up the river Thames, when the moon makes them leaſt out at ſea: for when ſhe riſes above the horizon, our tides are leaſt, when in the open ocean they are greateſt. In ſhort, if this general theory be well underſtood, there are few particular caſes that will not find an eaſy ſolution. Thus, if it be demanded why the Caſpian, Mediterranean, and Baltic ſeas have ſcarce any tides, it is eaſy to reply, becauſe they have no con⯑ſiderable communication with the ocean. The leſs extenſive the ſurface, the leſs will be the tides; their's is not the hun⯑dredth part of the ocean, and their tides will be therefore in proportion.

AS the moon's influence is ſo ſtrong upon the watery fluid that covers the face of our globe, it muſt have alſo an equal power over the aerial fluid [350] that ſurrounds it, and will conſequently produce tides in the air. Many have thus accounted for the trade winds, that blow continually in the ſame direction with the ocean, from eaſt to weſt. But as the air is attracted only in proportion to its quantity of matter, and as that is but very ſmall in proportion to the ſpace it occupies, theſe aerial tides muſt be imperceptible to ſenſe, and they can produce no alte⯑ration here below.

PHILOSOPHERS have not been con⯑tent with thus accounting for the tides upon earth, but they have given alſo a theory of the tides in the moon. If the moon, ſay they, can raiſe water ten feet upon earth, the earth will raiſe water an hundred and ten feet upon the moon; but as the moon has always the ſame face turned to the earth, its waters, ſay they, will ever remain at the ſame height, and there⯑fore all the tides it perceives muſt [351] be occaſioned by the ſun. But no mat⯑ter for the tides in the moon; it is very well if they have ſatisfactorily explained the tides upon earth.

CHAP. XXII. Hydroſtaticks.

IN almoſt every phyſical ſpeculation, wherever experiment can reach, the ſubject admits of illuſtration; wherever that is denied, the reaſonings are but vain and conjectural. Thus we are ig⯑norant of the form of the parts of which water or any other fluid are compoſed, becauſe we can make no ex⯑periments which may reduce theſe ſub⯑jects into the primary particles of which they are compoſed. Thus, if we reduce water, by evaporation, to the ſmalleſt parts our ſenſes can diſtinguiſh, yet if we examine any of theſe with a mi⯑croſcope, the little ſpherical drop will be found as fluid as the water in the veſſel from whence it aroſe; the minute drop hath its ſmaller parts, which give it fluidity; theſe parts can be ſeparated from each other, and thus made to eſcape microſcopic obſervation; but ſtill, where⯑ever [353] water or its parts are ſeen, they are fluid.

AS we are ignorant therefore of the nature of theſe parts ſeparately, becauſe we cannot ſeparate them enough, we muſt be contented to enquire into thoſe appearances which ariſe from their combination. Like all other bodies, we know they have weight, and therefore preſs downward by the force of gravity. A glaſs filled with water, is heavier than an empty one; a ſponge floats while dry, but ſinks when filled with water. We know alſo, that they yield to every preſſure, for each of theſe minute parts being capable of making only a very ſmall reſiſtance, the combination of minute reſiſtances will appear like one uniform reſiſtance, oppoſing, yet giving way to every impreſſion.

FROM this accumulation, and this reſiſtance of the parts of any fluid, but particularly of water, many very ſtriking [354] appearances ariſe. Their different force, in preſſing the bottom of a tall veſſel and a ſhallow one; their ſupporting heavy bodies floating on their ſurface; their riſing in one pipe to the ſame height from whence they deſcended, and thus aſcending up the ſide of an hill, contrary to their natural weight; theſe and ſeveral other phenomena attract our curioſity, and demand explanation.

IN entering upon the firſt part of this theory, which ſhews how much the parts of fluids preſs upon the bottom and ſides of veſſels, or upon bodies which are plunged in them, we muſt be contented to begin with one property, verified by experience alone; we muſt ſtart from an obvious appearance in all watery fluids, for which theory has been unable to account. The property of all waters is, that in a ſtate of reſt their ſurface is level.

NOW then let us ſuppoſe three tubes or veſſels united, and to have a com⯑munication [355] with each other; (fig. 36.) we know that if water be poured into the perpendicular veſſel A, it will run into the horizontal veſſel C, and riſe in the other perpendicular veſſel B, to the ſame level at which it ſtands in the veſſel A.

FROM this obvious experiment we learn, that fluids preſs in all direc⯑tions, upwards, ſideways, downward, and in ſhort, every way. For let us ſup⯑poſe that the tube B, were intirely taken away at b, it is evident that the water in the horizontal tube C, would ſtill preſs againſt the part b, with as much force as it did before, whether the tube were there or not; and if the tube C were taken away, the water in A would preſs againſt the part a, with as much force as it did, whether C were there or not; water therefore preſſes the ſides and bottom of the veſſel that contains it in all directions. Thus far experience alone muſt be permitted to guide; and if we knew the figure of the parts of [356] water, we might be able to tell how they come to be endued with this property; but as that is unknown to us, farther illuſtrations would only increaſe the obſcurity.

AGAIN, ſuppoſe water were made to ſtand only at half the height d, in the tube A, it would then only riſe to half the height e, in the tube B. The preſ⯑ſure therefore upwards at b, would then be but half as powerful as in the former caſe, when the water roſe to B; of con⯑ſequence therefore, the preſſure at a would be but half of what it was before; and therefore the preſſure of the water in the veſſel A, upon its bottom, would be but half of what it was before. From hence we may in general conclude, that the preſſure which water at any depth ſuſtains will increaſe, as the height of the water above it increaſes. Thus, for in⯑ſtance, if the veſſel be very high, the preſ⯑ſure at the bottom will be ſuch as would make water riſe to an equal height in [357] another veſſel, and conſequently it muſt be great.

FROM this laſt property we learn the cauſe why, if an hole opens in the bottom of a ſhip at ſea, the water burſts through it with much greater violence than if an hole were broke in the ſhip's ſide, near what the mariners call the water's edge. In the firſt caſe, the water being greatly preſſed by the weight of water over it having a free paſſage into the ſhip, preſſes in with a force, equal to the preſſure itſelf ſuſtains; on the other hand, the water in the latter caſe is not much preſſed by the fluid above, as the hole is near the ſurface, and it there⯑fore preſſes in with much leſs violence.

ALL this is inconteſtible; but the hydroſtatic paradox we are now going to explain, will not be admitted ſo readily, though undoubtedly true. It is this: The weight with which water preſſes upon the bottom of any veſſel which holds [358] it, will be great in proportion to the height of the water in the veſſel, and not to the quantity of water it contains. Thus, for inſtance, let there be two veſſels A and B, both with their bottoms equally broad, and both equally high, but as we ſee of very different capacities; the bottom C of the ſmaller will be as much preſſed by the water, as the bottom C of the larger, though one of them may contain but a few quarts, and the other as many hogſheads.

WE will firſt prove this from theory, and then ſhew it true by experiment. Let us ſuppoſe two tubes a b inſerted into the bottom of each veſſel, the water will be preſſed into both with ſuch a force as will make it riſe to a level with the reſt of the water in both the veſſels; but as the water is at equal heights in both veſſels, the preſſure up the tubes muſt be therefore equal. Now what is true of one tube, is equally true of a thou⯑ſand, if they could all be inſerted into [359] the bottom; therefore, univerſally, the preſſure of the water in each veſſel upon every part of the bottom, and upon the whole bottom, muſt be equal.

IF two veſſels of equal bottoms, but unequal capacities, as A and B, could have their bottoms ſo contrived as to fall out upon a certain degree of preſ⯑ſure; if, for inſtance, the bottoms were of braſs covered with leather, to make them water tight, and capable of falling off when water was poured in to a certain height; it would be conſtantly ſeen that the braſſes would fall when the water roſe to a ſimilar height, in either veſſel.

ONE of the moſt uſeful machines to ſhew that a ſmall quantity of water is capable of great preſſure, is the hydroſta⯑tic bellows. This machine (fig. 37.) con⯑ſiſts of two thick oval boards, each about ſixteen inches broad, and eighteen inches long, united to each other by leather, [360] like a pair of common bellows, or a barber's puff. Into the lower board a pipe B, three feet high is fixed at e. Now, in ſhewing experiments with this ſimple machine, which even the reader himſelf might eaſily make, let water be poured into the pipe at its top c, which will run into the bellows, and ſeparate the boards a little: then to ſhew how much a little water will be able to effect by preſſure, let three weights, each of an hundred pounds, be laid upon the upper board. Now if we pour more water into the pipe, it will as before run into the bellows, and raiſe up the board with all the weights upon it. And though the water in the tube ſhould weigh in all but a quarter of a pound, yet the preſſure of this ſmall force upon the water below in the bellows, ſhall ſup⯑port the weights, which are three hun⯑dred pounds; nor will they have weight enough to make them deſcend, and conquer the weight of the water, by forcing it out of the mouth of the pipe.

[361]IT is inconceivable what force a ſmall quantity of water ſhall be made to exert, upon the bottom or ſides of a veſſel, when it ſtands in a high tube inſerted into the veſſel. A ſtrong hogſhead may by this means be ſplit, and I have ſeen the experiment performed. Into the bunghole was inſerted a ſtrong, though ſmall tube made of tin, and twenty feet high; when water was poured in through this, it filled the hogſhead, and when it roſe within about a foot of the top of the tube, the hogſhead burſt, and the water ſcattered about with incredible force.

FROM hence we may ſee, that fluids will always riſe to the ſame heights in pipes, from whence they deſcend. Thus, if there be a ſpring upon the brow of one mountain, and ſhould it be required to conduct its waters acroſs the valley, up the ſide of an oppoſite mountain; nothing more is neceſſary than to lay pipes of lead or hollowed timber along [362] the ſurface of the ground, leading from the ſpring down one mountain ſide, along the valley, and riſing up by the other; this will conduct the waters to any heights, which do not exceed the height of the ſpring from whence they are originally drawn. And the reaſon is obvious; all water will riſe to its own level: we have ſeen it riſe to the level, in the three ſmall tubes A B C, and it would riſe to the ſame, were theſe tubes each a mile in length, and equally high. But though in theory, water may be thus made to deſcend from the higheſt moun⯑tains, down the deepeſt vallies, and thus riſe again on an oppoſite mountain's ſide, yet in practice this can ſcarcely be per⯑formed from any very great heights, be⯑cauſe the preſſure of the water is ſo very great in the pipes at the bottom of the valley, that no pipes can be contrived ſtrong enough to endure it. We have ſeen how the preſſure of twenty feet of water would burſt a common hogſhead: now if we ſhould ſuppoſe the mountain [363] four hundred feet high, we ſhould find much difficulty to make any pipe ſtrong enough to reſiſt the water's weight at ſuch an height. Pipes hollowed through rocks of marble, would in a ſhort time burſt, like thoſe whoſe ſides were of paper. For this reaſon, when the height is more than an hundred feet, engineers, inſtead of pipes, are obliged to raiſe aque⯑ducts; theſe raiſing the water more to a level, the force againſt the ſides of the tube is leſſened, and it riſes to the mode⯑rate height from whence it fell, without any injury to the pipe that conducts it. It is generally ſuppoſed, that this con⯑trivance of carrying water down through vallies, and up againſt hills by pipes, was unknown among the ancients; but this is not the caſe, as could eaſily be ſhewn: they uſed aqueducts in their ſtead, becauſe leſs ſubject to want repair, and furniſhing water in greater abundance.

CHAP. XXIII. Of the Specific Gravity of Bodies.

WHEN an unſpongy or ſolid body ſinks in a veſſel of water, it removes a body of water equal to its own bulk, out of the place to which it deſcends. If, for inſtance, a copper ball is let drop into a glaſs of water, we well know that if it ſinks, it will take up as much room as a globe of water equal to itſelf in ſize took up before.

LET us ſuppoſe for a moment, that this watery globe removed by the ball were frozen into a ſolid ſubſtance, and weighed in a ſcale againſt the copper ball; now the copper ball being more in weight than the globe, it is evident that it will ſink its own ſcale, and drive up the oppoſite, as all heavier bodies do when weighed againſt lighter; if, on the contrary, the copper ball be lighter than the water globe, the ball will riſe. [367] Once more then let us ſuppoſe the cop⯑per ball going to be immerſed in water, and that in order to deſcend, it muſt diſplace a globe of water equal to itſelf in bulk. If the copper ball be heavier than the globe, its preſſure will overcome the other's reſiſtance, and it will ſink to the bottom; but if the watery globe be heavier, its preſſure upwards will be greater than that of the ball downward, and the ball will riſe or ſwim. In a word, in proportion as the ball is heavier than the ſimilar bulk of water, it will deſcend with greater force; in proportion as it is lighter, it will be raiſed more to the ſurface.

FROM all this we may deduce one general rule, which will meaſure the force with which any ſolid body tends to ſwim or ſink in water; namely, every body immerſed in water, loſes juſt as much of its weight as equals the weight of an equal bulk of water. Thus, for inſtance, if the body be two ounces, and an equal [368] bulk of water be one ounce, the body when plunged will ſink towards the bottom of the water with a weight of one ounce. If, on the contrary, the ſolid body be but one ounce, and the weight of an equal bulk of water be two ounces, the ſolid when plunged will remove but one ounce, that is, half as much water as is equal to its own bulk, ſo that con⯑ſequently it cannot deſcend; for to do that, it muſt remove a quantity of water equal to its own bulk. Again, if the ſolid be two ounces, and the equal bulk of water two ounces, the ſolid, wherever it is plunged, will neither riſe nor ſink, but remain ſuſpended at any depth.

THUS we ſee the reaſon why ſome bodies ſwim in water, and others ſink. Bodies of large bulk and little weight, like cork or feathers, muſt neceſſarily ſwim, becauſe an equal bulk of water is heavier than they; bodies of little bulk but great weight, like lead or gold, muſt ſink, becauſe they are heavier than an [369] equal bulk of water. The bulk and the weight of any body conſidered together, is called its ſpecific gravity, and the proportion of both in any body, is eaſily found by water. A body of little bulk and great weight, readily ſinks in water, and it is ſaid to have great ſpecific gra⯑vity; a body of great bulk and little weight, loſes almoſt all its weight in wa⯑ter, and therefore is ſaid to have but little ſpecific gravity. A woolpack has actu⯑ally greater real gravity, or weighs more in air than a cannon ball; but for all that, a cannon ball may have more ſpecific gravity, and weigh more than the wool⯑pack in water. Denſity is a general term that means the ſame thing; ſpecific gravi⯑ty is only a relative term, uſed when ſolids are weighed in fluids, or fluids in fluids.

BUT before we proceed in this theory, it may not be amiſs to get over an objection that will naturally ariſe. It may be ſaid, that as in the deſcent of heavy bodies in fluids, the deeper they deſcend, the more they muſt be reſiſted; [370] how comes it that by the time they get towards the bottom, they are not totally ſtopt from deſcending, and driven by the increaſed reſiſtance upward? The anſwer is eaſy; the lower ſurface of the deſcend⯑ing body is preſt with encreaſed reſiſtance upwards, it is true; but at the ſame time the upper ſurface is preſſed with increaſed reſiſtance downward. Theſe two in⯑creaſed and oppoſite forces balance each other, and make no difference in the deſcent.

IF however a method were contrived, while the heavy body was deſcending, to take away the preſſure from above, and leave that below all its increaſing force, then indeed the increaſed preſſure from below, would actually prevail over the body's ſuperior weight, and drive it upward; ſo that by this means, lead or gold itſelf might be made to ſwim upon water. The experiment has been conducted in the following manner. A glaſs tube C D, (fig. 39.) open at both ends, was fitted with a leaden bottom [371] half an inch thick, which was held cloſe to the tube by pulling a ſtring fixed in its middle, up through the tube, as ſo the bottom could not thus fall off. In this manner the tube was immerſed in water, in the glaſs veſſel A B, to the depth of three inches only below the ſurface of the water at K, by which means the leaden bottom was plunged ſomewhat more than to eleven times its own thickneſs. At that depth the bottom, which had no preſſure of water above it, and had a ſtrong preſſure below, would not ſink nor fall from the tube, but actually ſwam at that depth upon the water. If however, a preſſure above were made, by pouring a little water into the tube, then the lead would ſink with its uſual velocity.

IN the ſame manner as an heavy body was made to ſwim on water, by taking away the upward preſſure, ſo may a light body like wood, be made to remain ſunk at the bottom, by depriving it of all [372] preſſure from below; for if two equal pieces of wood be planed, ſurface to ſurface, ſo that no water can get between them, and then one of them be cemented to the inſide of the veſſel's bottom, then the other being placed upon this, and while the veſſel is filling, being kept down by a ſtick, when the ſtick is removed and the veſſel full, the upper piece of wood will not riſe from the lower one, but continue ſunk under water, though it is actually much lighter than water; for as there is no reſiſtance to its under ſurface to drive it upward, while its upper ſurface is ſtrongly preſſed down, it muſt neceſſarily remain at the bottom. The following method of making an extremely heavy body float upon water, is more elegant than the former. Take a long glaſs tube, open at both ends, ſtopping the lower end with a finger, pour in ſome quickſilver at the other end, ſo as to take up about half an inch in the tube below. Immerſe this tube, with the finger ſtill at the [373] bottom, in a deep glaſs veſſel filled with water; and when the lower end of the tube is about ſeven inches below the ſurface, take away the finger from it, and then you will ſee the quickſilver not ſink into the veſſel, but remain ſuſpended upon the tube, and floating, if I may ſo expreſs it, upon the water in the glaſs veſſel.

AS every ſolid ſinks more readily in water, in proportion as its ſpecific gravity is great, or as it contains greater weight under a ſmaller bulk, it will follow, that the ſame body may very often have different ſpecific gravities, and that it will ſink at one time, and ſwim at another. Thus a man, when he happens to fall alive into the water, ſinks to the bottom; for the ſpecific gravity of his body, is then greater than that of water: but if by being drowned he lies at the bottom for ſome days, his body ſwells by putrefaction, which diſunites its parts; thus its ſpecific gravity becomes [374] leſs than that of water, and he floats upon the ſurface.

THERE is a pretty childiſh contrivance by which the ſpecific gravity of the body is ſo altered, that it riſes and ſinks in water at our pleaſure. Let little images of men, about an inch high, of coloured glaſs, be beſpoke at a glaſs-houſe, and let them be made ſo as to be hollow within, but ſo as to have a ſmall opening into this hollow, either at the ſole of the foot or elſewhere. Let them be ſet afloat in a clear glaſs phial of water, filled within about an inch of the mouth of the bottle; then let the bottle have its mouth cloſed with a bladder, cloſely tied round its neck, ſo as to let no air eſcape one way or the other. The images themſelves are nearly of the ſame ſpecific gravity with water, or rather a little more light, and conſequently float near the ſurface. Now when we preſs down the bladder, tied on at the top, into the mouth of the bottle, and thus preſs the [375] air upon the ſurface of the water in the bottle; the water being preſſed will force into the hollow of the image through the little opening; thus the air within the image will be preſſed more cloſely together, and being alſo more filled with water now than before, the image will become more heavy, and will conſe⯑quently deſcend to the bottom; but upon taking off the preſſure from above, the air within them will again drive out the water, and they will riſe to the ſame heights as before. If the cavities in ſome of the images be greater than thoſe in others, they will riſe and fall differently, which makes the experiment more amuſing.

THIS is but an experiment of mere amuſement; much more important uſes are the reſult of our being able exactly to determine the ſpecific gravities of bodies. We can, by weighing metals in water, diſcover their adulterations or mixtures, with greater exactneſs than by [376] any other means whatſoever. By this means the counterfeit coin, which may be offered us as gold, will be very eaſily diſtinguiſhed, and known to be a baſer metal. For inſtance, if I am offered a braſs counter for a guinea, and I ſuſpect it; ſuppoſe, to clear my ſuſpicions, I weigh it in the uſual manner againſt a real guinea in the oppoſite ſcale, and it is of the exact weight, yet ſtill I ſuſpect it; What is to be done? To melt or deſtroy the figure of the coin would be inconvenient and improper: a much better and more accurate method remains. I have only to weigh a real guinea in water, and I ſhall thus find that it loſes but a nineteenth part of its weight in the balance; I then weigh the braſs counter in water, and I actually find it loſes an eighth part of its weight, by being weighed in this manner. This at once convinces me that the coin is made of a baſe metal, and not gold; for as gold is the heavieſt of all metals, it will loſe leſs of its weight by being weighed in water than any other.

[377]THIS method Archimedes firſt made uſe of, to detect a fraud with regard to the crown of Hiero, king of Syracuſe. Hiero had employed a goldſmith to make him a crown, and furniſhed him with a certain weight of gold for that purpoſe; the crown was made, the weight was the ſame as before, but ſtill the king ſuſ⯑pected that there was an adulteration in the metal. Archimedes was applied to, who, as the ſtory goes, was at firſt unable to detect the impoſition, but the reſiſtance he found from the water, in going into a bath, gave him the hint of weighing the crown hydroſtati⯑cally. A maſs of pure gold was pro⯑cured, which weighed equal with the crown in air; but when both were weighed in water, the crown proved much the lighter of the two, a poſitive proof that the metal, of which it was compoſed, was not ſo heavy as pure gold.

UPON this difference in the weight of bodies in open air and water, the hydro⯑ſtatic [378] balance has been formed, which differs very little from a common ba⯑lance, but that it hath an hook at the bottom of one ſcale, on which the weight I want to try may be hung by an horſe hair, and thus ſuſpended in water, without wetting the ſcale from whence it hangs. Firſt, the weight of the body I want to try, is balanced againſt the parcel or weight E, in open air; (fig. 40.) then the body is ſuſpended by the hook and horſe hair at the bottom of the ſcale, in water, which we well know will make it lighter, and deſtroy the balance. We then can know how much lighter it will be, by the quan⯑tity of the weights we take from the ſcale E, to make it equipoiſe; and of conſequence, we thus preciſely can find out its ſpecific gravity compared to water. There are ſeveral different ways in which the hydroſtatic balance is con⯑ſtructed; if the ſcales be very nice, it matters little as to the reſt.

[379]THIS is the moſt exact and infallible method of knowing the genuineneſs of metals, and the different mixtures with which they may be adulterated, and it will anſwer for all ſuch bodies as can be weighed in water. As for thoſe things that cannot be thus weighed, ſuch as quickſilver, ſmall ſparks of diamond, and ſuch like, as they cannot be ſuſ⯑pended by an horſe-hair, they muſt be put into a glaſs bucket, the weight of which is already known; this, with the quickſilver, muſt be balanced by weights in the oppoſite ſcale as before, then im⯑merſed, and the quantity of weights to be taken from the oppoſite ſcale, will ſhew the ſpecific gravity of the bucket and the quickſilver together; the ſpe⯑cific gravity of the bucket is already known, and of conſequence the ſpecific gravity of the quickſilver, or any other ſimilar ſubſtance, will be what remains.

AS we can thus diſcover the ſpecific gravity of different ſolids, by plunging [380] them in the ſame fluid, ſo we can diſ⯑cover the ſpecific gravity of different fluids, by plunging the ſame ſolid body into them; for in proportion as the fluid is light, ſo much will it diminiſh the weight of the body weighed in it. Thus we may know that ſpirit of wine has leſs ſpecific gravity than water, becauſe a ſolid that will ſwim in water, will ſink in ſpirit; on the contrary, we may know that ſpirit of nitre has greater ſpecific gravity than water, becauſe a ſolid that will ſink in water, will ſwim upon the ſpirit of nitre. Upon this principle is made that ſimple inſtrument, called an Hydrometer, which ſerves to meaſure the lightneſs or weight of different fluids. It is nothing more than an hollow copper ball, with a ſhort ſtalk or ſtem fitted into, or if I may ſo expreſs it, growing out of the ball; this ball is ſo made, as partly to ſink but not entirely in water, and ſo poiſed that the ſtem ſhall always ſtand upright: the lower it ſinks, the lighter the fluid; and on the [381] contrary, the higher it ſwims, the more heavy the fluid thus ſupporting it. How much it ſinks or ſwims may be very exactly known by the ſtalk, which is graduated or marked; and this inſtrument is often uſed by thoſe, whoſe buſineſs is to examine the different denſities of liquors, ſuch as drunkards, inn-keepers, diſtillers, and exciſemen.

THIS inſtrument, I ſay, will ſerve to meaſure the ſpecific gravities of different liquors, for it is found by experience, that liquors weigh very differently from each other; an experiment or two to ſhew this will ſuffice. Suppoſe we take a glaſs veſſel which is divided into two parts, communicating with each other by a ſmall opening of a line and an half diameter. Let the lower part be filled up to the diviſion with red wine, then let the upper part be filled with water. As the red wine is lighter than water, we ſhall ſee it in a ſhort time riſing like a ſmall thread up through the water, and [382] diffuſing itſelf upon the ſurface, till at length we ſhall find the wine and water have changed their places; the water will be ſeen in the lower half, and the wine in the upper half of the veſſel.

IN the ſame manner we may pour four different liquors, of different weights, into any glaſs veſſel, and they ſhall all ſtand ſeparate and unmixed with each other. Thus, I take mercury, oil of tartar, ſpirit of wine, and ſpirit of turpentine, ſhake them together in a glaſs, let them ſettle a few minutes, and each ſhall ſtand in its proper place, mer⯑cury at the bottom, oil of tartar next, ſpirit of wine, and then ſpirit of tur⯑pentine above all. Thus we ſee liquors are of very different denſities, and this difference it is that the hydrometer is adapted to compare. In general, all vinous ſpirits are lighter than water, and the leſs they contain of water, the more light they are. The hydrometer therefore will inform us how far they [383] are genuine, by ſhewing us their light⯑neſs; for in pure ſpirit of wine it ſinks leſs than in that which is mixed with a ſmall quantity of water.

YET after all, we are not entirely to depend, and with geometrical certainty rely upon either the hydrometer or the hydroſtatic balance, for there are ſome natural inconveniences that diſturb the exactneſs, with which they diſcover the ſpecific gravities of different bodies. Thus, if the weather be hotter at one time than another, all fluids will ſwell, and conſequently they will be lighter than when the weather is cold; the air itſelf is at one time heavier than at another, and will buoy up bodies weighed in it; they will therefore appear lighter, and will of conſequence ſeem heavier in water. In ſhort, there are many cauſes that would prevent us from making tables of the ſpecific gravities of bodies, if rigorous exactneſs were only expected, for the individuals of every kind of [384] ſubſtance differ from each other, gold from gold, and water from water. In ſuch tables therefore, all that is expected is to come as near the exact weight as we can, and from an inſpection into ſeveral, we may make an average near the truth. Thus, Muſchenbrook's table makes the ſpecific gravity of rain water, to be nearly eighteen times and an half leſs than that of a guinea; whereas our Engliſh tables make it to be but ſeven⯑teen times and an half nearly leſs than the ſame. But though there may be ſome minute variation in all our tables, yet they in general may ſerve to conduct us with ſufficient accuracy.

IN general it may be obſerved, that the pureſt gold is the heavieſt of all other ſubſtances whatſoever, being nearly nineteen times and an half heavier than water; next to gold, is a ſemi-metal of late diſcovered, called Platina; this, if I remember right, is ſixteen times one third heavier than water; mercury is [385] next in weight, and is a little more than fourteen times heavier than water; lead, eleven and about a quarter; fine ſilver, about eleven only; copper, is eight and three parts; ſteel, ſeven and three parts; and thus of the reſt; diamond is about three times and an half heavier than water; glaſs, about three and a quarter; rectified ſpirit of wine, is about one third lighter than water, and cork is more than four times as light.

NOW then, ſuppoſe a body to be a mixture of gold and ſilver, and it is deſired to know the quantities it contains of each; I firſt find, by the hydroſtatic balance, the ſpecific gravity of the compound. We know that its ſpecific gravity is leſs than that of gold, but more than that of ſilver; let us ſubtract then the known ſpecific gravity of ſilver, which we ſaid was eleven, from the ſpecific gravity of the compound, and let us ſubtract the compound itſelf from that of gold, which is nineteen; [386] the firſt remainder ſhews the bulk of the gold in the compound, the other that of the ſilver: and as we know the bulk of each, and the ſpecific gravities of each, we may eaſily know their real weights or gravity, by multiplying the bulks by the ſpecific gravities.

ALL expreſſed oils, ſuch as olive oil, rape oil, and the like, which are preſſed out of kernels or ſeeds by means of heat, theſe and all fatty ſuety ſubſtances, are about a tenth part lighter than water, and therefore ſwim upon its ſurface. From hence it is eaſy to conceive the reaſon, why animals that are fat ſwim better than thoſe that are lean, ſince the former contains a quantity of oil within their ſurface, which is ſpecifically lighter than water, and conſequently keeps them buoyant. Thus the country people aſſure us, that a fat hog ſwims better than any other animal; and they have reaſon for their aſſertion.

[387]OF all animals thrown into water, man is the moſt helpleſs. The brute crea⯑tion receive the art of ſwimming from nature, while man can acquire it only by practice; the one eſcapes without danger, the other ſinks to the bottom. Some have aſſerted, that this ariſes from the different ſenſibilities each have of danger: the brute, unapprehenſive of danger, and unterrified at its ſituation, ſtruggles through, while his very fears ſink the lord of the creation. But much better reaſons may be aſſigned for this impotency of man in water, when com⯑pared to other animals; and one is, that he has actually more ſpecific gravity, or contains more matter within the ſame ſurface, than any other animal what⯑ſoever. The trunk of the body in other animals is large, and their extremities proportionably ſmall; in man it is the reverſe, his extremities are very large, in proportion to his trunk: the ſpecific weight of the extremities is proportion⯑ably greater than that of the trunk in [388] all animals, and therefore man muſt have the greateſt weight in water, ſince his extremities are largeſt. Add to this, that in order to ſwim, other animals have only to walk forward, if I may ſo expreſs it, upon the water; the motion they give their limbs in ſwim⯑ming, is exactly the ſame with that they uſe upon land: but it is different with man, who makes uſe of thoſe limbs to help his motion upon water, which, upon land, he employs to very different purpoſes.

AS we have obſerved above, that liquors of different denſities ſupport bo⯑dies in proportion to their denſity; that the heavier the liquor, the heavier will be the weight it can ſupport; it is not to be wondered at, that in ſwimming, we ſhould find ourſelves much better buoyed up and ſupported in ſea-water than in freſh. For ſea-water is actually heavier, and this from the ſalts mixed with it which increaſe its weight about a fiftieth part.

[389]IN order to facilitate our power of remaining on the ſurface of water, or of breathing when at the bottom, different methods have been contrived. As to the firſt, the cork waiſtcoat anſwers the pur⯑poſe tolerably well; for the latter, the di⯑ving bell is a well known ſecurity. Doctor Halley, in a diving bell of his own con⯑trivance, remained fifty two feet deep at the bottom of the ſea, for the ſpace of an hour and an half.

THE diving bell is an inſtrument long known and in uſe. That made by Doctor Halley, was in the form of a great bell, and was coated with lead, ſo as to make it ſink in water: (fig. 41.) it was three feet wide at top, five feet wide at bottom, and eight feet high. Into this great bell the diver entered, and ſate upon a ſmall ſeat within-ſide, prepared for that purpoſe, and received light from a ſtrong glaſs at top. Thus prepared, by means of a rope, the bell, the man and all was let down to the [390] bottom, in order to ſearch for goods, or fix cords to wrecks of ſhips, and ſuch like purpoſes.

WHEN the bell is let down into the ſea, the water riſes into it to a certain height, but it cannot fill the whole of the bell, for the air within it (as we ſhall ſee hereafter) will ſtill keep ſome room at top, and prevent the water's riſing and filling it any farther. It is in this topmoſt part, which is empty or only filled with air, that the diver keeps his head, and breathes that air which thus reſiſts the aſcending water; here he can remain for ſome time, living upon the condenſed air, and at the ſame time performing what he deſcended for.

BUT to be more particular in the deſcription of Doctor Halley's bell. In the top was fixed, as mentioned above, a ſtrong clear glaſs to let in the light from above, and likewiſe a cock to [391] let out the hot air, that had been polluted by repeated inſpiration below. It was ſuſpended from the maſt of a ſhip, and ſo hoiſted over the ſhip's ſide as to be let down without danger. In this, two or more divers were let down to the bottom, and two barrels of air were let down to them, to ſupply them with freſh air, which alternately roſe and fell like two buckets. As the air from the barrels was let into the ſpace in the bell free from water, it entered cold, and ex⯑pelled the hot air which had been ſpoiled, out through the cock at the top. By this method air was communicated in ſuch plenty, that the Doctor informs us, that he was one of five who were together at the bottom in ten fathom of water, for above an hour and an half at a time, without any ſort of ill con⯑ſequence; and he might have continued there as long as he pleaſed, for any thing that appeared to the contrary. By the glaſs at the top of the bell, ſo much light was tranſmitted when the ſun [392] ſhone, and the ſea undiſturbed, that he could ſee perfectly well to read and write, or to find any thing that lay at the bottom; but in dark weather, and when the ſea was rough, he found it as dark as night at the bottom. But then this inconvenience might be remedied, by keeping a candle burning in the bell as long as he pleaſed; for he found by experience, that a candle polluted the air by burning, juſt as a man would by reſpiring, both requiring about the ſame quantity of freſh air for their ſupport, to the amount of nearly a gallon in a minute.

THIS machine was ſo far improved, that one of the divers might be detached to the diſtance of eighty or an hundred yards, by a cloſe cap being put upon his head, with a glaſs in the fore part for him to ſee through, and a pipe to ſupply him with air, communicating with the great bell; this pipe was flexible, coiled round his arm, and [393] ſerved him as a clue to find his way back to the bell again. The only in⯑convenience that Halley complained of was, that upon their firſt deſcending, his companions and he found a ſmall pain in their ears, as if the end of a quill were thruſt forcibly through into the aperture of the ear. One of the divers however, willing to remedy this inconvenience, ſtuffed his ears with chewed paper, which, as the bell de⯑ſcended, was ſo forcibly preſſed into the cavities of the organ, that the ſur⯑geon could not extract the ſtuffing with⯑out great difficulty.

Triedwald, a Swediſh engineer, has made ſome improvements on this ma⯑chine, ſince Halley's time. That contrived by him is leſs than Halley's, and con⯑ſequently more eaſily managed; it is illuminated with three convex glaſſes inſtead of one. It has been found, that the nearer the diver's head is to the ſurface of the water in the bell, the [394] better he breathes, for the air at that place is moſt comfortable and cool. In Triedwald's bell, the diver's head is therefore nearer the water, and when there is a neceſſity for his lifting up his head to the top of the bell, he has a flexible pipe in his mouth, with which he breathes only the air at the ſurface of the water at the bottom of the bell.

WE are told of a much more uſeful method than either of the former, put in practice by a gentleman of Devonſhire. He has contrived a large caſe of ſtrong leather, perfectly water proof, which may hold about half an hogſhead of air. This is ſo contrived, that when he ſhuts himſelf up in this caſe, he may walk at the bottom of the ſea, and go into any part of a wrecked veſſel, and deliver out the goods. This method, we are told, he has practiſed for many years, and has thus acquired a large fortune.

IN this manner we find, that no part of nature is wholly ſecluded from human [395] viſitation, ſince thus means have been contrived, to deſcend without danger to the bottom of the ocean, and to explore that abyſs which ſeems, at firſt view, to retire from curioſity. Without the con⯑trivance above mentioned, men, when at ſuch vaſt depths below the ſurface of the water, would feel the effects of its weight in a very ſenſible manner. Divers who go to the bottom without this ma⯑chinery, often return with ſigns of the violent preſſure of the water upon the ſurface of their bodies; their eyes are ſeen ſwolen and blood-ſhot, they often bleed at the mouth and noſe, and feel a total laſſitude over their whole bodies. Theſe ſymptoms are moſt violent, in ſuch as firſt undertake this kind of em⯑ployment; but they leſſen by degrees, ſo that an accuſtomed diver feels no great inconvenience, by remaining ſome mi⯑nutes at the bottom: thoſe of this pro⯑feſſion, are only remarkable for the redneſs of the white of their eyes.

[396]BEFORE I quit this ſubject, it may not be improper to mention a benefit that may accrue, from plunging or bathing in ſea water, not yet that I know taken notice of by others. Many arts have been tried to make ſea water freſh and potable; the benefit of which would be, that in long voyages, when a ſhip's company wanted freſh water, they might make uſe of ſea water as a very eaſy ſubſtitute, by freſhening it according to art. The beſt method of freſhening ſalt water is, by mixing it with calcined bones, and then diſtilling it; for it is found that the calcined bones will lay hold on the ſaline parts of the water, unite with them, and keep them at the bottom of the ſtill; while on the other hand, the freſh fluid will riſe in vapours to the top, and thus ſeparate from the impure mixture below. There is but one objection that I know of, to theſe calcined bones and this ſtill, and that is, that they take up almoſt as much room in the ſhip, as ſo much freſh water as [397] they could make would do. If the Captain of a veſſel therefore, is appre⯑henſive that they may want water in his voyage, inſtead of ſo many hundred weight of calcined bones, he may take ſo many ſupernumerary hogſheads of freſh water, and that will do as well. Com⯑mon water will be almoſt as conveniently carried, much more wholeſome, and in⯑finitely cheaper; for this reaſon we never ſee captains of ſhips carry out calcined bones to ſea; for if danger is foreſeen, they ſupply themſelves with ſuperfluous ſtores of water. In unexpected calami⯑ties, perhaps the following method would for ſome time preſerve life without freſh water.

IF we are weighed upon going into a warm bath, we ſhall find upon our returning out of it, that we have gained conſiderably from the fluid in which we have been plunged, being often increaſed in weight ſome pounds; the reaſon is, that there are numerous [398] veſſels opening at the pores of the ſkin, that ſuck up the water like ſo many ca⯑pillary tubes, and theſe veſſels run from every part of the ſurface of the body into the inteſtines, and diſcharge them⯑ſelves there. Theſe very fine ſlender veſſels are a modern diſcovery, and ſtill conteſted by different anatomiſts, each claiming the firſt obſervation of them to himſelf. We find alſo by experience, that though we be never ſo thirſty upon entering a warm bath, the bath inſtantly relieves that complaint, and we feel drought no more. What then, if in caſes of extremity at ſea, a warm bath of ſea water were made, in which each of the ſhip's company might bathe, and thus, by the pores of the ſkin, drink in a ſufficient quantity of watery fluid to ſuſtain nature, and to dilute their other aliments? We know by experience that they would thus imbibe freſh water alone, for the pores of the ſkin are too minute to let the ſaline parts of water enter. The body, when plunged in a [399] bath of ſalt water, acts like a filter upon the fluid, and its pores ſuffer nothing but the thinneſt and pureſt part to enter them; while the ſalt ſtands like hoar froſt upon the ſurface of the ſkin, and may be wiped away with a towel. I do not care to drive an hint of this na⯑ture farther than it ſhould go; nor is it to be wiſhed that the aſſiſtance this may afford, ſhould induce men to be leſs aſſiduous in providing the more ade⯑quate means of ſecurity.

CHAP. XXIV. Hydraulics.

HYDROSTATICKS, as we have ſeen, determines the weight or preſſure of fluids upon ſolids, or upon each other, in veſſels where the water is not ſuffered to eſcape but remain at reſt; hydraulics is a different part of this ſcience, which teaches us to eſtimate the ſwiftneſs or the force of fluids in motion.

IT has been always thought an en⯑quiry of great curioſity, and ſtill greater advantage, to know the cauſes by which water ſpouts from veſſels to different heights and diſtances. We have obſerved, for inſtance, an open veſſel of liquor upon its ſtand, pierced at the bottom; the liquor, when the opening is firſt made, ſpouts out with great force, but as it continues to run, becomes leſs vio⯑lent, and the liquor flows more feebly; [401] a knowledge of hydraulics will inſtruct us in the cauſe of this diminution of its ſtrength; it will ſhew preciſely how far the liquor will ſpout from any veſſel, and how faſt, or in what quantities it will flow. Upon the principle of this ſcience, many machines worked by water are entirely conſtructed; ſeveral different engines uſed in the mechanic arts; various kinds of mills, pumps and foun⯑tains are the reſult of this theory, judi⯑ciouſly applied.

AND what is thus demonſtrated of the bottom of the veſſel, is equally true at every other depth whatſoever. Let us then reduce this into a theorem. The velocity with which water ſpouts out at an hole in the bottom or ſide of any veſſel whatſoever, is in proportion to the ſquare root of the height of the water in the veſſel: that is, in other words, If the water in one veſſel be nine times higher than in another, it will ſpout with three times as much velocity; if the veſſel be [402] four times as high as the water, it will ſpout with twice the velocity. We need ſcarce obſerve that the quantity of water ſpouted, is always equal to the velocity with which it ſpouts; ſo that a veſſel nine times as high as another, will ſpout through a ſimilar hole three times as much water, in the ſame ſpace of time, or a veſſel four times higher, will ſpout twice as much water. As an experi⯑mental proof of this, we may take two veſſels, one five inches high, the other four times that height, and make a cir⯑cular orifice in the bottom of each, of the ſixth part of an inch diameter, and being both filled with water let them be ſet a running, and let the water be ſup⯑plied above as faſt as it runs out below; the taller veſſel will diſcharge about two pounds of water avoirdupoiſe, in the ſpace of a quarter of a minute; the veſſel four times as ſhort, will diſcharge juſt half that quantity.

AS the preſſure the bottom ſuſtains, is ſuſtained alſo by the ſides of a [403] veſſel in proportion to their height, water will flow from the ſide of a veſſel with the ſame force that it does down⯑ward; for it is found to flow out of both with the ſame velocity, provided they are at equal depths below the ſurface; and therefore the velocity of water flow⯑ing out at an orifice in the ſide of a veſſel, is in the ſame proportion as before, that is, as the ſquare root of the height of the water above the orifice, which a repetition of the former ex⯑periment may prove, by uſing veſſels with orifices at the ſides.

NOW as we are thus informed of the velocity with which water flows through an hole in the ſide of a veſſel, it may be requiſite to know to what diſtance it will thus ſpout ſideways. To know this, let us ſuppoſe the water ſpouting from the ſide of a veſſel, to move uniformly forward, with the ve⯑locity it has received, which is as the ſquare root of the height of the veſſel; [404] now this velocity would drive it uni⯑formly forward, through a ſpace equal to twice the height of the veſſel; for we ſhewed formerly, that a body having acquired a certain velocity by falling, would, if it moved uniformly forward with that velocity, go through double the ſpace from whence it fell; and this is the caſe with the ſpout of water, which if nothing prevented would always ſpout forward to double the diſtance of the height it ſtands in the veſſel.

BUT now we know that gravity acts upon it, and draws it downward, ſo that the ſpout is impreſſed by two forces that influence it, one forward, the other downward; theſe motions by no means deſtroy each other, the ſpout obeys both, and like all projected bodies it moves in the curve of a parabola. Let us then ſuppoſe the water is let flow through an hole in the veſſel B, at its top b; as it has no height of water there above it, it will not ſpout at all, but drivel down the [405] ſide of the veſſel: let us, on the contrary, ſuppoſe it to be let flow through an hole c, juſt near the bottom on the ground; now ſtrictly ſpeaking, it will not ſpout there neither, for as the ſpout is always deſcending by its gravity, it will meet the ground the moment it leaves the orifice, and thus have no ſpout at all. Thus at b, the water had no ſpout for want of height to drive it; at c, the water hath no ſpout for want of room to deſcend; it will therefore have the greateſt ſpout at the greateſt diſtance from theſe two deſtroying extremes, and at a, it will go forward, as we ſaid before, to twice as far as the water is high above it; and at all other heights or depths of the veſſel the water will ſpout in a ſimilar proportion, and from all holes equally diſtant above and below the middle, the jets of water will be made to ſimilar horizontal diſtances. I would only obſerve here, that the uſual method by which ſome determine the diſtance to which water will ſpout by a ſemi⯑circle, &c. is erroneous.

[406]THUS we may univerſally conclude, that water ſpouts to double the diſtance of its height, provided it is raiſed above the level of the ground ſo as to take its full range. But though this is true in theory, yet we find in practice that there are great deviations from all the rules preceding; for we muſt now obſerve, that the water does not ſpout in a com⯑pact parallel ſtream from an hole in the veſſel's ſide; for Newton has juſtly obſerv⯑ed, that the diameter of the ſpout is largeſt immediately iſſuing from the hole, that then it contracts its diameter as it pro⯑ceeds a little way, and laſtly, it ſcatters about in all directions; ſo that we may compare the ſpout to a cone, the baſe of which is at the mouth of the hole, and the point at ſome diſtance from it. It is not the diameter of the hole therefore that ſhould be meaſured, to know the quantity of water that pours out in a certain time, but the diameter of this point or vein, at a little diſtance from the hole; and the admeaſurement of this [407] Bernouilli has actually attempted, but with what ſucceſs I will not pretend to determine; it may only be obſerved, that the cauſe of this convergence in the ſpout is ſtill in diſpute among the learned: the argument, from its intri⯑cacy, it is probable, will not be eaſily adjuſted; however, let us not enlarge upon ſo minute an enquiry, when there are ſo many greater to engage our attention.

TO remedy this ſcattering of the fluid as it iſſues from the hole, we all know of the contrivance of the foſſet or ajutage, which is only a pipe ſtuck into the hole, that ſerves to give the fluid a proper direction; this, while it anſwers the end propoſed, at the ſame time diminiſhes both the velocity of the ſpouting fluid, and the diſtance to which it would go. The length of the ajutage may be conſidered as a column of water of an equal height, reſiſting the force of the fluid that ſpouts through it; ſo [408] that if the ajutage be as long as the ſpouting water is high, the two oppoſite forces will thus deſtroy each other, and there will be no ſpout to any diſtance whatever.

THUS far as to water ſpouting hori⯑zontally, or as we uſually ſay ſideways from a veſſel; now as to its ſpouting directly upward, water will ſpout up⯑ward with ſuch a velocity as will carry it to the ſame height with the water in the veſſel from whence it ſpouts, becauſe the velocity it has at the bottom, is equal to the velocity it would acquire in falling down from the top of the water; and this velocity has force enough to carry it an equal ſpace upward, as we formerly explained. The water there⯑fore will ſpout in all fountains to nearly an equal height with the water in the veſſels from whence it flows; I ſay nearly, becauſe, as we know, the air will give it ſome reſiſtance, and muſt leſſen the force of all jets whatſoever, and [409] make them fall ſhort of the height of the water in the reſervoirs. But there is another cauſe that diminiſhes the height of the water's play; for when the water at the top of the ſpout has loſt all its motion, it reſts for ſome time on the part below, and by its weight obſtructs the motion of a new column iſſuing from below, and thus prevents it from riſing. The reſiſtance ariſing from this cauſe is ſo great, that the jet is frequently deſtroyed by it; the riſing water being by fits and ſtarts preſſed down to the very orifice from which it ſpouts. But this inconvenience is remedied if we give the jet a little inclination, for then the uppermoſt parts, when they have loſt all their motion upward, do not fall back as before, but are made to fall off from the reſt, and thus do not incumber the riſing fluid. From hence therefore we may underſtand the reaſon, why ſuch jets as are a little inclined, riſe higher than thoſe, whoſe aſcents are perpen⯑dicular.

[410]IT is the difference in the figure of the ajutage, that gives a diverſity of play to the fountain, and nothing can be more pleaſing to the eye than the different manner in which water is made to ſpirt in theſe machines. But they give additional pleaſure in ſultry climates, ſuch as Italy, where they contribute to cool the air as well as to enliven the proſpect: with us they are chiefly made for the purpoſes of embelliſhment alone, for in our northern climate, the air is ſeldom diſagreeable from too much warmth, and if there were fountains of fire, they would often make the moſt grateful ornament. I only mean this as an hint, concerning the unneceſſary expence which many are at to procure fountains, in a country where the cli⯑mate calls for different modes of embel⯑liſhment. Our groves and our fields are greener than in any other region in the world; to improve the beauty of theſe, our artiſts ſhould bend their chief efforts, and in this they will find nature con⯑ſpiring with their induſtry.

[411]WE have hitherto ſpoke only of the flowing of water from veſſels and reſer⯑voirs that are open; we muſt now ob⯑ſerve, that from veſſels cloſely ſhut it will not ſpout at all. We all very well know that the liquor will not run from a cloſe caſk, unleſs the air is let in from above; for this purpoſe, when a hogſ⯑head of liquor is broached, there is always a vent hole made at top, which is occaſionally opened when we want to draw liquor through the foſſet or ajutage below. The cauſe why a fluid will not run from a cloſe caſk without the admiſſion of air, ſhall be explained more largely when the properties of air come to be examined. Let it ſuffice to obſerve here, that the air preſſes with great force upon that part of the ſurface of every fluid to which it has admiſſion. If an hole is opened in the ſide of a caſk that is quite full of liquor, the air preſſes upon that hole with great violence, and prevents the liquor from coming out; if now another hole be opened at the top of [412] the caſk, the air will preſs into this alſo with equal force, and preſs the liquor out: theſe two forces balance each other, ſo that the weight of the fluid, if I may ſo ſay, turns the ſcale, and it flows out. In general however, as our caſks are not filled quite full, there is a little air left at the top of the veſſel; immediately therefore, when the ſide of the caſk is pierced, this air preſſes down, and there is a ſpirt of the liquor, but as the liquor continues to flow it leaves more room at the top of the caſk; and the air not being capable of filling this room as before, preſſes with leſs force down, than the external air preſſes at the mouth of the orifice up; ſo that the fluid will no longer continue to flow, until more air is let in by a vent-hole at top, to balance that which preſſes againſt the egreſs of the liquor at the hole below.

FROM hence we ſee the neceſſity of having a vent hole, or ſome contrivance of this kind, in all caſks that have liquors [413] upon draught; and from hence alſo we may deduce a reaſon why liquors, that have been long upon draught, grow vapid or four; for the ſpirits being light⯑eſt always float and mix with the air at the top of the caſk, and every time the vent-hole is opened, we may per⯑ceive them fly out with ſome violence. Thus by frequently opening the vent-hole almoſt all the ſpirit evaporates away at laſt, and leaves the liquor either vapid or ſour. If this be true, might not a contrivance be made that would give a ſufficient preſſure to the upper ſurface of the fluid, without permitting the ſpirit to evaporate? What if a ſmall tube were contrived, with a valve, which being inſerted at the top of the caſk, we might force in as much air as we thought proper into the caſk above, while at the ſame time none of the air or ſpirit in the caſk, would be permitted to come back through it or eſcape; this would at once give a ſufficient force to make the liquor flow, and would alſo confine [414] the ſpirit from evaporation. Whether this method has been already practiſed I know not; it is here only offered as a conjecture, Valeat quantum valere poteſt.

THE human frame as well as that of all other animals, is uſually repre⯑ſented as a moſt compound hydraulic machine, with an infinite number of tubes, conveying their reſpective fluids from one part of the body to the other. In this ſyſtem of veſſels philoſophers have ſuppoſed the various kinds indued with various powers; they have fancied ſome acting as pumps, others as capillary tubes, nor has there been wanting ſuch as have made mention of the glandular ſcrew. The moſt diſtant reſemblance between the veſſels of the human body and theſe artificial machines, have given men, whoſe imaginations were ſtrong, frequent opportunities of completing the picture. This, in common converſation, is called ingenious error; yet ſurely falſe philoſophy can have no ingenuity whatſoever: for what is it that can make its rigid inſtitutions pleaſing, but that [417] we ſuppoſe them true. Philoſophy, that attempts to rectify the mind, is its phyſic, not its food; and it is but a ſmall honour to that phyſician of whom it is ſaid, that his pills are ſweet but inefficacious.

IN this manner attempts have been made to determine the velocity with which the blood circulates through the body. Some of theſe ſpeculators have not even taken into conſideration the flexibility of the canal, through which the animal fluids move, but have given us hydraulic theories, drawn from the ſpouting of fluids through glaſs pipes. Nothing can be more erroneous than this, but if it were only a ſpeculative error it would be ſcarce worth combating; no⯑thing can be more dangerous too; and in fact, very dreadful practice has been recommended, in conſequence of theſe ill guided calculations. But though we ſhould ſuppoſe that even the whole theory of fluids ſpouting through flexi⯑ble [418] and elaſtic tubes were known, (and it is not till of late that an ingenious modern has attempted the inveſtigation) yet we ſhould be ſtill as far from under⯑ſtanding the velocity of the circulating fluids of the human body as before. To treat this with any preciſion, we muſt firſt know exactly to what degree a vein or an artery is capable of dilating, we muſt know the figure of the veſſels, their elaſticity, their different openings into each other, the force and the diſpoſition of their valves, the degree of heat and tenacity of each fluid, and the force which drives them forward. If all theſe were known, where would the mathe⯑matician be found, that could unite ſuch various elements into one calculation? Even to determine the force of fluids in flexible tubes, alone, almoſt exceeds geometrical ſtrength; what then muſt be the caſe in ſuch a complication of component parts? Modern phyſic has with great juſtice exploded thoſe idle and dangerous algebraic dreams, con⯑ceived [419] in an age when geometry walked from her circle to conduct mankind to error, and was ſeen daily applying her compaſs to the incommenſurable parts of nature.