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OBSERVATIONS ON SOME OF THE PROBABLE EFFECTS OF MR. GILBERT's BILL; TO WHICH ARE ADDED Remarks deduced from Dr. PRICE'S Account of the NATIONAL DEBT.

By the Reverend Mr. BRAND, M. A.

LONDON: Printed for J. ROBSON, and Co. NEW BOND STREET.

MDCCLXXVI.

OBSERVATIONS, &c.

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THE defects of our ſyſtem of poor laws have lately engaged the attention of the public; and a variety of eminent writers upon the ſubject have diſcuſſed ſeveral parts of it with great ability: my object is, to add ſome ſupplemental remarks to what they have laid down, which I think may tend to ſtrengthen and confirm the opinions of thoſe who have recommended houſes of induſtry.

The moſt eligible method of drawing up a general plan for the ſupport of the poor would poſſibly be, to mark off in ſome of the beſt treatiſes which have been publiſhed upon the ſubject, ſuch principles and practical obſervation as appear moſt firmly founded upon political reaſon, or drawn from facts properly ſtated; theſe detached materials may be reduced to their general heads, and the vacancies in the outline eaſily marked in: an architect from a few veſtiges and ruined members of columns, is able with the greateſt degree of certainty to make a drawing of the building in all its original magnificence: the happineſs of a great people, is certainly [2] worthy the ſame enlightened and perſevering attention, which has frequently been miſapplied to reſtore ſome gothic deſign of claſſical antiquity.

But it is by no means my intention to purſue the ſubject ſo extenſively: the only points I mean to go into are, the ſtate of the preſent burthen and charge of the poors rate, the different expence of maintaining the poor in the preſent mode, and in incorporated diſtricts; and the probable amount of the advantage of adopting Mr. Gilbert's plan, with ſuch alterations as may be found neceſſary: I ſhall endeavour likewiſe to add ſomething to what has been ſaid upon the advantages of a better and more regular education for the poor, and how far ſuch incorporations are favourable or adverſe to the ſpirit of the conſtitution.

I ſhall firſt conſider the charge of the rate, laying down firſt this diſtinction, that by charge we are to underſtand the ſum paid, be the value of money what it will, by burthen, the proportion of that ſum to our ability to pay it. Mr. Potter, in a very ingenious pamphlet publiſhed laſt year upon this ſubject, ſtates the total amount of the poor's rate at three millions, the [3] advance in nine years at 800,000: during that period the price of proviſions has increaſed in a geometrical progreſſion, the increment of the poor rates has at laſt followed the ſame law, (*two poſitions which will be demonſtrated in the Appendix) the rate of the 8th year will be 2,898,370l. and the augmentation of perpetual expence the ninth 101,630; and the value of this perpetuity, at 3½ per cent. 2,903,714; the increaſed charge therefore to the public, is equal to that ſum added to the funded debt at 3½ per cent. This augmentation gives the annual increaſe of the rate 3,506 per cent. and by the table in the Appendix, this rate of increaſe appears very moderate.

Taking the ſurplus of the public revenue, which may in time of peace be applied to the diſcharge of the debt at 900,000l. a ſum it was ſuppoſed to produce before the annual payment of 400,000 from the Eaſt India company was withdrawn; the value of the perpetuity 2,903,714 exceeds that ſum in proportion as 3⅕ to 1.

Hence the poor rate appears to increaſe the national expence three times as faſt as that [4] ſurplus can diminiſh it, uniformly applied to the diſcharge of that debt in the time of peace; ſuppoſing it to increaſe every year even with the ſame celerity as the poor rate.

It may be worth while, in order to point out the true extent of a charge thus increaſing, to enquire what ſum of money the public ought to pay down, to be delivered from it for ever.

Divide 100 by the difference of the rate of increaſe, and the rate of intereſt (uniformly taken at 3½) the quotient will be the number of years purchaſe of the original ſum, which will equal the required payment.*

Caſe the 1ſt. If we ſuppoſe the rate to continue perpetually the ſame, or without increaſe, it will be worth 28½ years purchaſe: let the preſent amount be 2,500,000 only, the purchaſe money will be 71,250,000.

Caſe the 2d. Let the annual increment be 1½, or about ½, the increaſe of the price of proviſions; the number of years purchaſe will then amount to 50, and the ſum 125 millions: very nearly equal the funded debt.

Caſe the 3d. The leaſt rate of advance given in the tables, is 2,39 per cent. and to be relieved [5] from a charge perpetually increaſing in that ratio, the public ought to give 90,09 years purchaſe; or a ſum exceeding 225 millions.

Caſe the 4th. But the increaſe of charge exceeds the rate of intereſt: if it were barely equal, the former ſubſtracted from the latter leaves no remainder, and the number of years purchaſe becomes 100/0, or infinite.

The truth of this laſt concluſion may be eaſily proved in the following manner; the rate at the end of the firſt year becomes by the ſuppoſition 103,5, the preſent value of which is 100; at the end of the ſecond year it is increaſed to 107,12, the preſent value of which is 100: rate of the third year 110,87, the fourth 114,75, the preſent value of each of which is likewiſe 100; ſo that to be diſcharged from the next year's rate, we muſt pay down a ſum equal to the preſent or 100l.; for the next two 200; the three firſt years 300, or ſo many years purchaſe of the preſent value of the rate as we mean to be diſcharged from: therefore to be diſcharged from all future expence, we muſt pay down a ſum equal to the preſent rate, multiplied by the number of years to the end of time, or infinity.

[6]How far the poor rate has been an increaſing burthen, is the next particular which offers itſelf to our conſideration.

As ſpecie repreſents ſome real value in goods and commodities, the burthen of a rate muſt be in proportion to that real value which the ſpecie it raiſes repreſents; if at one time 100l. repreſent, or will purchaſe twice the real value in goods and neceſſaries which it does at another, a man who pays 10l. to a rate at the former period, has double the real value taken from him which he would have in the latter; or the burthen is double upon him: in general, the burthen is always to be eſtimated by the value of money and the ſum conjointly, or their product: when the value of money augments, the burthen increaſes with it; when it diminiſhes, it decreaſes in the ſame proportion.

Having the rate of increaſe of the charge given, to determne that of the burthen, we muſt endeavour to diſcover the annual decrement of the value of money.

The real value of a ſum of money at different periods, is proportioned to the number of people it will maintain with the neceſſaries of life.

[7]The price of wheat, and the intereſt of money, have been both conſidered as the ſtandard of this value: the former, being perhaps the greateſt article of neceſſary conſumption, and much affecting the price of the reſt, will have a great effect upon it; but not one can riſe or fall without influencing it in ſome meaſure.

The rate of intereſt is a ſtandard ſtill more inadequate: this rate has continued the ſame for ſome years laſt paſt, if particular circumſtances have not rather contributed to raiſe it: 100l. at the end of the year produces 3l. 10s. ten years after it produces the ſame ſum; but will that ſum at thoſe different periods repreſent or equal the ſame real value of the neceſſaries of life? To prove 100l. of the ſame value at the one period as at the other, we muſt make this aſſumption, that 3l. 10s. at the end, is equal in value, or repreſents the ſame real value with 3l. 10s. at the beginning; the very principle wanted to be proved.

To determine the value of money, we muſt find the quantity of commodities in kind which a certain number of men conſume in a year, and multiply each ſeparate quantity by its price in the given year, adding theſe together for a total: repeat the [8] ſame operation for any other year, and the two ſums will be reciprocally as the value of money at thoſe periods: or the greater ſum will repreſent the value of money at the cheaper period, the leſs at the dearer.

But if we want to enquire into the law of increaſe or decreaſe, more of theſe periods muſt be taken, and the hypotheſis tried by the totals they exhibit.

The account of the ſtate of the houſe of induſtry at Nacton, drawn up by order of the Houſe of Commons, contains all the different prices of wheat, beef, malt, and cheeſe for 17 years; and the variations for every year carefully marked: I reduced the different prices of each article in every year to a mean, and from thence formed the four tables given in the Appendix.

This account begins with the year from Eaſter 1757 to 58; the average of the firſt four years will give the mean price of wheat Michaelmas 59; the following four Michaelmas 63, the ſucceeding five at Eaſter 68, and the laſt four Michaelmas 72: this operation is to be repeated with the other three tables, and we may thus obtain a correct ſtate of the advance upon each of theſe commodities for thirteen years.

[9]To aſcertain the quantities conſumed in kind of each of theſe particulars, I copied an account of the conſumption of eight weeks, from the books of the houſe of induſtry at Heckingham; this gives us the total conſumption of 2016 perſons for one week, from whence we eaſily deduce that of ten perſons for a year. Multiplying the quantity of every article of this reſult by its price in each of the four years above mentioned, the ſum of the prices of all the articles in each year will be as the value of money that year, if thoſe articles had compriſed all the neceſſaries of life.

To inſert the reſt, I computed from the beſt information I could procure, and principally derived from the ſame houſe, the additional expence at this preſent, for cloathing, fireing, &c. and found it amount to 30s. a man. I then ſuppoſed the advance upon theſe articles, two thirds that of the others, that I might be ſure the concluſion might be below the truth.

The reſult of theſe operations gives us the following rate of increaſe for the price of proviſions:

 Michael. 59Michael. 63Eaſt. 68Michael. 72
Price of Proviſions703..4810..8896..4½1018
Geometrical Progreſſion703788895..51018

[10]The lower ſeries are four terms in an interrupted geometrical progreſſion, where the diſſtance of the terms is equal the intervals of the time.

Theſe coincide ſo nearly with the numbers above them, as to point out that ſuch a law nearly took place. Whatever the cauſe of this decrement of the value of money may have been, it ſeems nearly uniform for the given time.

The annual decrement of the value of money during the whole period was 2,89 per cent. but in the firſt four years, it amounted to 3,63 per cent. The rate of advance of the price of proviſion was conſiderably more from 59 to 63, than from 63 to the preſent time; which is contrary to the general received opinion; it appears in thoſe four years to have been accelerated ,75 annually per cent. nearly ¼ more than its mean increaſe: the four years from whence the ſecond term is obtained, are the years 61, and thoſe immediately following; and this irregularity ſeems to form no objection to the law, but to be the effect of the great ſums of money the ſucceſſes of the laſt war brought into the nation: a cauſe which was barely beginning to operate [11] in the firſt period of four years, the average of which is therefore nearer its true level.

I have choſen to explain the principles upon which theſe tables are grounded at ſome length, as the conſequences deduced from them, upon a very important queſtion treated of in the Appendix, differ from what is delivered by ſome very reſpectable writers.

From what has been here laid down, we are able to determine the ratio of increaſe of the burthen of the poor rate: an eſtate which laſt year paid to the rate 100, will be by the average advance charged 103,506 for the expence of the preſent; but by the riſe of proviſions 102,89 at the end of a year, is equal in value to 100 at the beginning; therefore the burthen of thoſe two periods will be in proportion of 102,89 to 103,506, or as 100 to 100,6, and the advance of the charge is to the advance of the burthen as 6 to 1 nearly.

The further obſervations I had to make upon this head are referred to the Appendix;* I have there demonſtrated the operations of this payment upon the price of proviſions.

[12]The laſt thing remaining is to determine the probable ſaving to the public, by adopting a general bill for houſes of induſtry.

But we ſhall be able to give a much more certain anſwer to the queſtion, by enquiring what would probably have been the ſum ſaved, if ſuch a bill had taken place at the ſame time Colnies and Carlton hundreds were incorporated; and having diſcovered that, we ſhall eaſily determine the advantage ſought.

The year ending at Eaſter 1753, was the middle term of the ſeven years, from which their average charge was aſſeſt: I collected the rates of ten pariſhes for that year and the year 74, ſix of them ſituated near the incorporated hundred, and added to them four pariſhes in Norfolk: the charge in the firſt of theſe years amounted to 806..6, &c. and in the laſt to 1345..5, &c. the annual rate of advance appeared to be 2,39 per cent. Upon theſe grounds we find the preſent value of all the payments of a diſtrict equal to the incorporated hundreds for the laſt 17 years; the difference between this ſum and the preſent value of all the payments of the corporation, adding the balance between [13] their debt and ſtock, will give the amount of the ſum ſaved in ſeventeen years paſt.

The annual payment of the hundreds is 1487..13, &c. which increaſing in the proportion ſuppoſed, would have become at the latter period 2506..7: from this we obtain the probable preſent value of the ſums which would have been expended for maintaining the poor in the hundred,*

Upon the old ſyſtem48296
Upon the new with the balance added37053
Balance in favour of the latter11243

Proportion of expence nearly as 4 to 3.

To determine the value of the future advantage: ſuppoſe even the annual increaſe of the expence of maintaining the poor in the old mode diminiſhed ⅓, this can only be true in caſe the price of proviſions advance with no more than ⅔ the preſent celerity; conſequently the expence of maintaining the paupers in the houſe will follow the ſame law, the preſent [14] value of all the future payments, had there been no act of incorporation, would be—£. 105565

Of the incorporation87440
Future ſaving18125
Paſt do.11243
Sum ſaved preſent value29368

This amounts to 19,8 years purchaſe of the rate of theſe hundreds in 1752, ſuppoſing an average of ſeven years equal the rate of the middle year.

Or 11,7 of the probable amount of the rate of 1774. And the preſent values of the expence of the two different modes of ſupporting the poor for thoſe hundreds £. 153861 and 124493.

The proportion of theſe ſums is nearly as 35 to 29, or as 5 to 41/7.

Before we proceed any further, let us apply this concluſion to Mr. Gilbert's bill, and ſuppoſe that a third of the kingdom from local circumſtances is incapable of being incorporated, but that the remaining ⅔ had been divided into incorporated diſtricts 17 years ſince; and [15] aſcertain the preſent value of the ſum which would in all probability have been ſaved by it.

The amount of the rates of ⅔ of the kingdom is two millions.

Preſent value of the ſum ſaved in 17 years8,972,865
Probable future ſaving14,465,280
Total advantage23,438,145

The number of years purchaſe of a rate which theſe ſums are equal to, have been joined to the reſults given above; that if there ſhould have been any error in fixing the amount of the poors rate of the whole kingdom at three millions, the account of the total advantage may be readily corrected.

The rate of intereſt in theſe computations has been taken 4 per cent. the rate of advance of the charge has been taken 2,39; while the price of proviſions by the table has increaſed 2,89 per cent. this muſt be far beneath the average increaſe; as the price of labour though ſomewhat augmented, has not increaſed faſter, or even equally with the price of neceſſaries; and [16] the number of paupers relieved has been generally increaſing: all theſe circumſtances together have co-operated to leſſen the account given of the value of the charge of maintaining the poor under the preſent laws.

On the other hand the ſum ſaved at Nacton has been the leaſt of any houſe I have examined; the weekly expence of a pauper excluſive of repairs, furniture, ſurgeons and officers, has been at Nacton 2s. 7d. at Melton 2s. 1½d. and at Heckingham 1s. 10½d. either of the two latter would have given the advantages much more.

A method which would have brought us far nearer the truth, would have been to have taken the mean advance of the rates exhibited in the table as the advance of the poors rate, and compared the total expence for ſeventeen years upon ſuch a ſuppoſition, with the mean expence of a houſe of induſtry; the weekly expence at Melton approaches neareſt to ſuch a medium.

* But let us imagine the expence of the houſe [17] at Nacton would have been thus diminiſhed in proportion of 2s. 3d. to 2s. 7d. or 27 to 31: the preſent value of expence of the houſe for the firſt ſeventeen years would have been reduced to 32272, and that of the future expences to 76157.

The probable expence of the firſt term, if the poor had continued under the management of the overſeers, would have been 56,066; and that of the ſecond 195,390; the compariſon therefore ſtands as follows:

 Incorporation.Poor under Overſeers.Total ſaved.
Expence to 17753227256,066 
Future do.75792195,390 
 108,064251,456143,392

[18]The ſum which ſhould be given by any diſtrict to be free for ever from the charge of the poor rate appears here to be upwards of ſixty years purchaſe of the next year's expence; the intereſt being taken 4 per cent. the general rate in the country: had I taken 3½, the firſt ſum would have been diminiſhed, but the ſecond increaſed in a far greater proportion.

But ſuppoſing the true future charges of both ſyſtems ought to be taken at a medium from the ſums ſtated above, and the value of the perpetuity of the annual charges of two ſuch equal diſtricts, the firſt with a houſe of induſtry eſtabliſhed ſeventeen years ſince; the ſecond with the poor continuing under the overſeers, admitting both to remain fixed at their preſent payments for ever.

Continuing the intereſt at 4 per cent. the perpetuity of the future charge upon the houſe would be 37433 l.; of the preſent expence of maintaining the poor under pariſh officers 79378 l. and the future expence will be found by

 New Syſtem.Old Do.
Hyp. 1ſt.75792195,390
2d.3743379,378
Sum113225274768
Mean56612137384

The advantages by this corrected Hypotheſis ſtand ultimately as follows,

 Incorporation.Old Syſtem.
Exence to 753227256066
Future do.56612137384
 88884193,450

The difference then appears to be 104,566.

The probable amount of the rates of Colnies increaſing every year 3,506 per cent. would be at the end of ſeventeen years equal the average 1487 l. multipied by 1,0350622; twenty-two years being paſt ſince the year when the amount equaled the average; this difference therefore is 32,933 years purchaſe of the preſent rate: if therefore a bill had been paſſed at that period to have incorporated ⅔ of the kingdom, as ſuppoſed [20] above, the preſent value of the paſt and future ſaving would at this time have been 65,866,000; or (taking intereſt at 3½ per cent) at its firſt eſtabliſhment ſeventeen years ſince, 36,701,000 l. which was the value then, of the difference of expence to the nation, between the two modes of providing for the poor.

But the annual increaſe of the rates ſince has a little exceeded the diſcount on the former ſum, therefore the preſent value of the difference is at leaſt ſixty-five million.

The future expence 137384 is nearly equal 54 × 2506 and therefore about fifty-four years purchaſe of the preſent rates.

The rate of annual advance in this ſtate per cent. 2,18 about 9/10 of the leaſt increaſe near the preſent period, I have been able to diſcover.

And the charge of the two different modes is to each other, as 88884 to 193450; or as 1 to 2 2/11 very nearly.

If we ſuſpect a concluſion to be exaggerated which brings out the value of a rate fifty-four years purchaſe, the reſult of the following ſuppoſition may tend to deſtroy the objections we entertain againſt it: Admit the true value of a rent charge to be ſo high as 3½ per cent. and [21] that for twenty-five years laſt paſt, the rates of a pariſh have increaſed in the ſame proportion we have ſeen them for a conſiderable period laſt paſt, and then ſtop forever: how many years purchaſe of the firſt year's rate is the value of ſuch a perpetual payment?

Here the rate of increaſe ſomewhat exceeds the rate of intereſt; but admitting it to be equal, and the rates of the pariſh 100 l. a year: by reaſoning as before on the ſame caſe the preſent value of the firſt twenty-five years payments at the beginning of the term will be 2500 l. or twenty-five years purchaſe; the remaining perpetuity at the end of the term, will be worth the rate of the twenty-ſixth year, multiplied by 28½ the number of years purchaſe it is worth, if it continues without augmentation for ever: but the preſent value of that rate at the beginning of the twenty-five years is equal 100 l. and the value of the perpetuity 2850 l. or 28½ years purchaſe of the original rate: ſuch a rate therefore appears to be worth 25 × 28½ = 53½ years purchaſe; the reduced hypotheſis gives it fifty-four years.

A pariſh which twenty-five years ago had given to redeem its poor rates, the then preſent [22] vale of all the ſums it has paid ſince, added to the perpetuity of the preſent rate, would have ſaved all the probable future advance upon it; therefore 53½ years purchaſe was leſs than the value of ſuch a rate by all the probable future advance; an hypotheſis which ſtates it at 54, muſt fall nearly as far below the truth — we ſee that all the reaſons which might have been then urged againſt its being an eligible contract, would at this inſtant been refuted by the experience of the paſt period; and what arguments can be now brought againſt it, which could not have been urged with equal or ſuperior probability then; they had not then to encounter and bear of the paſt period.

But to remove every degree of doubt about the reſult, I added together the rates of all the pariſhes which I had taken for long periods: all of them but one accidentally happen to give the loweſt annual increaſe; the rate of increaſe of the whole thus added was ſomething under the general advance, being equal to 3,4742 per cent. the rates for the term of twenty-five years were worth at the beginning of that period 24,09, and the remainder of the perpetuity 28,39; the whole 52,48: which deducted form 54, leaves [23] about 1½ years purchaſe of the rates twenty-five years ſince, or about 17/26 of the value of a rate at preſent, as equal to all the future advances which may happen.

That I may finiſh here every thing that relates to calculation, I ſhall add ſome obſervations on the bills of mortality in houſes of induſtry; on the proportion of power to be granted to guardians and directors; and on the probablility of theſe inſtitutions being neglected in future periods.

The regiſters in houſes of induſtry have uſually been kept in the general mode: But the names of the paupers who died, with their ages and diſtempers, and day of admiſſion into the houſe, has been generally entered into the report book at Heckingham ſince March 1772: by the aſſiſtance of that entry, and ſuch information as the governor ſupplied me with concerning ſo recent a period, I was able to diſtinguiſh thoſe who died of diſtempers with which they were admitted into the houſe, from thoſe who died by diſorders contracted after their entry: the number of the former in this period were 70, of the latter 123; but during this term a malignant fever raged very much both in the houſe and country from Chriſtmas 73 to Midſummer 74; [24] in periods of average health theſe numbers were as 21 to 22; and therefore taking a medium between theſe proportions, the corrected reſult comes out as 21 to 29, and the deaths 29/50 of the total exhibited by the regiſters: as theſe diſtinctions have not been made in thoſe returns to the houſe of commons I have ſeen, I thought it neceſſary to inſert them here, to obviate an objection which might otherwiſe be very reaſonably made to the mortality of the ſeveral houſes.

In the time of the general illneſs mentioned, forty-nine died admitted ill from the country, and an hundred and one reſident in the houſe; this diſorder, which was of the putrid kind, was brought into the houſe from the country: the ſtate of the air ſeemed at that time particularly fatal to old perſons, of the latter number no leſs than twenty were above ſeventy-five; the ſmall pox carried off ſix or ſeven, and three were loſt by inoculation; incidents which will reduce the number nearly to its juſt proportion.

When we want information we are generally ſo happy as to diſcover, what would have been the proper form to digeſt records, which at preſent are ſo kept as to be of very little uſe; I am ſenſible that the ſcale upon which theſe obſervations [25] are formed, is not ſo extenſive as it ought to be; but they are the beſt grounds I could procure: I had drawn up ſome obſervations upon regiſters before I knew what had been done upon that ſubject by Dr. Price, I incorporated his obſervations afterward with my own, and have given them in the Appendix.

It was an obſervation of one of the directors of this houſe, and confirmed by the governor, that the children when admitted had too generally a very meagre emaciated appearance; and that the difference between thoſe newly entered, and thoſe who had been in the houſe ſome time, was very ſtriking: in that caſe it muſt preſerve a number of uſeful lives to ſociety.

The only ſufficient reaſon for entruſting a ſet of men with the exerciſe of any power, or the expenditure of a certain revenue, is their intereſt in the application of it, or their ability or both conjointly: in conſidering theſe particulars we ſhall eaſily determine how far the old law, which in its operation has flung the diſpoſition of the ſums collected for the poor into the hands of the overſeers in the firſt inſtance, was political or right; we ſhall be thence likewiſe able to form an idea, what weight their diſſent to the [26] incorporation of a particular diſtrict ought to carry; and with what reaſon they may complain of an abridgement of their powers by the late acts.

The average length of leaſes throughout the kingdom is difficult to aſcertain; but though we cannot aſſign a term of years which ſhall preciſely equal it, we may aſſume one, which we are ſenſible from the nature of things muſt greatly exceed it: to compute the proportional intereſt of the landlord and tenant in the poor rates, I have therefore ſuppoſed all the lands in the kingdom under leaſes of fourteen years, and upon that ſuppoſition the intereſt of the owners to that of the occupiers will be as 14⅔ to 1: but this gives the tenant's intereſt greatly above the true value; had we ſtated the average length of leaſes at nine years, it would have fallen conſiderably ſhort of half as much.

Had theſe two claſſes of men been equally raiſed above temptation, equally enlightned with reſpect to the true political principles upon which the extenſive detail of police depends, in that caſe ſuch would have been the proportion in which authority juſtly would have been diſtributed to them: it is true, that among the occupiers [27] there are perſons to be found reſpectable for their character and information; I am not certain whether Emerſon farms his own eſtate: but a conſtant attendance upon their own affairs, and an education not training them much to reflection, will ſtamp a general character upon the whole claſs, which will render them improper for public duties: yet ſuch is the order of the the people to whom the ſpirit of the laws now in being commits the expenditure of a revenue, whoſe preſent purchaſe appears to be equal to the national debt: expoſed to the peculation or miſmanagement of every diſhoneſt or ignorant man to whoſe charge it is intruſted: experience points out what numbers may be fairly ranged under both theſe heads—an error in legiſlation perhaps ſingle in its kind.

The magiſtrate has by law ſome check upon the officer; but the inſtances of poſſible miſconduct are ſo numerous, that the remedy in its operation is far from being in any degree equally extenſive with the evil —Every ſubſequent check poſſible may be provided, but where the expenditure of a fund in the firſt inſtance, without ſuperior direction, is lodged in the hands of the moſt improper claſs of people, the manner [28] in which it will be applied will be ſtrongly marked with the characters of the men: a ſtream which takes its riſe and flows over a ſoil full of mineral particles will imbibe all its noxious qualities; nor will it be greatly altered by the addition of a trifling rivulet, which may fall into it in ſome part or other of its courſe.

But to this it may be replied, "that there will be little advantage reſulting to the public, from removing theſe powers out of the hands of perſons who may abuſe, to place them in the hands of thoſe who will abſolutely neglect the uſe of them; while the ſpirit which planned and formed a new inſtitution ſubſiſts, the attendance given by the managers is conſtant; but like every other kind of enthuſiaſm it is ſtrongeſt at its firſt apparance; difficulties in the execution damp it, but the tedium of attendance wear it out entirely: the original inſtitutors had a kind of perſonal attachment to their own plan, which engaged many others to a duty which bore the appearance of perſonal attention to them; but to their ſucceſſors it is only a common care in which they are equally engaged with many; this is a ſecond and certain ſource of diminution of attendance, and what is the ſum total which we [29] obtain by the alteration of eſtabliſhed ſyſtems? to exchange old abuſes with old names, for old abuſes with new ones.

This is an objection which has been much dwelt upon; we muſt meaſure the effect of theſe cauſes to diminiſh the attendance of directors by what experience has already pointed them out to be: the moſt proper inſtance will be that of the oldeſt eſtabliſhment of this kind, where they will diſcover themſelves moſt fully and clearly: and here it has happened that every one of the cauſes mentioned in the objection have operated with greater force than in any other inſtance which (to the beſt of my knowledge) can be produced: the average numbers attending the annual meetings at Nacton from 60 to 75 incluſive, were for the firſt five years ten, the ſecond 12⅖, the third 134/5, and in the laſt year 20: the book from whence I extracted this account goes back no further than 1760.

Another branch of ſubject which I propoſed to conſider was the advantages of a better and more regular education, which this ſyſtem in a conſiderable degree provides for the poor.

The elegant and fanciful Rouſſeau has attacked all education in general; and made [30] happineſs to conſiſt in every human ſavage, living alone in his cave, being very dirty, wearing no cloaths, and keeping his nails long enough to dig his own pignuts; this puts him above the artificial wants contracted in ſociety: but a much ſuperior philoſopher of our own country has particularly written againſt the education of the poor; and very clearly demonſtrated that ſharpers, highwaymen, and pickpockets, were the moſt patriot characters: his concluſion from this principle was very properly drawn: you muſt ſuffer your poor to remain uneducated, otherwiſe they will not be quite ſo beneficial to the public.

Bad principles in philoſophy joined with great and uſeful diſcoveries, ſeem to have the ſame fortune with the little qualities of great men: they have ſo much falſe luſture flung upon them by the neighbourhood they ſtand in, that they almoſt ſeem to ſhine by their own light: it is particularly unlucky for my preſent argument, that theſe objections againſt the utility of education ſtand in ſuch reſpectable company; that will be enough to deter me from attacking them in detail, but not from laying down what I think may be urged on the contrary ſide.

[31]The man who writes, and the man who reads, have frequently very different opinions of the importance of the branch of the ſubject under preſent conſideration; but the conſequences which I think may be drawn from this head, will induce me to go into it with particular attention.

Thoſe paſſions whoſe irregular indulgencies produce the worſt effects in ſociety, do not attain any degree of ſtrength before the period of a common education is paſſed; and the principles of ſympathy and compaſſion implanted in mind by nature, diſcover themſelves there a long while previous to them: for this reaſon, in the earlier ſtages of life, we receive and retain impreſſions of virtue much eaſier than thoſe of vice; on account of their nearer analogy to that ſet of emotions which then reign in their full ſtrength, while thoſe which afterwards attain more than power enough to counterbalance them, have not yet arrived at force or maturity.— Impreſſions of this kind early made on the mind, are long retained; and being frequently repeated, by virtue of that repetition become ſo deeply and habitually infixed, as to obtain the ſame force and permanent efficacy with thoſe impreſſions [32] originally ſtamped there by nature: in this manner a few firſt principles early inculcated, and frequently repeated, win their way into the heart, and maturer years fortify by reflection, what habit before had rendered almoſt a ſecond nature.

We cannot long perſonate any character but that ſome part of it will attach itſelf to us and become our own; that warmth with which we endeavour to render the deception compleat, carries us beyond the mark deſigned, and converts appearance into reality: the conſtant action of an internal principle produces the external appearance of it; and by a kind of reflex operation, the aſſuming the external appearance, conſtantly fortifies or even gives birth to the internal principle: we have frequently ſeen a bare external ſhew of religion improve into genuine piety; while a mock defence of the deſolate maxims of the morales lubriques, or an air of libertiniſm worn in the gaiety of ſome unhappy hour, has fixed a bias on the mind which has not with eaſe been ſhaken off: thoſe who have attacked the utility of all inſtitutions for the education of the children of the poor, have owned that they produce an external appearance [33] of decorum, induſtry, and aſſiduity, the tendency of theſe external appearances to ſtrike deeper root, and improve into reality, converts this conceſſion into a ſtrong argument in favour of ſuch inſtitutions.

To live agreeably in any ſociety, our general conduct muſt be ſuch as not to draw upon ourſelves any particular degree of diſeſteem from it: few people I believe were ever ſo abſurd as to go for pleaſure, or even to propoſe tolerable conveniency to themſelves, in a road where there is an inceſſant multitude continually thronging the oppoſite way: elbowed on one ſide, puſhed on another, 'tis hard to ſtruggle againſt popular opinion: there are not many practical principles whoſe operations by an inſpection into the actions of mankind at large we can diſcover to be ſo extenſive, and in their effects ſo infallible: a kind of external force operating upon us either prevents us from deviating from that train of action public opinion has marked out for us, or the pain we receive from every excentricity quickly recals us to it: if we ſhould admit that the efficacy of that education I am recommending extends no further than correcting our opinions, without correcting our principles, [34] the oblique effect of ſuch reformation of our ſentiment muſt be well worth ſecuring, and be productive of the moſt advantageous conſequences to the manners and morals of ſociety.

Let us endeavour to trace its effects from the obſervation I had before laid down: a man who by a better education is improved only in his judgment of virtue and vice, when the merits of an individual with whom he is unconnected by relation, prejudice or favour, comes to be diſcourſed of, will candidly pronounce of them according to thoſe improved ſentiments he has imbibed; far the greater part of ſociety ſtand in this very identical relation to every individual of which it is compoſed; hence the public at large will appreciate the merits of any action the better, the more generally thoſe principales by which it ought to be judged are diffuſed; that general cenſure on every deviation becomes more preciſe, more enlightened, and more certainly paſſed: the train of action marked out by public opinion being rendered more agreeable to the laws of reaſon and virtue, becomes more agreeable to the public intereſt, and in the path thus marked out for them, the generality of mankind will always walk. But [35] whatever lights the ſuperior part of mankind may thus enjoy, if they do not reach the claſs below, they will certainly fail of producing this effect among them. If a man do not run counter to the ſentiments of that claſs of life in which his principal connections lay, to violate the ideas of right or wrong entertained by thoſe much above, or much below, can little affect him; in this reſpect he may be ſaid to live in a different ſociety; and from hence ariſes the neceſſity, that theſe grounds of judgment ſhould be equally diffuſed in every rank of life.

Nor does it form a reaſonable objection to ſuch an education, ‘that its effects are by no means infallible: that nature and paſſion will frequently triumph over ſuch ſlight obſtacles as habit and education oppoſe to them; that their efficacy is always found leaſt when the moſt urgent neceſſity calls for their ſupport: there are ſome men whoſe violent appetites tranſport them with ſuch exceſs, that no education can infuſe a proper counterpoiſe to them; other whoſe paſſions balanced in the exacteſt moral equilibrium, are ſo harmonized as to preclude the neceſſity of every degree of inſtruction; with the former it muſt [36] be inefficatious, with the latter ſuperfluous.’ But in the ſcale of human diſpoſitions there are many intermediate degrees between theſe two extreme limits, near which we find them very thinly ſcattered; and almoſt every character occupies a ſpace much nearer the middle point than is commonly aſſigned; conſequently the conſtant operation of habit and education (though their power were much leſs than experience ſhows it to be) may determine on which ſide they ſhall be found; and it would be abſurd to reject any deſign generally uſeful, becauſe its benefit could not be extended to every uncommon caſe an inventive imagination can propoſe.—Education operates on the mind with a gentle and ſecret influence: yet this unſeen bias, though not diſcoverable perhaps in one or two particular inſtances, will be clearly diſcerned in a ſeries of many actions, and form the predominant character of them. It is like a ſlight bias given to a die; which in a large number of caſts will not fail to demonſtrate itſelf in a degree proportioned to its ſtrength, with ſuch a regulated certainty that we are able almoſt infallibly before hand to determine its preciſe effect, though from ſome [37] aſſignable cauſes, it may not be indicated in a ſingle experiment.

Though the general inſtitution of houſes of induſtry will not provide for the education of all the children of the poor, yet the good effect which would reſult from a general proviſion will be anſwered in proportion to the extent of the partial proviſion propoſed.

The reaſoning above laid down ſeems in ſome degree confirmed by an effect already experienced: it was an obſervation of the governor of one of thoſe houſes I have viſited, that the children born in the houſe or admitted very young, were the moſt orderly and induſtrious: thoſe whoſe relations or parents came into the houſe with them, being abetted and encouraged by their friends, were extremely irregular and idle; and that this difference in their behaviour was very perceptible. A remark which clearly points out two facts very important to the preſent ſubject, that the training the children of the poor receive in their cottages is of the worſt kind, and that the education and controul of a houſe of induſtry provides an adequate remedy to it.

[38]But theſe inſtitutions have been attacked upon another ground: it has been alledged that ‘a pauper is deprived of his civil liberty by being ſhut up in one of theſe magnificent priſons, and put under the controul of a governor: nor does the inconſiſtency end here, every law ſhould have a certain analogy to the principle upon which the government of a ſtate is founded: where it is inconſiſtent with it, it claſhes with and tends to weaken that principle if it be only local; if general, it ſaps its very foundation: this maxim is the fundamental ground of the true ſpirit of law in every country: the principle of this government is civil liberty, and can that principle remain unimpaired, when a law is made, which actually reduces a great number, and ſubjects half a people to a probability of perſonal confinement?’

Before we admit this reaſoning (which I think I have propoſed in its full force) it will be neceſſary to ſee how low down the idea of civil liberty can extend in the freeſt government; and in what manner a diſciple of Locke, the moſt enlightened and zealous advocate of freedom, would take it up.

[39]Every man, he would reply, when he enters into ſociety, gives up a certain proportion of his natural liberty to the magiſtrate, in return for the protection he receives from him; and the remainder, after ſuch a ſurrender, is called his civil liberty. If beſide protection he want maintenance, and have no property to procure it, he then becomes a ſervant to ſome individual; which* ‘commonly puts him into the family of his maſter, and under the ordinary diſcipline thereof; and gives his maſter a temporary power over him, which extends to whatever is contained in the contract and no further—that maſter and ſervant are names as old as hiſtory,’ that is, as the hiſtory of civilized ſociety and human happineſs. If the ſtate or a diſtrict which provides maintenance for thoſe who have no property to procure it, do not acquire the ſame rights over the perſons maintained, it muſt be from ſome difference in the circumſtances of the caſe. A ſervant goes into the family of his maſter and the ordinary diſcipline thereof—by an expreſs contract into which he is obliged to enter by the impoſſibility of ſubſiſting [40] without it; from which he cannot be diſengaged until the end of his contract, if he be able to ſupport himſelf in a manner he likes better: the ſervice he undertakes to do in return for maintenance and wages generally overpaying conſiderably the expence to his maſter.—A pauper enters into a houſe of induſtry provided by the diſtrict, and the diſcipline thereof defined by written laws—by a tacit contract into which he is obliged to enter by the impoſſibility of ſubſiſting without it—from which he is of courſe diſcharged if he be able to ſupport himſelf in a manner he likes better—and his ſervice in return for maintenance and gratuities is generally much beneath the expence to the diſtrict. The differences then appear to be theſe, the ſervant is ſubject to the ordinary diſcipline of his maſter's houſe, which in its nature muſt be ſomewhat diſcretionary—the pauper in a houſe of induſtry to a diſcipline defined by written laws—the ſervant is not diſengaged from his maſter until the end of his contract, although he be able to ſupport himſelf in a manner he likes better—in that caſe the pauper is of courſe diſcharged—the laſt circumſtance in which theſe ſtates are contradiſtinguiſhed, appears to be that the ſervices of the [41] former are beneficial to the individual, thoſe of the latter do not nearly repay the expences of the diſtrict which maintains him—What rights can the pauper retain in the latter caſe, where upon the whole he is a burthen upon the public, which the ſervant has not a tittle to in the former, where upon the whole his labours are beneficial to the individual would be difficult to diſcover: the only reaſon which can make againſt a diſtrict having this power is, that it reduces the poor to a worſe ſituation than the preſent, without being attended with any conſiderable benefit to ſociety: the error of the former part of this reaſoning has been very ably refuted by an* impartial ſtate of their ſituations under both theſe ſyſtems, which the enquiries I have made upon this ſubject enable me to pronounce not exaggerated: that of the latter I flatter myſelf to have demonſtrated in the former part of this eſſay.

After all, is it certain that the liberty remaining to the poor, conſidered as an aggregate body, is at all abridged by theſe inſtitutions? or that it does not gain in one reſpect more than it loſes [42] in another? A pauper at preſent cannot remove from the place of his ſettlement without a certificate, which the officers may refuſe to grant; the general adminiſtration of this law is nearly as rigorous as the ſpirit of it: in diſtricts under the latter acts of incorporation, a certificate muſt be granted for the pauper to remove to any place within them: the liberty of reſidence, by the old law circumſcribed to a ſingle pariſh, is by the new one extended to large diſtrict; all the poor are benefited by this enlargement, while but a ſmall part of them are put under the reſtraint complained of: balance theſe circumſtances, and we ſhall be induced to think, that the poor enjoy upon the whole a greater proportion of civil liberty under the new than old law.

We may further obſerve, that this new ſyſtem in its conſequences is highly favourable to every improvement in legiſlation, and the ſpirit of that civil liberty to which it is held out as being ſo ſubverſive: the happineſs and freedom of every ſtate depend ultimately upon the laws by which it is governed—If we enquire what is the leaſt poſſible reſtraint of law in a ſtate? the anſwer will be, it ought to be ſuch as added to [43] the reſtrant which the manners of a people oppoſe to thoſe irregularities which deſtroy the peace of ſociety, forms a ſufficient counterpoize to thoſe paſſions which would betray us into them, for if it be leſs it is inadequate, if more unneceſſary: and every unneceſſary reſtraint is a degree of deſpotiſm. An inſtitution which improves the manners of ſociety, makes way therefore for a more moderate and improved ſyſtem of legiſlation: agreeably to theſe obſervations it has been found, that thoſe refinements in civil policy which take place in polite ages and nations, would be of no uſe when endeavoured to be put in practice in a hoard of barbarians, on account of their ſavage ferocity of manners: as theſe manners have gradually improved, laws (*which to be efficacious muſt neceſſarily bear a relation to them) have refined likewiſe, and ſocieties grown powerful and happy: 'tis thus that improvements in manners generally diffuſed throughout a ſtate, have always preceded and [44] ſerved for the baſis of improvements in civil policy. But theſe advanced virtues muſt be diſſeminated through the greater part of ſociety before thoſe ſucceſſive amendments in legiſlation can be introduced; and here we diſcover in a ſtriking light the further utility of thoſe inſtitutions which tend ſo eminently to reform the morals and manners of the inferior members of the ſtate, of which that majority is compoſed: every advancement toward a more perfect ſyſtem of laws, in its turn promotes the virtue of ſociety: theſe reciprocal improvements are in this manner multiplied to a degree of infinity, like the images of an object placed between two oppoſite reflectors.

When we ſurvey the manners of mankind in this ſtate of continual and gradual improvement, the proſpect ſo much brightens upon us, that we are led to imagine, that thoſe excellent forms of government and regulations of ſociety, which have ſubſiſted only in the minds of a few abſtracted philoſophers, will ſome ages hence be actually realized. If one view the gradual advances which have taken place in the ſcience of legiſlation, we ſhall diſcover, that they have always had a tendency to this, as that [45] ultimate point to which nature originally deſtined human ſociety to attain and reſt in, and which alone is worthy that noble appellation, the State of Nature. I am not now to be told that this is looked upon rather as a matter of curious ſpeculation, the ingenious amuſement of a few men of refined imagination, than as a thing which ever can exiſt: the negative of ſuch a queſtion ought always to be maintained, with the ſame diffidence and reſerve with which the affirmative is advanced: there are certainly ſome inſtitutions which now exiſt, and are celebrated as maſter-pieces of policy, which the moſt penetrating politicians once cenſured, as plauſible in idea, but what would be found in the execution, chimerical and impracticable: I venture to aſſign as an inſtance of this, the noble edifice of the conſtitution of England; planned by the wiſdom, founded by the labours, cemented by the blood of a long illuſtrious line of legiſlators, patriots, and heroes. That philoſophical hiſtorian Tacitus has told us, * That in every nation [46] the government is in the hands of the people, the nobility, or a monarch: a conſtitution ſelected and compounded of theſe three rather recommends itſelf as ſpecious in idea than practicable, and if put in execution, could never exiſt for any time.’ Yet that conſtitution was then forming in the woods of Germany: and* Tacitus himſelf has tranſmitted to us the original outline of its foundation.

APPENDIX.

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ARTICLE I.

On the Burthen of the Public Debt.

A Writer of the firſt abilities, Dr. Price, has in a late publication repreſented the burthen of the national debt to be ſo much increaſed, as to threaten the ſubverſion of public credit: as the data I have collected to point out to what degree the burthen of the poor rate is augmented, and the principles laid down to determine it, appeared to me during my enquiries upon this latter ſubject to apply equally to the former, I ſhall endeavour to diſcover upon theſe grounds what has been the increaſe of the public burthen ſince the commencement of the laſt war, what operation it has had upon the price of proviſion, and the probable period in which we may expect to be able to diſcharge it.

There cannot be a ſubject on which an error on either ſide can be attended with worſe conſequences; an opinion of the near danger of public bankruptcy produces almoſt all the evils which could come upon us were the danger [48] real: it annihilates public credit, it tempts the attacks of our enemies, to which our ill grounded fears make us oppoſe a very ineffectual reſiſtance; it deſtroys that public vigour, and perſevering ſpirit of private enterprize, which form the beſt treaſure and happineſs of a ſtate, and even where they do not find ability create it. —But the danger is equal on the oppoſite ſide: When a nation has but a few laſt means of ſafety left, if they be ſquandered away by a confidence in reſources which do not exiſt, it renders certain and precipitates a ruin which wiſer meaſures might have avoided.

I am ſenſible of the difficulty and extent of the ſubject; which is to be enquired into upon the principles of a ſcience which I never purſued to any great length, and which I have ſome years entirely laid aſide; and believe I ſhould have ſuppreſſed any obſervations which might have occurred to me upon it, if the enlightened attention of the public which ſome late writers of great merit have called out, had not rendered it almoſt impoſſible for any error to paſs into a general opinion.

The burthen of a tax, or the total taxes of a country, muſt be in proportion to that part of [49] the ſubſiſtence of the people which it takes away: if a tax took away 1/10 part of the ſubſiſtence of a people twenty years ſince, and an equal portion at this preſent time, its burthen is preciſely equal: if it take away more it increaſes, if leſs it diminiſhes: Money repreſents ſome real value in goods and commodities, and if a tax at two different periods take away the repreſentative of 1/10 of our ſubſiſtence, the buthen of that tax upon a people at thoſe different times is equal.

In this calculation and thoſe which follow I take the ſum of our annual charges and my data in general from Dr. Price: the amount of the taxes in 55 was 5,097,617, excluſive of the land tax at two ſhillings in the pound 866,666; and the total payment 5,964,283: from which the difference of the burthen in that year, and the year 74, when the total amount of the taxes was ten million, is eaſily derived: we are firſt to inveſtigate what ſum of money in 74 was of equal value with the ſum of the taxes in 55; this term comprehends nineteen years, admit the value of money to have decreaſed at the rate of 2,16 per cent. annually, for the whole term: the real [50] value then of 5,964,283 in 55, was equal to 5,964283 × 1,021619 or 8,963,800, in 74: or theſe ſums at thoſe periods were equal burthens upon the people.

The taxes in 1774 amounted to ten millions; the proportion of the public burthens in 55 and 74 was as 89638 to 100,000; or as 1 to 1, 11: but the reſult would have been as 1 to 1, 67, if we had confounded the charge and the burthen as the ſame thing; a mode of proceeding which gives the advance of the latter ſix times too great: for this reaſon the concluſions of Dr. Price, and thoſe writers who never lay down that diſtinction when they treat of increaſing burthens, and the meaſure of their effect upon the national credit, muſt be erroneous.

The annual decrement of the value of money upon which this calculation and ſome which follow are founded, is I think aſſigned with moderation: the article in the table from which I deduced it which advanced with the greateſt celerity was corn: yet it ſeemed uniform through all the period obſerved, which points out a permanent cauſe. Many might be eaſily inſtanced, that luxury introduced by the fortunes made in the laſt war, over and above the immediate conſequence [51] of an increaſe of wealth; a change of the manner of life in the farmers who raiſe theſe commodities; who have in their own conſumption ſubſtituted more expenſive articles, inſtead of the cheaper and ſimpler which formerly ſupplied them: and the fortunes made by many in a ſhort time, which have excited the avidity of almoſt all to grow rich in haſte: theſe if entered into at length would be found beſt to correſpond to the effects obſerved. If the former years of the period (for which the regiſter of prices I have uſed was kept) were rather more plentiful than the latter, the exportation permitted then tended on the other hand to raiſe thoſe prices, and the reſtraint in the latter to diminiſh them: and during thoſe years of greater plenty the advance was found moſt rapid: but that advance could not be owing to exportation only, or the ſame cauſe at any other period would have produced the ſame effect: nor would any thing but a deficiency in the productions of the earth increaſing every year, produce it, which can with no probability be ſuppoſed: it was out of the power of an uniform deficiency to have cauſed it: the price muſt have come to its utmoſt heigth in a ſhort time, and there remained [52] fixed indeed, but not progreſſive.—But that the annual decrement of the value of money might be ſuſpected of no exaggeration, I have ſuppoſed the value of corn to have riſen only half the ſum the Nacton table points out, and from thence deduced the rate of decreaſe 2,16 per cent. annually.

If we had taken the fall of money 2,89 as exhibited in the table, the burthen of the taxes would have appeared diminiſhed 1/40, or 245,610 l. yearly: that of the peace eſtabliſhment 1/13, and that of the debt increaſed 1/10

The public annual charges are compounded of the intereſt of the debt added to the other current expences, which may deſerve to be conſidered ſeparately. The debt at the beginning of of the laſt war was ſeventy-two millions, and ſuppoſing the intereſt paid the public creditors equal in both times, ſuch a burthen was equal to 108,2 [...]0,000 at the end of 74. The public debt then amounted to 137 millions, and the proportion of the national burthens in thoſe years was as 108 to 137, or as 1 to 1,266. To ſuppoſe the burthen and actual ſum the ſame, would give this rate of increaſe as 1 to 1,903: [53] or the difference of burthen nearly 3,4 times too much.

If we deduct the intereſt of the debt from 5,964,283 l. the total taxes of 55, the remainder will be the peace eſtabliſhment together with the ſums applied to the diſcharge of the debt: the intereſt amounts to 2,565,000 l. admitting it to be proportional to that of the preſent debt; the difference applied to the purpoſes mentioned above amount to 3,399,283 l. which equalled in value 5,108,900 in 74: the remainder of the public revenue in 74 applied to theſe purpoſes after the diſcharge of the intereſt of the funded debt was 5,119,320, exceeding the former ſum 1/500 which gives the addition to the burthen. During the laſt peace we have annually paid off 916,666 l. of the debt, during the former 750,000, the difference is 166,666 l.

The expence of the peace eſtabliſhment has been loudly objected to: it appears however from the laſt conſideration to have been a decreaſing burthen, though a much more conſiderable force has been kept up by ſea and land than before the commencement of the laſt war.

The debt in 1715 was fifty-five millions, and nearly the ſame it is to be ſuppoſed at the peace [54] of Utrecht. The national intereſt then was ſix per cent. the preſent debt 137, its intereſt 3½; and admitting both theſe ſums to be redeemable funded debts, the intereſt on each will be 3,300,000 l. and 4,795,000 l. if we calculate the value of money for 1715 from an average of ten years of which that is the middle term, we ſhall find a revenue of 3,300,000 at that period, equal in value to 4,699,000 in 1774. Our burthen therefore in thoſe forty-nine years is augmented barely 1/50; and we may in reaſoning upon this ſubject ſuppoſe them perfectly equal.

It ſeems to follow from this concluſion, that the total of all our national exertions ſince the peace of Utrecht, have been no more than equal to our abilities; becauſe our burthens have not been increaſed.

That there is no more reaſon to apprehend a national bankruptcy now, than there was at that period; and the fears which were then entertained, have been ſince refuted by experience.

It has been obſerved of late years that ſome of our funds have become more productive, the advantages reſulting to the nation from ſuch a circumſtance deſerve a little attention.

[55]The proportion of the preſent value of the perpetuity of an encreaſing to a fixed fund, is as the rate of intereſt, to the difference between that and the advance—That of a decreaſing fund, as the intereſt to the ſum of the intereſt and rate of advance—And that of an increaſing to a decreaſing fund, as that ſum to the difference mentioned above. An example will make this ſufficiently clear—Let there be three funds each of 100,000, the firſt increaſing 1½ per cent. annually, the ſecond fixed, the third decreaſing at the ſame rate the firſt increaſes; let 3½ be the rate of intereſt, the value of the increaſing fund will be to that which remains fixed as 3½ the rate of intereſt to 2 the difference of the advance and intereſt, or as 7 to 4: the real value of the firſt is five millions, the ſecond 2,857,142, and the difference 2,142,858—The value of the decreaſing to the fixed fund will be 3½ to 5, or 7 to 10, and the perpetuity of the third fund will be 2,000,000, the loſs 857,142; and the difference between the increaſing and decreaſing fund 3½+1½, to 3½−1½, as 5 to 2.

Therefore the loſs upon five funds perpetually decreaſing at the rate of 1½ per cent is only equal to the gain upon two increaſing funds.

[56]And let there be ſeven pariſhes aſſeſt at an equal ſum to the poors rate, let the charges of five annually decreaſe at 1½ per cent. and the remaining two increaſe at the ſame rate; the decreaſe of the former will be balanced by the augmentation of the latter.

After having ſaid ſo much on the relative meaſures of burthens, the next ſubject which naturally offers itſelf to our conſideration is its abſolute meaſure, or what every man pays in the pound in proportion to his conſumption of commodities.

There are no data I believe to determine this queſtion exactly, the utmoſt we can do is by a probable conjecture to approach near the truth.

A land tax of 4s. in the pound according to the aſſeſſments, was ſome years ago eſtimated to raiſe no more than 1s. 6d. of the rack rent: the rent of the kingdom will thus appear to amount to 23 millions; the product taken as three times the rent 69 millions; admit the additional value of our manufactures 2/7 of our whole production, the value of our manufactures will thus come out 27,600,000; and ſuppoſing ⅔ conſumed at home, that conſumption amounts to 18,400,000l. and our exports to 9,200,000. For which we [57] import foreign commodities of which the value to the conſumer will be 10,120,000, reckoning 10 per cent. only for freight and mercantile profit; I have here ſuppoſed no balance of trade in our favour: our annual conſumption therefore appears to be 97,520,000 l. add 10 millions the ſum of the taxes, and the total expence of the kingdom is 10,752,000 a year, and the abſolute meaſure of the burthen [...], or [...] of our total expence; ſomething leſs than 1..10½ in the pound. Mr. Maſſie in 1761 calculated the taxes paid by the farmer in proportion to his conſumption at 1s. 10d. in the pound; upon what ground he formed his concluſion I do not know.

The intereſt of the debt being nearly half the taxes its burthen will be 11¼ in the pound. Mr. Hanway has endeavoured to compute the annual conſumption of the kingdom upon different principles; he begins his account with a ſuppoſition which can no ways be admitted, that the ordinary rent is twenty times the value of a land tax at one ſhilling in the pound, this evidently gives the reſult far too little.

That the land annually produces on a medium four rents, I have ſuppoſed but three.

[58]That the other articles to be added are half the produce, exceeding the proportion aſſumed here as 5 to 4.

If he had ſuppoſed the rents to bear the common eſtimated proportion to the land tax, the conſumption of the kingdom would have come out 138 millions annually; the total expence of taxes and conſumption 148; the burthen 1/15, or more nearly 1s. 5d. in the pound.

Of the effect of public burthens on the price of proviſions.

Suppoſing the unreduced advance of prices drawn from the tables true, it appears that the price of proviſions and the money levied in taxes, have ſince the beginning of the laſt war advanced almoſt in equal degrees; it may be proper therefore to examine upon this ſuppoſition, whether the increaſe of the public expences have not raiſed the prices of proviſion, and thus created an apparent ability to ſupport them, at the expence of a much heavier evil.

Let us ſuppoſe the quantity of money, of proviſion, and the number of people in a ſtate to remain the ſame for an indefinite term of years; [59] the price of neceſſaries will remain the ſame—Imagine now by a deficiency of the productions of the earth, or any other cauſe, the quantity of proviſion in one ſingle year is reduced in a certain proportion, as for inſtance 1/39; it is evident the price of proviſions will riſe that year in ſome ſimilar proportion, not perhaps preciſely equal, ſuppoſe it 5 per cent. the next year upon the return of the old quantity they will fall again nearly to their original rate, which they will after a certain period acquire: if this period extend to five years (for the term is of no importance) and the decreaſe of price every year be equal, or that the addition to the firſt price ſhall be in the 1ſt year 5, the 2d 4, the 3d 3, the 4th 2, the 5th 1, the 6th 0, or return to its old level— let the quantity of proviſions to be diminiſhed again a ſecond year, the effect of the diminution of the firſt year will have left an advance of four upon the price, the preſent year increaſes this with an additional advance of five, ſo that the total advance of the ſecond year will be nine; in like manner for the third year, the advance from the deficiency of the firſt will be three, the ſecond four, the total ſeven, and generally in the

[60]

Advance from the deficiency in year the
 1ſt234567Year.
15432100 
2 543210 
3  54321 
4   5432 
5    543 
6     54 
7      5 
 591214151515 

* Here we ſee that the price of proviſion, by withdrawing every year 1/30 of the whole quantity, increaſes continually to the fifth year; but in the ſixth and ſeventh year, and ever after, no further increaſe is made; the effect is in that year come to a maximum.

And let the price of neceſſaries increaſe during this period from any other cauſe acting in conjunction with this; as for inſtance the augmentation of the quantity of money, in the ſame number of years the effect of the annual diminution of proviſion will be at its greateſt height, and at all ſubſequent periods, the rate of increaſe [61] of price will go on in the ſame proportion as if it had been effected by the quantity of money alone.

If inſtead of commodities in kind their repreſentative ſpecie had been ſubſtituted, its effect would have been the ſame, if the ſums taken had at the different times aſſigned, repreſented the ſame real value: for no reaſon can be aſſigned why taking away the repreſentative ſhould produce a greater effect than taking away the real value repreſented by it.

When the proportion of neceſſaries thus taken or ſpecie repreſenting them uniformly increaſes, it continually tends to increaſe the price of proviſion which then has no maximum. The increaſe of the burthen of the poor rate has been 1,00616 for nine years laſt paſt; its efficacy to raiſe the price of proviſion has poſſibly been to that of all the other cauſes operating with it as 616 to 2,89, about ⅙ of the whole.

When the burthen decreaſes the prices of proviſion (if no other cauſes operate) decreaſe with it. If we admit the decrement of the value of money which the table gives to be true, the burthen of our annual taxes ſince the commencement of the laſt war has decreaſed 1/40; therefore [62] a fortiori they have not been the cauſe of any decrement in the value of money.

If we reaſon from the reduced hypotheſis which gives the value of money 2,16, our burthen being now no more than it was at the death of Queen Anne, the preſent difference of the price of proviſion compared with that of three or four years after, cannot be aſcribed to it: for if it had continued the ſame during the whole interval, it would have produced its utmoſt effect in three or four years after the peace of Utrecht; and the ſubſequent advances muſt have been attributed to ſome other cauſe.

There is a ſtriking difference between the operation of a debt with its annual intereſt levied upon the public, and a tax of the ſame amount applied to the current ſervice: for the two annual payments of the public ſimply as ſuch would produce the ſame effect upon the price of proviſion: but if there had been no fund to veſt the capital of the debt in, a great part of the money now compoſing it would have been laid out in the purchaſe of lands; this would have increaſed their price; to reimburſe himſelf this extraordinary expence, the new purchaſer raiſes his rents, and this raiſes the price of proviſion. [63] And the intereſt paid to foreigners again diminiſhes its efficacy, being a diminution of the quantity of money in the kingdom.

But admitting the decrement of the value of money aſſigned too high, there is another argument which I think puts this beyond a doubt: a nation which funds inſtead of defraying the current expences of war and peace by immediate taxation, at firſt is eaſed of paying the principal, by only taking the burthen of the intereſt: as the debt increaſes this intereſt increaſes until it becomes as much as would have equalled the average expence of war and peace if there had been no debt; its laſt ſtage is where the intereſt exceeds that average. During the firſt two periods the ſum of all its taxes will have been much leſs than in the former ſyſtem, and therefore they will have produced an effect conſiderably leſs in raiſing the price of proviſions; we are now nearly in the ſecond of theſe periods as I ſhall have preſently occaſion to ſhew, and therefore proviſions have hitherto been cheaper on account of our funding.

Yet I am by no means inclined to extenuate the conſequences of a ſyſtem, which if not receded from in time, may ſtill for a certain period [64] continue to lighten our own burthens by the ruin of poſterity: but a general diſpondence from views which I conceive preſent our ſituation in too dark a point of light, may diſcourage and even diſable us from making uſe of thoſe reſources which remain to us. Though the debt appears not to have been an increaſing burthen, funding may very well be conceived to be an ineligible mode of defraying the public expence. Let us therefore enquire into the preſent value of the difference of our ſyſtem of funding, and that of raiſing ſuch taxes uniformly ſince the beginning of laſt war, as would have compleatly diſcharged the ſums it was then neceſſary to borrow, at the end of that term of years for which we might reaſonably expect the continuance of peace. This ſum added to our peace eſtabliſhment will give us the amount of our taxes in caſe we had no debt, and enable us to determine the loſs of the kingdom by funding according to the preſent ſtate of that debt.

The proportion of the number of years of war to thoſe of peace ſince the commencement of the preſent century, has been as 7 to 12: the operations of the laſt war begun in the ſpring of 1756, and included ſeven years; and the probable [65] expectation of peace was twelve years. The debt contracted in the war was 76 millions, and ſuppoſing the annual grants all equal, the extraordinary expence amounted to 10,857,142l. per annum, an extraordinary revenue of 5,011,400, would have diſcharged that debt with its intereſt by the time another war would probably have commenced: we muſt add to this the peace eſtabliſhment for the army, navy, civil liſt, and the annual debt upon theſe articles amounting to 4,850,000l. and the whole revenue annually raiſed upon the public would thus amount to 9,861,400l. which falls ſhort of the preſent ſum raiſed by the taxes 139,600 l. about 1/70.

During the peace the debt has been diminiſhed to 65 millions, but to have diſcharged that ſum in the ſame term of time, 4,286,066l. a year muſt have been levied in additional taxes, or in the whole 14,016,746l.: in both theſe caſes we ſhould have begun the ſubſequent war with the ſame debt upon us we did the former, but the different ſums of money to be raiſed upon the people to bring us into the ſame ſituation would have been as 98 to 140, or as 7 to 10: which I think to be the difference of the real value to the kingdom in our preſent circumſtances, [66] between the ſyſtem of funding and that deſcribed above.

If the debt were annihilated it does not ſeem that we ſhould be able to reduce our taxes without the probability of being obliged to create a new one; becauſe the intereſt of the debt is very nearly equal the ſum we ſhould annually pay to prevent coming into that circumſtance.

But notwithſtanding, this points out the neceſſity of purſuing for a certain term of years the moſt efficacious methods of reducing the public debt: I therefore proceed to enquire into the means Dr. Price has recommended to effect this.

He has ſuppoſed we may be able at leaſt to obtain of America a fund of 300,000 a year.

The colonies are ſaid to double their numbers in 25 years, but let us ſuppoſe the term 35 in which the quantity of land flung into cultivation is doubled. If a tax be laid upon the land already broken up, amounting to 300,000 per annum, which he ſeems upon the authority of Lord Shelburne to conſider as attainable, and all future grants be aſſeſt at half as much again for the ſame quantity of land; the rate of increaſe of cultivated land will be 2 1/35 or 1,219 [67] per hundred acres yearly; which would be the increaſe of the tax if the lands newly brought into cultivation were aſſeſt at the ſame rate with the old; but they are ſuppoſed to pay half as much again, or the tax to increaſe 1,8285 per cent yearly, and taking the intereſt of money at 3 1/2, and the debt at 137 million, it would be diſcharged in 70,3 years by that fund, and an annual burthen of 4,880,0 [...]0 annihilated, with a clear addition to the revenue at the end of that term of 1,066,530 l.

There is one particular property attending ſuch a mode of taxation, that all frauds at the original aſſeſſment, and thoſe which may be committed afterwards, act contrary to and will nearly deſtroy each others effect. A fixed ſum is to be paid; if the preſent poſſeſſor in his account delivered in diminiſh the quantity of land he holds, ſuch a diminution will augment the tax upon equal quantities, and the ſum will remain the ſame; but it will alſo augment the revenue from lands afterwards brought into cultivation in the proportion of 3 to 2: and if the future frauds in reſpect of quantity be equal to the paſt, the revenue will upon the whole gain; if they [68] exceed them in proportion of three to two, it will not loſe.

But beſide the tax from the colonies, which I ſuppoſe to remain as ſtated above, the following are ſome of the reſources which he points out as remaining to the nation for the diſcharge of the debt.

1. The annual ſurplus of the revenue 300,000l.

2. The land tax to be continued at 4s. in the pound the amount of the additional ſhilling 450,000 nearly to be thus applied.

3. In 1781 there will be an addition to the annual ſaving of 189,863l.—18,986,300l. principal debt falling from 4 per cent. to 3.

4. In 1782 a further addition of 22,500l.— 4,500,000l. more being reduced from 3½ to 3 per cent.

5. In 18 years the greateſt part of 224,580l. per annum annuities will be extinguiſhed; as theſe will fall into the ſavings gradually, let us ſuppoſe them all to ſubſiſt together 12 years, and then at once to fall off. Then in 17 [...]8 the fund will be further augmented 224580l.

Theſe funds conjointly will diſcharge the debt in [...] years, and if we further were to ſuppoſe [69] the affairs of the Eaſt India Company ſo far retrieved, as to be able in two or three years to pay 300,000 a year to government, the debt will be diſcharged in 37 years nearly.

In determining this period I ſuppoſed the rate of intereſt 3¾ per cent. for the following reaſons; when a fund ſinks below par, as for inſtance to 90, it may be privately bought up; if it riſe above as to 110, the creditor will ſubmit to a reduction of 8 per cent. rather than be paid off at 100: theſe particulars have been fully pointed out by Dr. Price, I have therefore ſuppoſed their effect equal to ¼ per cent. added to the common rate of intereſt.

It is impoſſible perhaps to form any well-grounded hypotheſis of the future annual decrement of the value of money; but upon a ſuppoſition that it will be for the next 71 years ⅔ what the following table gives it for the term it comprehends, that our future wars ſhall have the ſame proportional length as the former in this century, and our operations be as extenſive as in the laſt, our new debt will be paid off in 30,88 years, the whole in 72, and the burthen continue nearly the ſame during the entire term of payment. But toward the latter end of [70] theſe periods, the diſcharge of the debt might be perhaps too much accelerated; and ſuch a quantity of money be flung into the hands of the public creditors, as muſt greatly and rapidly encreaſe the price of land and conſequently of proviſion; the effects this might produce upon commerce and induſtry merit ſome conſideration, there is a limit which the payment of the Britiſh creditors ought not to exceed; when it gets to that, it might perhaps be expedient with the overplus to begin to diſcharge the principal due to foreigners, which therefore it would be right to reſerve 'till nearly the laſt; becauſe we might be obliged to ſtop in the courſe of payment earlier than we otherwiſe ſhould be neceſſitated to; nor ought even that in any period of its diſcharge to exceed a certain proportion of the balance of trade in our favour, it might otherwiſe deprive us of our ſpecie.

I ſhall cloſe theſe obſervations on the debt with a recapitulation of what has been endeavoured to be proved:

I. That the burthen of the taxes from 56 to 74 increaſed 11/100.

[71]II. That in reaſoning upon this ſubject if we conſider burthen and charge as ſynonimous terms, the increaſe reſulting will be ſix times too much.

III. That the increaſe of the burthen of the debt in the ſame period is only 266/1000, but according to the ſecond method of eſtimating it, it appears to be 903/1000, or 3,4 times too great.

IV. That the peace eſtabliſhment has not been an increaſing burthen, notwithſtanding the ſuperior force kept up.

That the burthen of the annual ſum paid to the public creditors, was the ſame nearly at the peace of Utrecht as at preſent.

The burthen of paying off the debt with a given annuity at that period the intereſt 6 per cent. and that of the preſent the intereſt 3 ½ per cent. would be found not differing in a very great proportion: but to aſſign this, it would be neceſſary to go into a detail exceeding the limit which ſhould be allowed to a ſubject merely collateral.

That the gain by a fund which becomes annually more productive, greatly overbalances the loſs by a decreaſing fund.

[72]That the ſyſtem of funding has not yet raiſed the price of neceſſaries.

That the abſolute burthen of the taxes is 1s. 10½d in the pound, of the debt 11¼d: but that the difference between the preſent ſyſtem of funding, and impoſing ſuch taxes as might probably at the diſcharge the expence of one war by the commencement of the following, is as 10 to 7.

But that all fears of public bankruptcy, grounded upon a meaſure of public burthens, which does not take the decreaſe of the value of money into conſideration, appear for that reaſon ill founded.

That theſe concluſions may be compared and underſtood with more facility, I have digeſted them into the form of a table.

[73]

 YearsChargeDecrement of moneyBurthenIncrement of burthenAbſolute burthen in the pound.
Total Taxes17555,964,283 10   
177410,000,0002,89,975−, 025£.s.d.
2,161,11+ ,11 110½
0,001,67+ ,67
6 times too great
   
Debt175572,000,000 10   
1774137,000,0002,891,108,108   
2,161,266,266  11¼
0,001,903,903
3, 4 times too great
   
Peace Eſtabliſhment & Surplus17553,399,283 10   
  2,89,925−,075   
17745,119,3202,161,002+ 002  11¼
  0,001,506+,506   
    253 times too great   

ARTICLE II. Of the Advance of the Price of Proviſions from the Report of the State of Nacton Houſe of Induſtry.

[74]
YearsWheat per quarterAveragesMalt do.Averages
 s.d.s.d.s.d.s.d.
175837  28   
928429821623
6028   22   
61253  214  
62306  26   
33237230 28
439   298  
5466  28  
66439  316  
7523  344 1/ [...]291
8514310½296  
935   239  
7037  264  
7155  316  
2548  34 34
354¾531037   
4515  36   

[75]

 Beef per Stone.Cheeſe per 100 w t.
   Averages  Averages
 s.d.s.d.s.d.s.d.
175833  30   
93¾31 15/1626272 10/16
603   256  
13  27   
623   2710½  
33334306309 14/16
43  322  
53  329  
663  326  
7310½  32   
68338 14/10
17/20
325332 6/16
9310½  34   
7039  353  
71310½  356  
2442 1/1638 343 7/16
34  32  
443  316  

Proviſions conſumed in kind in eight weeks, from the books at Heckingham.
PerſonsMeal StoneFlour Second. St.Meat Beef St.Cheeſe StoneBeer Barrels
260792018176
2607819, 718176
264731818176
26066161717
25666161717
24066161717
238681516175
238681516175
2016 Per Week.564135½13713644½
10 Perſons per Annum.145, 534, 96  11, 5
*Wheat 6, 07 qrs.35, 3535, 12, 704

Malt qrs.

Increaſe of the Expence of maintaining Ten Men One Year from Michaelmas 1759, to Michaelmas 1772.
CommoditiesQuantityExp. Michael. 59Michaelmas 63Eaſter 68Michaelmas 72
Wheat qrs.6, 07471..10½180.. ¾555..8½225.. 7¼622..8½266..3¾718... ¼326..9¼
Malt qrs.2,70462..8¾77.. 2¼78..7¾93..7
Beef Stone35, 35109..8117.. 9132..1147..3
Cheeſe Stone35, 1119..5135.. 2145..8150..5
Sundries 231..6¼254..11½273..6300..—
Increaſe of Prices703..4¾810..8896..4½1018..—¼
Geometrical Progreſſion703788895,551018..—

Annual advance per cent. 2,89 for thirteen years the whole term; 3,63 for the firſt four years.

[78]This annual advance is equal the annual decrement of the value of money.

The numbers in the laſt article, ſundries, were found in the following manner; the preſent expence for 10 paupers in one year, from the beſt eſtimate of particular articles I could obtain, amounted to 15l. the rate of increaſe was then aſſumed equal to ⅔ that of the other articles.

But there is an apparent irregularity in the advance; an acceleration in the firſt period of ,74 per cent. the cauſe of this, and its preciſe meaſure may very probably be aſſigned.

We very eaſily diſcover two temporary cauſes of acceleration which then took place; the increaſe of taxes, and the fortunes made in the laſt war, and brought over from the Eaſt Indies. We will ſuppoſe the effect of the latter ⅗ that of the former: The annual average increaſe of the debt laſt war was about 11 millions, and in the middle of that period we are conſidering it was nearly 126 millions, and the annual increment of the burthen 11/126; we found the abſolute burthen when the debt was 137 millions to be 11¼ in the pound; at 126 it therefore was 10¼, and the increment in pence 112,75/126: admit with Dr. Price that ¼ more is raiſed upon the public for [79] commodities by the increaſe of taxes, than the ſum paid to government; the total increment of the price of proviſions will be 140,9375/126, or in the terms of a pound [...], or [...] per cent.: the effect of the influx of money ⅗ of the former amounts to [...] per cent.; and their joint operation [...] for the acceleration of the increaſe of the price of proviſion = ,7457 per cent. but the mean advance by the table appears to be 2,89, the accelerated advance 3,63, and the effect of the accelerating cauſe ,74 as determined above.

To this it may be objected that it has been demonſtrated, that taking the decrement 2,89 the increaſe of taxes has not raiſed the price of proviſions in 19 years, but the reaſons alledged above not only admit that the taxes in ſome of the given years increaſe the prices of commodidities, but even aſſign the quantity of that augmentation.

The period mentioned was during the war, the operation of a tax newly laid on is to raiſe the price of neceſſaries, and conſequently to drop the value of money: during a war of ſeven years, if taxes increaſe in a ſuperior proportion to the fall of the value of money, the public [80] burthen increaſes; if money continue to fall (as the table points it out) in every ſucceſſive year of peace the ſame tax will have leſs value, or become a leſs burthen than the former; and as there are twelve years of peace to ſeven years of war, the decrement of burthen in twelve years, taking the yearly rate 2, 89, will balance the increaſe in ſeven.

The numbers therefore corrected by removing theſe cauſes of perturbation would ſtand thus:

Prices703788896,331018
Geo. Prog.703788895,551018

I muſt obſerve here, that the correction of the numbers, founded on a probable hypotheſis, is probably, but not perhaps mathematically true; there being no demonſtration of the aſſumption on which it is founded, it is certain however that ⅝ of the irregularity ought to be ſubtracted, if we allow no efficacy to the influx of money; but whatever be allowed will abate the remaining ⅜. There is the greateſt probability that the annual decrement of the value of money has not been over-rated after the reduction I have allowed; [81] it is much more probable that it falls ſhort of the true meaſure.

Conſiderable uſes might (I ſhould be inclined to think) be derived from accurate tables kept in this manner.—Government has already ordered regiſters to be kept of the principle articles in it; if the others were likewiſe added, the buſineſs of granting relief to the poor, might be regulated upon ſuch fixed principles as to be always proportioned to the neceſſity of the pauper applying for relief in every variation of prices: the quantities of the different neceſſaries of life to be conſumed in kind by a family of every probable number, may be found with very little difficulty; then the different expence of maintaining ten men for a year deduced as above may be given in the firſt column of a table, and in a line with every different charge (which need not exceed twelve in number) the weekly expence of a family of every different ſize: ſuch a table might be compriſed in one folio page and need no alteration for many years. The prices of many articles of proviſion are I believe delivered in at the quarter ſeſſions; a clerk might every half year draw out an account of the charge of ſupporting ten men annually [82] at the rates of the time being; it would be compleated in four or five ſhort multiplications. The numbers in the line oppoſite the neareſt ſum in the table, would give the weekly expence of a family of every probable ſize: the the weekly earnings of the pauper ſubſtracted from this, will give the weekly allowance: proper diſcretionary additions may be made in caſe of ſickneſs.

If the relief thus proper to be granted to a family of every ſize (tranſcribed from the general table) were publiſhed in the provincial papers at the ſame times, they would form a check upon either the avarice or profuſe folly of a pariſh officer.

Poſſibly ſome very good conſequences might be derived from general abſtracts of the accounts of the different houſes of induſtry being yearly advertiſed in the county papers, with the average expence of maintaining ten paupers for the laſt year, compared with the charge of the ſame number formed by the prices of that part of the country, as in the forgoing article. If ſuch an inſtitution by the negligence of the directors in general ſhould be ſuffered to fall into improper hands (of which I think there is no probable [83] danger) this compariſon would be an account of their miſmanagement, the meaſure of it exactly defined, and their own accuſation to the public. The different expence of maintaining that number of paupers in different houſes would be eaſily compared, and the cauſe examined into by the director of that diſtrict whoſe charge amounted to the greater ſum: it would be a check upon the unneceſſary expence or illiberal parſimony of either, and all ſuch corporations be continually approaching to the beſt plan of providing for their poor.

It would render this new ſyſtem likewiſe capable of being made more general: the probability of the abuſe of ſuch inſtitution ariſes from the want of a ſufficient number of directors, but diminiſhing the probability you make fewer directors neceſſary.

We may thus likewiſe approach tolerably near the ſolution of a political difficulty of ſome conſequence; to regulate the price of labour by the ſtate; if ever it ſhould be found expedient to attempt ſuch a meaſure.

The legiſlature may know at what mean price the public intereſt requires work of a certain kind to be fixed, but determine that price invariably [84] by ſtatute, and every labourer (let his ſtrength or ſkill be ever ſo different, as the quantity of neither can be defined) receives equal wages: as the value of money falls, there will be a neceſſity of frequently altering the ſtatute, or the labourers are reduced to the moſt abject diſtreſs: fixing labour of different kinds to rates which riſe and fall by the prices of proviſions deduced from a table formed in the manner I have given, would take away the latter objection, but leaves the firſt. To remedy that, when a ſervant was hired for a certain period, the ſum fixed by agreement might be conſidered as a rate or proportion; and the payment ſhould increaſe or decreaſe with the variations of the value of money. A ſhort annual table might be given before Michaelmas for the whole kingdom, which would contain every variation of rate, or the juſtices of the peace for the ſeparate counties might draw up one at the preceding ſeſſions, as the prices of the different counties are not perfectly equal. It is eaſy to ſee that there would never be occaſion for any alteration of the rate of hireing—That the labourer would be paid according to his abilities and the neceſſity of his maſter for his ſervices—That he would always receive the real value in proportion to the [85] terms of his agreement, inſtead of a nominal ſum— Wages always bearing nearly the ſame proportion to the price of proviſions, equal labour would generally procure an equal quantity at every price; which would tend to diminiſh popular inſurrections.

Suppoſe the price of labour to be now a certain number of years behind the price of proviſions as four or five; every other circumſtance is eaſily deduced from that point of time when fixed: but there certainly is ſome delicacy requiſite in fixing it.

I had occaſion to conſider before in the Appendix, the effect of a land tax in a country not fully ſettled, but where population and ſettlement advanced with great rapidity. If far the greater part or the whole of the revenue a country draws from its colonies were by ſuch a tax, the rate of which was made fixed and permanent, it would give greater ſecurity to the coloniſt for the peaceable enjoyment of the reſt of his property, than ſucceſſive taxes impoſed at various times to make up the ſame amount. There certainly is no injuſtice in ſubjecting a future age to bear the ſame burthens, and contribute the ſame real value to the parent ſtate their predeceſſors did; if the abſolute taxation for equal [86] quantities of land varied every ten years, according to the variation of the value of money in the colony for the preceding term, deduced from a table of this kind, the burthen of an individual would at the moſt diſtant period of time always be in proportion to his ability, and be equal upon equal property. The money produced by it would increaſe in a complicate proportion of the increaſe of the ſettlement, and the riſe of proviſions; this augmentation would continue after ſuch a ſettlement was fully peopled, in proportion as they applied themſelves to arts and commerce. For a people ſtrong by ſea, without numerous land forces, large iſlands, but ſuch as are not capable of ſupporting above 600,000 inhabitants, ſeem the beſt ſettlements. If leſs, their people will ſoon ceaſe to increaſe, and the ſettlement be entirely cultivated; and perhaps there is a vigour of character, and a degree of refinement attainable in a middling ſociety which ſmaller one's are not capable of: if they be larger, it may be difficult to reſtrain them in the bounds of a proper ſubordination, and they have this further recommendation, nature ſeems to have ſeparated them, and prevented all temptations to a dirty detail of inſidious left [87] handed artifices, and the unpolitical errors of an unmanly policy.

ARTICLE III. On the Increaſe of the Charge and Burthen, of Poors Rates. HYPOTHESIS.

WHEN the price of labour remains conſtant, and the price of neceſſaries increaſe, the number of poor to be ſupported by the public ſhall increaſe at leaſt in the ſame proportion.

It is eaſy to demonſtrate that this ſuppoſition falls ſhort of the truth; the paupers who receive weekly collection in a very populous diſtrict, being lately numbered amounted to 700; thoſe of one ſingle pariſh which pays ⅓ of the rates are in the whole far more than double that number: let us ſuppoſe that 1/6 of the number receive collection; double the price of proviſion [88] without increaſing that of labour, and ⅔ of the whole number of poor could infallibly become chargeable: but the hypotheſis gives the increaſed number only 2/6 or ⅓.

Let N ∷ the number of poor, R ∷ the amount of the rate, P ∷ the price of proviſions, L ∷ the price of labour, then R ∷ P × N; and N ∷ P / L by the hypotheſis when the price of labour remains conſtant or L ∷ Po, then N ∷ P, and R ∷ P2: let us now ſuppoſe the price of labour to increaſe in the ſame proportion with the price of proviſions, then P ∷ L, N remains conſtant, and R ∷ P1. And in all the intermediate degrees of increaſe, of the price of labour it will be repreſented by ſome pure power of P, as P 1/m: for aſſuming a ſeries with coefficients, and comparing the terms with the known caſes they will be found ſeverally equal to O. Then N ∷ P / L∷ [...] but the rate [...] And in the years 0 . 1 . 2 . 3 . 4 . 5 The price of proviſion P. Pp. Pp2. Pp3. Pp4. Pp5 Or ∷ — — 1. p . p2 . p3 . p4. p5 And the poor rate ∷ [...]

[89]Where the indices being in arithmetical progreſſion, the rate ſhall be in geometrical progreſſion according to the aſſumption.

Of the abſolute burthen of the poors rate, let us ſuppoſe its preſent amount 2,500,000, that ſum is ¼ of our taxes, the burthen of the taxes is 1s. 10½d. in the pound; that of the poor rate is nearly 5¾d. If we compare it with the rents of the kingdom, it will appear to be 2s. 2½d. in the pound.

If we take the land tax as a ſtandard to eſtimate it by, it exceeds it in proportion of 3 to 2; or is equal a land tax and a half at 4s. in the pound, or 2 of 3.

[90]

Table of the ratio of Increaſes of the Charge and Burthen of the Poor's Rate in different Diſtricts.
 YearsChargeIncreaſe of charge percent.Burthen, Do.
Mr. Potter's numbers general amount92,200,0003,506+ ,61,32
3,000,000
Briſtol from Dr. Woodward204,0004,688+ 1, 752, 47
10,000
Hundred of Fouhoe excluſive of 3 pariſhes1020303,885+ ,971, 69
2972
Hundreds of Mitford and Launditch excluſive of one pariſh734114,58+ 1,642,36
4162
Ten Pariſhes228002,39—, 486,22
1345
    Decrt. of money 2,16Decrt. 2,89

ARTICLE V. Obſervations on the Mode of Proceeding and data in ſome Political Calculations.

LET there be two ſeries of terms 1ſt a, a1 a2 a3 a4, The 2d b, b1 b2 b3 b4. [91] Suppoſe the ſecond ſeries to be formed from the firſt, by the addition or ſubtraction of ſome indeterminate quantities; as a=b+c, a1=b1−d, &c. yet under this reſtriction, that the ſum of the firſt (n) terms of the firſt ſeries, ſhall approach indefinitely near to an equality with the correſponding (n) terms of the ſecond. Let that ſum in either ſeries be called A, the ſum of the ſecond n terms = B, the third C, and ſo on: upon a given right line from a pt. Δ take the portions n, 2n, 3n, let theſe be parts of the abſciſſae of a parabolic curve, erect the perpendiculars= A, B, C, to thoſe abſciſſae, and drawing a cure through their extremities, the ordinate to any abſciſſa x ſhall be [...] ∷Y, then if there be a ſecond parabola deſcribed upon the ſame axis, the abſciſſae the ſame, and its ordinates =a, a1, a2, a3, &c.

xp + gxp−1 hxp−2 .... qx2 + rx + s ∷ Y

And to determine the celerity of increaſe of the ordinate, ſuppoſing x conſtant [...] but the former of theſe two equations will require a correction.

[92]The poors rates of a number of years being given, to determine the rate of a given year according to the mean degree of advance.

A rate of this kind is generally upon the advance, and though it may be ſome years lower than the mean rate of augmentation gives it, in others it will be higher: when theſe irregularities are as equally diſtributed as poſſible, we approach very nearly to the mean law of increaſe, which may be diſcovered by the application of the foregoing problem—Add the rates of ten ſucceeding years together; if the diſtrict from whence they be taken be large, thoſe irregularities will enter into ſuch a ſum nearly in proportion of their probability and magnitude; and the accidental exceſs of the rate, proceeding from accidental ſcarcity, want of trade, or any other cauſe in one year, nearly counterbalancing the defect in another, ſuch a ſum ſhall approach indefinitely near what the mean law of increaſe if known would have given. Repeat the ſame operation with the next period of ten years, call theſe totals ſucceſſively A, B, C, then ſhall Y be the annual payment of the year x, according to the mean rate of increaſe for that term; and the next form gives the celerity of increaſe, and repreſents [93] in every diſtinct period of time, the adequate meaſure of the effect of thoſe cauſes which have increaſed it.

The ſame mode of proceeding will give us the decrement of the value of money, and its acceleration: with this we may compare the cauſes which the hiſtory of that time ſuggeſts, and approach as near to certainty in our reſearches upon this head as the ſubject will give us leave. If the data deduced from hiſtory have any tolerable degree of preciſion, the concluſion will be ſufficiently accurate: and at all events, if enquiry into ſuch ſubjects be neceſſary or uſeful, we ſhould not decline the trouble of enquiring into them upon the beſt grounds.

On Pariſh Regiſters.

The want of good political data has been lamented by almoſt every perſon who has undertaken any operations of political arithmetic, the following corrections to the preſent plan of our regiſters might be of conſiderable uſe.

A pariſh regiſter of burials ſhould contain every perſon buried in that pariſh of whatever ſect or religion; it would be moſt conveniently divided into columns, the firſt containing the [94] ſurname of the perſon; the ſecond his chriſtian name; third, day of the month; fourth, age; fifth trade; ſixth, diſtemper; ſeventh, married man, widower or batchelor; eighth, number of children born; ninth ſurvivors.

By placing the ſurname firſt, it would moſt eaſily be inſpected— Inſerting the trade of the perſon would nearly point out the number of manufacturers of every kind in the kingdom: but by comparing it with the following column it would ſerve a very uſeful purpoſe, and determine in a few years how far particular manufactures abridged the lives of mankind; and point out to us, if luxury will have its gratifications even at ſuch an expence, what foreign manufactures it might be politic to encourage the importation of; as the money we loſe in one branch may by proper attention be retrieved in another, and the number of our people preſerved; the eighth and ninth columns, the number of children and ſurvivors will likewiſe point out the further effect of particular trades upon population; and in conjunction with the ſeventh, give us the ſtate of matrimony; this laſt which I added after I had planned the reſt, from Dr. Price, will be of [95] great uſe in determining the value of ſome kinds of ſurvivorſhips.

The regiſter of marriage ſhould contain the ages of the parties; this would further enable us to judge of the ſtate of marriage in the kingdom, for the ſame reaſon legitimate and illegitimate children ſhould be diſtinguiſhed in that of births.

The regiſter of deaths in a houſe of induſtry, ſhould contain the day of the pauper's admiſſion —If of an infirm conſtitution—If admitted in ſickneſs, and with what diſtemper.

On the Intereſt of Money as allowed in the following Computations.

The loſs to an individual from a ſum of money taken from him a given number of years ſince, is equal to its preſent amount at compound intereſt.

The whole uſe and benefit to an individual of equal ſums, for equal times, are equal: and his loſs by being deprived of them is equal. Let a man be ſuppoſed to have paid a given ſum (for inſtance 100l) ten years ſince to any rate or tax; he has loſt the uſe and benefit of 100 pounds for the term of ten years paſt, and for [96] ever after—Let him at the ſame time have laid aſide 100l. to increaſe at compound intereſt to this period at four per cent. this ſum will have amounted to 148l. at the end of the term: if then this ſum be taken from him by a ſecond rate or taxation, what is it he loſes? the uſe and benefit of 100l. for the paſt term of ten years, and for ever after. But his loſs in the firſt caſe is equal to that in the ſecond, or equal to a preſent loſs of the amount of the ſum for the given term at compound intereſt.

What has been demonſtrated of one individual paying a certain ſum, holds true of any aggregate body of individuals paying any ſums.

And for ſimilar reaſons the loſs to an individual in being obliged to pay a given ſum, at the end of a given term of years, is leſs than if he had been compelled to pay it immediately.

This will be readily admitted in the caſes of two kinds of people, thoſe who put out money at intereſt, becauſe their income exceeds their expenſe, or who borrow for the contrary reaſon; but are the intermediate claſs who neither hoard nor borrow affected the ſame way?

[97]If the intereſt of the ſum taken away be ſmall in proportion to ſuch a man's income, ſuppoſe 1/500 part, it may become imperceptible but is nevertheleſs real: for if poſſible ſuppoſe the contrary, that it was abſolutely nothing; then it would be nothing if multiplied indefinitely, or fifty times for inſtance: but an accumulation of ſuch nothings as cut off 1/10 part of a man's income who did not ſave before, would be found a real difference.

Some concluſions upon a queſtion of conſequence having been lately drawn from principles contrary to theſe, it will not perhaps be thought unneceſſary to have given this demonſtration of them at length before the following calculations.

ARTICLE VI. CALCULATIONS.

[98]

PROBLEM I.

TO find the amount of an annual payment increaſing every year in a certain ratio, the rate of intereſt and time being given.

And the amount being given to determine the time.

1ſt Year's payment=s amount of 1l. in 1 year=r

Rate of increaſe 1: a number of years =t

Years1234 [...] [...]
Paymentssasa2sa3sat—2sat—1

Amount at the end of t years intereſt as above srt−1 s.rt−2 a .. srt−3 a2 ... srt−4 a3 ... srat−2 sat−1

the ſum of all theſe terms the amount in t years [...]

[99]Let t the term of years be required.

[...]

Corol. 1ſt. Let A=1 or all the payments become equal.

[...]

Corol. 2d. Let α, b, c, d be ſeveral annual payments commencing ſeverally t, t—β, t—γ t—δ years before the expiration of the period (t); and their joint amount ſhall be at the end of that term [...] and if an increaſing annuity=s be added to them for the whole term, the amount thus augmented becomes, [...]

PROBLEM II.

[100]

To find the value of the perpetuity of an annual payment increaſing every year in a certain ratio, the rate of intereſt being given.

Retaining the former ſubſtitutions we ſhall have the ſeveral annual payments, at the end of

Year12345
 s,sa,sa2,sa3,sa4
Preſent values / rsa / r2sa2/r3sa3/r4sa4/r5
Sum=Y= [...]
  [...]

Corol. Let R be the intereſt of 100l. for a year, A=advance of the ſame ſum, P=the perpetuity, if s remain conſtant, I=if it increaſe, d=the perpetuity if it decreaſe: in the former caſe a=o, in the ſecond it is affirmative, and in the laſt negative, and [...] and taking R = 3½ A = 1½

P : I ∷ R−A : R ∷ 4 : 7

P : D ∷ R+A : R ∷ 10 : 7

I : D ∷ R+A : R−A ∷ 5 : 2

[101]Agreeably to what was laid down in the compariſon of funds remaining fixt, or becoming more or leſs productive.

1ſt. Let it be propoſed to determine the difference of expence between maintaining the poor in a houſe of induſtry, and providing for them in their ſeparate pariſhes.

Suppoſing the poor maintained at the ſame expence as at Nacton, and that the increaſe of the rates of the pariſhes in the hundreds of Colnies and Carleton, if they had not been incorporated would have been the ſame with that of the ten pariſhes in the table (being the leaſt diſcovered) we are firſt to find the difference of expence of the two modes for the time paſt.

By problem 1ſt. the expence of the poor under the overſeers [...]. and by Cor. 1ſt. Prob. 1ſt, that of the corporation [...]

The middle year of the term from which average of the hundreds was taken, ended at Eaſter 53;

Rates of the ten pariſhes 53 =16006s.in 75=26905
2 Hundreds in 53=29753 s.in 75=50013

[102]The rate of advance appears to be 2,39 per cent.

The probable amount of the rates in the hundreds at Eaſter 1759, the end of the firſt compleat year after the admiſſion of the paupers into the houſe =S=s×a6=29753×2,396=34282 intereſt 4 per cent. s=29753a=1,0239r=1,04 t=17 then, [...]

Preſent debt of the corporation£4300 
Value of buildings, ſtock and Caſh in hand2500 
Balance1800—1800
Total expence of corporation37053
Balance ſaved by the act. 11243

Theſe ſums are the preſent value of the expences paſt, the future are to be determined upon the following ſuppoſition, that the advance of [103] the poor rates as taken from the ſame pariſhes will be diminiſhed ⅓ hereafter; and conſequently the expence of maintaining the paupers in the houſe reduced in the ſame proportion.

For the charge of the poor continuing under the pariſh officers—The reduced rate of advance will be found 2,39×⅔=1,5933; and A=1,015933: the probable amount of the charge of maintaining the poor has been found at Eaſter 75 = 50013, at Eaſter 76=50013× 1,015933=S=50809 then by Prob. 2d, [...]. or 105,565l.

For the future Expence of the houſe.

Average expence of the four laſt years £ 1646.11 excluſive of work, of the year 60, 61, 62, 63. £ 1165.10 the ratio of increaſe for twelve years=2,92 per cent.; of which the future by the hypotheſis will be ⅔. Therefore a=1,01947, but the ratio of increaſe to that term will be 102,92; and the annual expence at Eaſter 76=32931s. × 1,02933 =35902=s but [...]. ſhillings, or 87440 £.

[104]2d. Suppoſe the expence of the houſe had been nearly the ſame as that of Melton, or reduced in proportion of 31 to 27; and the future advance ⅔ of the paſt.

That the annual expence of the poors rate in the hundreds without an incorporating act would have been 3,506 per cent. for the paſt period, and ⅔ of that rate or 2,3372 for the future.

To determine the expence of the two modes, and the ſavings on the former.

The paſt expence of the houſe is found by reducing the former charge in that period in proportion of 31 to 27.

The future Expence is thus determined.

Annual charge Michaelmas 73 found in the foregoing queſtion=32931, reduced to Melton 27/34×32931=28681 and the rate of advance 2,92 per cent. ⅔×2,92=1,947 expence Eaſter 76=S×A⅔×a=28681×1,0292⅔×a= 29947. [...] 1458700×a=1515840 s.=75792l.

Expence of the Poor under the Pariſh Officers.
[105]

The charge for ſeventeen years laſt paſt is thus diſcovered; the rate of advance being 1,03506. =a by Hypotheſis, proceeding as in the correſponding caſe of the former queſtion, we have [...]

Future Expence under the Pariſh Officers by this Hypotheſis.

The mean advance 3,506=2,3372 the reduced advance: the rate of 76=S=s×A22 ×a =29753×1,0350622 × 1,023372 = 64987s. [...]

Of the Reduction of this laſt Hypotheſis.

1ſt. The annual expence of the houſe in 75 was found in queſtion ſecond=29947 . . . intereſt four per cent. the perpetuity of this charge =25×29947=748675s:=37433l.: . 15s.

[106]2d. Annual expence of the poor in their ſeparate pariſhes s×A22=29753×1,035622= 63649s. and proceeding as before, the perpetuity will be found=79378l.

On the Compariſon of the Reſult of the reduced Hypotheſis with the total Rates.

This Hypotheſis gives the preſent value of the balance in favour of a houſe of induſtry, 104,566l. when the rate of 75 in an unincorporated diſtrict of equal ſize amounts to 3182l. ×: dividing the former by the latter ſum, it gives the number of years purchaſe of the preſent rate which that advantage amounts to = 104,566/3182 = 32,933.... ſuppoſe ſo many diſtricts capable of being incorporated ſeventeen years ſince, as now pay 2 millions annually to the rates, the preſent value of their ſavings is 65,886,000l. and the value at the commencement of that term was 36,70 [...],000l.

Compariſon of this Reſult with the Rates of Eleven Pariſhes increaſing in a Degree rather leſs than the mean Advance from 1750 incluſive; to Eaſter 75; upon a Suppoſition that the annual Payment never will be augmented after the latter Term.
[107]

Rate of ten pariſhes in 53=16006s. advance 2,39 per cent.

Rate of 50 = 16006/1,02393 = 14911......of 74..26905

Additional Pariſh...8333/23244.......25852/52757

Here the rate of advance [...] the number of years purchaſe of the original rate, equal to the value of the amount of all the preceding payments at the end of the firſt term [...] and for that period the number of years purchaſe equalling the preſent value at the beginning of the term=24,09.

To find the remaining perpetuity; the laſt payment 52757, the preſent value of the perpetuity = 52757×28,571, the value at the beginning of the term [...], the rate of [108] the firſt year 23244, and the number of years purchaſe it was then worth of that rate [...].

Of the Intereſt of Owners and Occupiers in the Poors Rate. PROBLEM III.

To determine the different proportions in which owner and occupiers contribute to the ſupport of the poor, having the rate of increaſe of the charge given=a, amount of 1l. in a year=r, and the average length of leaſes=t.

Let 10 l. be the ſum a farm let out upon leaſe paid to the poor's rate the year preceding the contract: and be the rent what it will, if the poor's rate had been 2l. leſs, the tenant would with equal advantage to himſelf have been able to have added 2l. to it; if 5l. he might and would have raiſed in the rent the ſame ſum; if that payment were inſtantly annihilated, it would be added to the rent: therefore for the term of the leaſe the rent will be diminiſhed 10l. or the landlord will pay it.... And upon an equality of chance, there will be an equal number of [109] tenants at the preſent time in the 1ſt, 2d, 3d, and every year of the common term of leaſes (t): and upon the ſame account there will be no reaſon why the occupations of the tenants now in the firſt year of their leaſes, ſhould be more than thoſe in the ſecond, third, or any ſucceeding year. The occupations of all the tenants in every term, will according to the laws of probability be equal; as alſo the numbers in each claſs: therefore their conjoint intereſt, will be to that of all the owners, as the intereſt of (t) tenants occupying equal farms, one being in the firſt year, one in the ſecond, one in the third, &c. to the intereſt of all their reſpective landlords.

Let s be the poor rate of a given diſtrict.

[110]

Then the Sum of the Poors Rates in Years012345... t
Put n=1/rs...sasa2sa3sa4sa5:.. sat
Of which the Tenant pays [...]
Then the Tenants Intereſt will be the beginning of the year =Y= 1 [...]
2 [...]
3 [...]
4 [...]
t. [...]

[111] [...]

Call the affirmative Series = W the Negative = X Then [...]

[112] [...]

[113]To determine the charge of the owner = Z

The deduction from his rent for the term of the leaſe = s; let the rate of intereſt here be 1/p, the perpetuity of the rent charge= 100 p s; but the laſt year of the leaſe the rate becomes s. a, therefore the deduction in the firſt years rent from the ſucceeding tenant will be s. at; and the ſecond diminution (which takes place at the end of the year after the termination of the leaſe [...]: the perpetuity of which when the leaſe expires will be worth [...], the preſent value of which at any term in the leaſe, added to the former perpetuity 100ps, gives the total charge upon the owner: this will be when the leaſe terminates in Years [...] and the correſponding charge upon (t) landlords will be equal to the ſum of all the terms of this ſeries; hence [...]

[114]Suppoſing the lands throughout the kingdom upon an average to be under fourteen year leaſes, intereſt four per cent. rate of advance of the expence of the poor 3,5 per cent.; to determine the proportion in which the owners and occupiers in fact contribute to this payment.

Taking s = 10, we ſhall find the charge upon the [...] Owners [...] And upon the occupiers, [...]

[115]Then the real charge upon the owners, to that upon the occupiers ſhall be as 5140 to 350, or as 14⅔ to 1.

We may derive a reſult ſomewhat near this by the following method, which as it depends only upon the principles of common arithmetic, will be more univerſally underſtood.

The advance of rates being given at 3½ as before, at the end of fourteen years a farm which paid 10l. a year, the laſt year it was in the former occupier, will be raiſed to £16,2. Here the advance for the term of the leaſe will be £6,2, and ſuppoſing it equal every year, the annual increaſe of charge will be, 443l. therefore the advance upon the farmer at the end of year

1234567
,443..,886..1,329..1,772..2,215..2,658..3,101
891011121314
3,5443,9874,434,8735,3165,7596,202

The intereſt of a farmer in the beginning of the laſt year of his leaſe will be equal to the ſum he has to pay above the deduction from his rent, or 6,202; and in the ſame manner a tenant in the laſt year but one will have an intereſt of 5,759, added to the former ſum; the intereſt of a tenant in the firſt year will be the ſum of the [116] whole ſeries, and the intereſt of a tenant in the year of his leaſe

   Landlord
146,202 + 06,20210
135,759 + 6,20211,96120
125,316 + 11,96117,27730
114,873 + 17,27722,15040
104,43 + 22,15026,5850
93,987 + 26,5830,56760
83,544 + 30,56734,11170
73,101 + 34,11137,20280
62,658 + 37,20239,86090
52,215 + 39,86042,075100
41,772 + 42,07543,847110
31,329 + 43,84745,176120
2,886 + 45,17646,062130
1,443 + 46,06246,505140
14 Tenants total payments and Intereſt449,575980

The deduction from the rent in ten years is 980l. but at the expiration of the leaſes (neither intereſt or diſcount are here taken notice of) the ſeveral eſtates will be ſubject to an annual deduction from the rent 16,2, which amounts for the whole number to 226, 8; the perpetuity of which is worth at 4 per cent 5670l. which added to [117] the former ſum 980, gives 6650 for the proportion of charge to the landlord: which is to that of the tenant, as 6650, to 450 nearly or as 14⅕ to unity. The reaſon of the difference of the groſs ſum is the neglecting all diſcount on both ſides equally, which brings out the proportion nearly the ſame.

On Revenues.

1ſt. To determine in what No. of years a land tax producing 300,000 a year at this time, and encreaſing in the degree laid down above, will diſcharge the public debt.

Put the No. of years = t, Y= the preſent debt; then by Problem 1ſt, [...] and for the firſt aſſumption take ⅓ rt = atrt = 7,626 and [...]

Put t = 71    
Putg t =rtatrt—at =7,626
Putg t = 7111,50163,62017,8815+Error ,2555
t = 7011,11223,55517,5551−Error ,0689
70+n=t    

and Emer. Alg. B. 1. Prob. 80. n [...] and t = 70,3 very nearly

[118]2d. To determine in what time a fund of 750,000l. with the addition of ſuch a tax from the colonies, being increaſed in the fifth year 189,863 l. in the next 22,500l. and in the tewlfth 224,580l. will pay off the public debt.

By Corol. 2d. Prob. 1ſt. we find [...]

Here α = 750,000, b = 189,863, c = 22,500, d = 224580, β = 5, γ = 6, δ = 12, s = 300,000, a = 1,018285, r = 1,035, X = 137,000,000 x = 5,137,500.

[119]

 Taking t =42t=41
A =2,770,1552,642917
+ B....550,180524652
+ C....62,17459114
+ D...453,083428588
+ E....2,747,9702,648647
 6,5835626,303918
−F....1,2532181,230715
 5,330,3445,073,203
x =5,137,5005,137,500
+ Error192844064297—Error
t=41 + n. . .n = 64297/257141 = ,25
  t=41,25 nearly

PROBLEM IV.

Let the durations of war and peace be as t to n, the ſum of money borrowed during a war be ts, what revenue (x) continued from the beginning of a war of t years, will diſcharge the whole in t+n years, ſo that a nation may probably expect to begin the next war without a debt?

[120]Here the annual extraordinary grants in the time of war=s; the preſent value of all theſe grants at the end of t+n years will be, putg r=the amount of 1l. in a year.

[...]

Call v the preſent value of an annuity of 1l. for t+n years; then vrt+ n ſhall be the amount of 1l. in t+n years, an x × vrt+ n the amount of the required additional revenue = A; then [...], and putting the ordinary expence=E, we get E + x = the total revenue.

Suppoſe in the term of peace n years, the debt reduced to ts; the annuity which would have diſcharged this in t+n years ſhall be x = [...]; let I the intereſt of the increaſed debt; then the annual payment ſhall be E + 1 + x: if the additional debt be propoſed to be diſcharged at the end of the probable term of peace.

And the proportion of expence upon theſe two ſyſtems ſhall be E + x, to E + x + 1.

In the preſent inſtance t = 7, n = 12, ts 76 millions; s = 10,857,142, and [...] [121] then ſhall v=the preſent value of an annuity of 1l. for 19 years=13,71 nearly, and [...]: and adding the ordinary expences with Dr. Price= 4,850,000 = E E + x = 9,861,400.

But eleven millions have been diſcharged, then ts = 65 millions; and [...]; and E = 4,850,000; therefore E + 1 + x = 14,016746.

In determining the abſolute burthen of the taxes, their annual amount was taken at 18 millions; and thus it appeared equal to 1s. 10½d. in the pound. The expences of collecting, &c. ought to have been added, which would have increaſed the 10 millions to nearly 12, and the burthen to 2s. 3d. It is requiſite to add, that the numbers are all copied from one of the former editions of Dr. Price's pamphlet, and are not according to his laſt alterations, which would have given reſults, rather more favourable ſtill, with reſpect to the different parts of the public burthen here enquired into.

FINIS.
Notes
*
Apendix, Note A. B.
*
Appendix, Note D.
*
Note E.
*
Note D.
Note D.
*
I have declined all computation of the advantages of theſe foundations deduced from the profit of Heckingham: at Midſummer next, nine years from the opening of the houſe, half the original debt of 7000 will be paid off; and the rate reduced. We cannot expect its ſucceſs to be univerſally equaled; the care of the directors, and the particular attention which Mr. Cooper has conſtantly paid to it, have put its funds upon a very ſuperior footing: the promoters of theſe inſtitutions muſt greatly regret that he has laid aſide an intention he had formed of adding a full account of the management of them, to the diſſertations upon this ſubject he has already given to the public.
*
Locke on civil government, B. II. c. 7.
*
Mr. Potter's obſervations, p. 25, 31.
*
Are the laws you have given the Athenians the beſt ſyſtems poſſible? The beſt, replies Solon, they are capable of receiving. An anſwer which every legiſlator ought thoroughly to underſtand. Monteſquieu, Eſp. de loix, L. 14. c. 21.
*
Nam cunctas nationes et urbes populus, aut primores, aut ſinguli regunt: delecta ex his et conſtituta reipublicae forma, laudari facilius quam evenire, vel ſi evenit haud diuturna eſſe poteſt. Tac. Ann. Lib. IV. c. 33.
*
De moribus Germanorum.
*
If we ſuppoſe theſe decrements continual proportionals inſtead of equal quantities, the numbers and ſums will be indexes of powers, the reſult the ſame, and the form of demonſtration: but the arithmetical progreſſion will be more univerſally underſtood.
*
That quantity of flour and meal made into bread, &c. equalling 6, 07 quarters of wheat at the mean price.
11, 5 Barrels of beer equalling in value 2, 704 quarters of malt, allowing 10½ combs of malt to 29 barrels.
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