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.
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 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 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, (
Apendix, Note A. B.
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 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.
Appendix, Note D.
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 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.
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.
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 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.
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.
59
Michael.
63
East.
68
Michael.
72
Price of Provisions
703..4
810..8
896..4½
1018
Geometrical Progression
703
788
895..5
1018
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 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;
Note E.
I have there demonstrated the operations of this payment upon the price of provisions.
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 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,
Note D.
Upon the old system
48296
Upon the new with the balance added
37053
Balance in favour of the latter
11243
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,
Note D.
the present value of all the future payments, had there been no act of incorporation, would be—£. 105565
Of the incorporation
87440
Future saving
18125
Past do.
11243
Sum saved present value
29368
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 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 years
8,972,865
Probable future saving
14,465,280
Total advantage
23,438,145
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 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.
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.
But let us imagine the expence of the house 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 1775
32272
56,066
 
Future do.
75792
195,390
 
 
108,064
251,456
143,392
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.
75792
195,390
2d.
37433
79,378
Sum
113225
274768
Mean
56612
137384
The advantages by this corrected Hypothesis stand ultimately as follows,
 
Incorporation.
Old System.
Exence to 75
32272
56066
Future do.
56612
137384
 
88884
193,450
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 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 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 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 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; 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 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 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 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 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 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 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.
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 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 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, 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 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 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 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.
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.
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
Locke on civil government, B. II. c. 7.
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 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 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
Mr. Potter's observations, p. 25, 31.
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 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 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 (
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.
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 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 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,
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.
That in every nation 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
De moribus Germanorum.
Tacitus himself has transmitted to us the original outline of its foundation.
APPENDIX.
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 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 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 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 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 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: 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 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.
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.
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 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.
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; 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
Advance from the deficiency in year the
 
1st
2
3
4
5
6
7
Year.
1
5
4
3
2
1
0
0
 
2
 
5
4
3
2
1
0
 
3
 
 
5
4
3
2
1
 
4
 
 
 
5
4
3
2
 
5
 
 
 
 
5
4
3
 
6
 
 
 
 
 
5
4
 
7
 
 
 
 
 
 
5
 
 
5
9
12
14
15
15
15
 
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.
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 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
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. 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 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 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, 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 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 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 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 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.
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.
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.
 
Years
Charge
Decrement of money
Burthen
Increment of burthen
Absolute burthen in the pound.
Total Taxes
1755
5,964,283
 
1
0
 
 
 
1774
10,000,000
2,89
,975
−, 025
£.
s.
d.
2,16
1,11
+ ,11
 
1
10½
0,00
1,67
+ ,67
6 times too great
 
 
 
Debt
1755
72,000,000
 
1
0
 
 
 
1774
137,000,000
2,89
1,108
,108
 
 
 
2,16
1,266
,266
 
 
11¼
0,00
1,903
,903
3, 4 times too great
 
 
 
Peace Establishment & Surplus
1755
3,399,283
 
1
0
 
 
 
 
 
2,89
,925
−,075
 
 
 
1774
5,119,320
2,16
1,002
+ 002
 
 
11¼
 
 
0,00
1,506
+,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.
Years
Wheat per quarter
Averages
Malt do.
Averages
 
s.
d.
s.
d.
s.
d.
s.
d.
1758
37
1½
 
 
28
 
 
 
9
28
4
29
8
21
6
23
2½
60
28
 
 
 
22
 
 
 
61
25
3
 
 
21
4
 
 
62
30
6
 
 
26
 
 
 
3
32
8½
37
2
30
 
28
6¾
4
39
 
 
 
29
8
 
 
5
46
6
 
 
28
7½
 
 
66
43
9
 
 
31
6
 
 
7
52
3
 
 
34
4 1/
29
1
8
51
1¼
43
10½
29
6
 
 
9
35
 
 
 
23
9
 
 
70
37
3½
 
 
26
4
 
 
71
55
2¼
 
 
31
6
 
 
2
54
8
 
 
34
 
34
7½
3
54
¾
53
10
37
 
 
 
4
51
5
 
 
36
 
 
 
 
Beef per Stone.
Cheese per 100 w t.
 
 
 
Averages
 
 
Averages
 
s.
d.
s.
d.
s.
d.
s.
d.
1758
3
3
 
 
30
 
 
 
9
3
¾
3
1 15/16
26
4½
27
2 10/16
60
3
 
 
 
25
6
 
 
1
3
1½
 
 
27
 
 
 
62
3
 
 
 
27
10½
 
 
3
3
3
3
4
30
6
30
9 14/16
4
3
4½
 
 
32
2
 
 
5
3
4½
 
 
32
9
 
 
66
3
4½
 
 
32
6
 
 
7
3
10½
 
 
32
 
 
 
68
3
9¾
3
8 14/10
17/20
32
5
33
2 6/16
9
3
10½
 
 
34
 
 
 
70
3
9
 
 
35
3
 
 
71
3
10½
 
 
35
6
 
 
2
4
5¼
4
2 1/16
38
 
34
3 7/16
3
4
1½
 
 
32
1¾
 
 
4
4
3
 
 
31
6
 
 
Provisions consumed in kind in eight weeks, from the books at Heckingham.
Persons
Meal
Stone
Flour Second.
St.
Meat Beef
St.
Cheese
Stone
Beer
Barrels
260
79
20
18
17
6
260
78
19, 7
18
17
6
264
73
18
18
17
6
260
66
16
17
17
5½
256
66
16
17
17
5½
240
66
16
17
17
5½
238
68
15
16
17
5
238
68
15
16
17
5
2016 Per Week.
564
135½
137
136
44½
10 Persons per Annum.
145, 5
34, 96
 
 
11, 5
That quantity of flour and meal made into bread, &c. equalling 6, 07 quarters of wheat at the mean price.
Wheat 6, 07 qrs.
35, 35
35, 1
2, 704
11, 5 Barrels of beer equalling in value 2, 704 quarters of malt, allowing 10½ combs of malt to 29 barrels.
Malt qrs.
Increase of the Expence of maintaining Ten Men One Year from Michaelmas
1759,
to Michaelmas
1772.
Commodities
Quantity
Exp. Michael. 59
Michaelmas 63
Easter 68
Michaelmas 72
Wheat qrs.
6, 07
471..10½
180.. ¾
555..8½
225.. 7¼
622..8½
266..3¾
718... ¼
326..9¼
Malt qrs.
2,704
62..8¾
77.. 2¼
78..7¾
93..7
Beef
Stone
35, 35
109..8
117.. 9
132..1
147..3
Cheese
Stone
35, 1
119..5
135.. 2
145..8
150..5
Sundries
 
231..6¼
254..11½
273..6
300..—
Increase of Prices
703..4¾
810..8
896..4½
1018..—¼
Geometrical Progression
703
788
895,55
1018..—
Annual advance per cent. 2,89 for thirteen years the whole term; 3,63 for the first four years.
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 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 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:
Prices
703
788
896,33
1018
Geo. Prog.
703
788
895,55
1018
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; 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 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 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 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 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 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 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 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 ∷
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.
Table of the ratio of Increases of the Charge and Burthen of the Poor's Rate in different Districts.
 
Years
Charge
Increase of charge percent.
Burthen, Do.
Mr. Potter's numbers general amount
9
2,200,000
3,506
+ ,6
1,32
3,000,000
Bristol from Dr. Woodward
20
4,000
4,688
+ 1, 75
2, 47
10,000
Hundred of Fouhoe exclusive of 3 parishes
10
2030
3,885
+ ,97
1, 69
2972
Hundreds of Mitford and Launditch exclusive of one parish
7
3411
4,58
+ 1,64
2,36
4162
Ten Parishes
22
800
2,39
—, 486
,22
1345
 
 
 
 
Decrt. of money 2,16
Decrt. 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, a
1
a
2
a
3
a
4, The 2d
b, b
1
b
2
b
3
b
4. Suppose the second series to be formed from the first, by the addition or subtraction of some indeterminate quantities; as
a
=
b
+
c, a
1=
b
1−
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,
2
n,
3
n,
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, a
1,
a
2,
a
3, &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.
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 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 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 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 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?
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.
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
Years
1
2
3
4
Payment
s
sa
sa2
sa3
sat —2
sat —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
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.
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
Year
1
2
3
4
5
 
s,
sa,
sa2
,
sa3
,
sa4
Present value
s / r
sa / r2
sa2
/r3
sa3
/r4
sa4
/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
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
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
=29753
a
=1,0239
r
=1,04
t
=17 then,
Present debt of the corporation
£4300
 
Value of buildings, stock and Cash in hand
2500
 
Balance
1800—
1800
Total expence of corporation
37053
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 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 £.
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.
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.
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.
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 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 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.
Then the Sum of the Poors Rates in Years
0
1
2
3
4
5...
t
Put
n
=1/
r
s..
.
sa
sa2
sa3
sa4
sa5
:..
sat
Of which the Tenant pays
Then the Tenants Interest will be the beginning of the year =Y= 1
2
3
4
t.
Call the affirmative Series = W the Negative = X Then
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 100
ps,
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
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,
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
1
2
3
4
5
6
7
,443..,
886..
1,329..
1,772..
2,215..
2,658..
3,101
8
9
10
11
12
13
14
3,544
3,987
4,43
4,873
5,316
5,759
6,202
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 whole series, and the interest of a tenant in the year of his lease
 
 
 
Landlord
14
6,202 + 0
6,202
10
13
5,759 + 6,202
11,961
20
12
5,316 + 11,961
17,277
30
11
4,873 + 17,277
22,150
40
10
4,43 + 22,150
26,58
50
9
3,987 + 26,58
30,567
60
8
3,544 + 30,567
34,111
70
7
3,101 + 34,111
37,202
80
6
2,658 + 37,202
39,860
90
5
2,215 + 39,860
42,075
100
4
1,772 + 42,075
43,847
110
3
1,329 + 43,847
45,176
120
2
,886 + 45,176
46,062
130
1
,443 + 46,062
46,505
140
14 Tenants total payments and Interest
449,575
980
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 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
1
st,
and for the first assumption take ⅓
rt
=
at
⅔
rt
= 7,626 and
Put
t
= 71
 
 
 
 
Putg
t
=
rt
at
rt —at
=
7,626
Putg
t
= 71
11,5016
3,6201
7,8815
+Error ,2555
t
= 70
11,1122
3,5551
7,5551
−Error ,0689
70+
n
=
t
 
 
 
 
and Emer. Alg. B. 1. Prob. 80.
n
and
t
= 70,3 very nearly
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.
 
Taking
t
=42
t
=41
A =
2,770,155
2,642917
+ B....
550,180
524652
+ C....
62,174
59114
+ D...
453,083
428588
+ E....
2,747,970
2,648647
 
6,583562
6,303918
−F....
1,253218
1,230715
 
5,330,344
5,073,203
x
=
5,137,500
5,137,500
+ Error
192844
064297—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?
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
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.