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Survivor of Two Lives of Equal Ages, or not more than five years' difference. The first col. gives the ages of the two lives, or of the younger of the two :

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Note-The first two columns of this Table were not included in the Act of 1808. They were supplemented by the Act of 1812.

No values beyond £80-81 are given in the tables, nor at that period did the stock ever reach that price. The scheme was propounded with a view to the reduction of the National Debt, and the annu. granted under it are called sinking fund annu. Returns of the amount of stock exchanged for such annu. were ordered to be laid ann. before Parl. In the following year the limit of the annuity or annuities to be granted on any one life was extended (by 49 Geo. III., c. 64) to £3000; and the personating of nominees, or forging certificates, made felony. In 1812, 1816, and 1817, further modifications.

We believe the recommendations from time to time made to the Gov. by Mr. Francis Baily, regarding the desirability of exchanging Gov. stocks for life annu., led to the passing of this measure. The annuitants of this class were included in the Obs. of Mr. John Finlaison in 1829, and of Mr. A. G. Finlaison in 1860.

Mr. Milne informs us that he mentioned the subject of these annu. more than once to a very able and well-informed member of the Gov., not long after the practice of granting them commenced. None were then granted on lives under 35 years of age; and the gentleman alluded to remarked that the applicants for annu. were chiefly aged persons, and it was desirable that a safe and advantageous mode of employing their savings should be afforded them. After 1816, those annu. were granted to persons of all ages above 21 years.

In 1808 Rev. Jeremiah Joyce pub. The Arithmetic of Real Life, which was stated to include "a complete reformation of all tables for calculation of annu., etc." We have never been able to meet with the work.

In 1809 Mr. Fortune, of the Stock Exchange, pub. a treatise on National L. Annu. In 1810 was pub. the first vol. of Mr. Francis Baily's famous work: The Doctrine of Life Annu., and Assu. analytically investigated and practically explained; together with several useful Tables connected with the subject. To which is now added an Appendix containing a new method of calculating and arranging such Tables. The 2nd and concluding vol. was not pub. until 1813; but it will be more convenient to speak of the entire work at one time, and we propose to do so under the first date. The author says:

In the year 1808 I pub. a Treatise on the Doctrine of Int. and Annu., wherein I entered into a full investigation of all the principles relative to that science; together with its application in the various questions arising from any commercial, political, or financial inquiries. In the preface to that work, I signified my intention of prosecuting the subject still further, so as to take in the whole doctrine of life annu. and assu. The present treatise therefore must be regarded as a continuation of the work above alluded to; and will, I believe, contain all that is useful or interesting in the science. The importance of the subject in the present day cannot be doubted. The incomes likewise annexed to all places, civil and military; all pensions and most charitable donations; these and others of a like kind are annu for life. Moreover the dividends arising from a great part of the cap. in the public funds are, by the wills of the donors, and from other causes, rendered of the same nature. Besides which, many life annu. have been granted by individuals, by parishes, by corp. bodies, and by the Gov. itself. So that a great part of the personal estate also of this country is involved in a consideration of this subject.

This work, from which we shall have occasion to quote very frequently in these pages, was in many respects the most practical and the most able which had appeared on the subject of Life Annu.

An appendix to the 2nd vol. was principally devoted to the purpose of explaining the construction and uses of tables for determining values of Life Annu., calculated at a vast sacrifice of time and labour by Mr. George Barrett since deceased; formulæ were given for calculating from tables of that kind the values of temporary and deferred Life Annu. and Assu., and also for determining the values of Annu. and Assu. when the annu. or the sum assu., instead of remaining always the same, increases or decreases from year to year by equal differences, with considerably greater facility and expedition than the same things could have been effected with by the tables and methods of calculation in previous use.-Milne.

In this year (1810) also Mr. Wm. Campbell pub. The Values of Annu., from £1 to £1000 p.a. on single lives from the age of 1 to 90 years; with the number of years' purchase each annuity is worth, and the rate of int. the purchaser receives. With the amount of the several rates of the legacy duty payable according to the statute on the value of annu. This vol. had absorbed a vast amount of labour. Its use has now passed

away.

In 1811 Mr. Wm. Inwood pub. first ed. of his now famous tables, and therein were contained tables of annuity values, etc.

In 1812 Mr. Francis Baily presented to the Royal Society an account of the labours of Mr. George Barrett, of Petworth, who clearly was the first discoverer in England of the modern arrangement of Life Tables. Mr. Baily says:

The more immediate object that I have in view is to lay before the So. a new method of arranging the tables for determining the value of life annu.: whereby a considerable portion of the time and labour employed in such calculations may be avoided, and their application to the solution of various problems connected with the subject rendered more extensive and easy.

There has been some controversy upon the question of priority of discovery of the method employed by Barrett, and we shall refer to it more in detail under head of COLUMNAR METHOD.

In 1812, by the 52 Geo. III. c. 129, the Acts of 1808-9 were amended to the extent that whereas in these Acts no provisions were made for regulating the value of annu. when the price of 3 p.c. Consolidated or reduced Bank Annu. should be under £60 or above £81, this present Act provided detailed values for fluctuation in prices between £50 and £60, and further provided that for values beyond £81, the annu. should be the same as for the value £81. To prevent the multiplying of tabular matter, we have included the values between £50 and £60 in the abstract of the table given in our notice of the Act of 1808.

In 1813, by 53 Geo. III. c. 141, sec. 2, The Amended Annu. Inrolment Act (which repealed the Act of 1777), it was enacted that within 30 days after the execution of every bond, instrument, or other assu., whereby any annu. or rent-charge should be granted for one or more life or lives, or for any term of years, or greater estate determinable on one or more life or lives, a memorial of the date of every such deed, bond, instrument, or other assurance, of the names of all the parties and all the witnesses thereto, and of the person or persons for whose life or lives such annu, or rent-charge should be granted, and of the person or persons by whom the same was to be beneficially received; the pecuniary consideration or considerations for granting the same, and the annual sum or sums to be paid, should be inrolled in the High Court of Chancery, in the form provided by that Act. Otherwise every such deed, bond, instrument, or other assurance should be null and void to all intents and purposes.

By sec. 3 of the same Act, it is further enacted that if any such annu. should be granted by, or to, or for the benefit of, any co. exceeding in number ten persons, which co. shall be formed for the purpose of granting or purchasing annu., it should be sufficient in any such memorial to describe such co. by the usual firm or name of trade. By sec. 8 all contracts for the purchase of an annuity with any person being under the age of 21 years should be and remain utterly void; any attempt to confirm the same after such person shall attain the age of 21 years notwithstanding.

The Act did not extend to Scotland or Ireland.

This Act was drawn by Mr. Sugden (now Lord St. Leonards), and its general effect was-for it required and received several amendments in details to render applications to the Courts to set aside "unconscionable bargains" of comparatively rare occurrence; and to place securities for L. annu. on as firm a foundation as any other class of security.

It is a remarkable fact, already noted, that the Tuscan Gov. by a law dated 30 Dec., 1814, authorized the use of Ulpian's Table for the valuation of L. annu.-a table that had lain dormant probably for near sixteen hundred years; and this too in the face of the existence of all the Tables we have here recounted as having been brought into existence since with all their acknowledged and progressive improvements.

Again we reach another very important land-mark-a double one-in the history of L. Annu.—that is, the pub. by Mr. Joshua Milne, in 1815-the Waterloo year-of A Treatise on the Valuation of Annu. and Assu., etc., in which was contained, and first made known, the since famous CARLISLE TABLE OF MORT. The work contained 50 T. of money values, all calculated upon results deduced from this new Mort. T.: those relating to L. Annu. being calculated upon the same extended scale as the T. deduced by Dr. Price from the Northampton Table.

The work of Mr. Milne, apart from the fact of its containing the Carlisle T., has always been justly regarded as one of very great weight and authority. We shall have occasion to make the reader familiar with a considerable portion of its contents in the course of these pages. The author gives in the introduction of the work the following outline of its contents, combined with some interesting notes on the labours of his predecessors: The values of annu. on lives are treated of in the 4th chap., and it will be found that the most intricate questions respecting them may be solved by means of tables containing the values of annu. on the lives involved, considered singly, and on the joint continuance of the lives in the different combinations that may be formed out of them. An easy and expeditious method of calculating such tables is furnished in the solution of the first problem, and its practical applications are illustrated by logarithmical formulæ, and specimens of the computations.

From hence it must be obvious that that first problem is of great importance in these inquiries; in fact, we owe all the best tables of the values of annu. on lives that have been calculated to the formula by which it is resolved, and for that formula we are indebted to Mr. Simpson, who at first gave it in the 7th corollary to the first problem in the Doctrine of Annu. in the year 1742, and showed its extensive utility.

It is remarkable that altho' the method of calculation indicated by the formula last mentioned is so simple that the truth of it may easily be demonstrated without algebra, and the labour saved by it is prodigious, yet it did not occur to our celebrated countryman Dr. Halley, who first constructed a table of mort., and showed how the prob, of life and death, and the values of annu. on lives, might be determined by such tables: he informs us that he had endeavoured in vain to discover a shorter method of calculation than that which he employed. Euler too was at one time stopped by this difficulty, but afterwards fell upon the method which Simpson had previously pub.

It is still more remarkable that M. de Parcieux, who has repeatedly mentioned Mr. Simpson's work, should not have availed himself of that compendious method of calculation, in constructing the tables of the values of annu. on single lives which he has given. They have cost him nearly 50 times the labour which would have been required in that way, and the chances of error have been multiplied in the same proportion: the necessary inference is that De Parcieux had not read this part of Simpson's treatise; it is also mentioned both by St. Cyran and Florencourt, and the same remarks apply to them, with reference to the tables of life annu. they have pub.

After further enumerating in a very careful manner the labours of his predecessors-or rather we should say, of some of the principal of his predecessors-in reference to the construction of Mort. T., he continues:

As none of these tables appear to me to give the values of life annu. for the common average of England, or for the bulk of the people in most of the other countries of Europe at present, with sufficient accuracy, I have calculated those in this work, by which in my opinion the values of lifeinterests in general, at least in this country, may be determined nearer than by any others extant; but this depends principally upon the determination of the law of mort., and that is discussed in its proper place.

The annuity values deduced from this the CARLISLE Table, are given in the margin.

Mr. Milne added the following, in which most of us will concur : "It may be useful to observe, that it is of much greater importance that T. of Values of L. Annu. should be derived from the true law of Mort., than that those which are calculated from any one T. of Mort. should be very copious."

In 1816, by the 56 Geo. III. c. 53, it was enacted that Long Annu. might (in add. to Consolidated and Bank annu.) be exchanged on annu. on the lives of the holders or their nominees under the provisions of the Acts of 1808, 1809, and 1812, the values to be governed by the prices quoted in the Gazette from time to time. Provision was also made as to payments of annu. to nominees who should go to reside abroad after annu. were granted; but only in Kingdoms or States in Europe "in amity with his Majesty"!

Table-4 p.c.

Age.

Years' Purchase.

IO

19.585

15

18.956

20

18.363

25

17.645

30

16.852

35

16.041

40

15'074

45

14'104

50

12.869

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Early in this year, Mr. Preston, M.P., moved in the H. of Commons for leave to bring in a Bill To restrain the Grants of Annu. on the terms of being re-purchasable. This was opposed by Mr. Serjeant Onslow, on the ground that such a Bill would increase the distress it sought to remedy; as most assuredly it would. Leave was given to bring in the Bill, but it was not proceeded with.

In this year also Mr. Wm. Rouse pub. An Investigation of the Errors of all writers on Annu., in their valuation of half-yearly and quarterly payments; including those of Sir Isaac Newton, De Moivre, Dr. Price, Mr. Morgan, Dr. Hutton, etc., etc. With tables showing the correct values, when payments are made in less periods than yearly and a specimen of a set of tables on a new principle (now in the press) for the valuation of leases, estates, annu., church livings, or any income whatever.

In 1816 also Mr. Milne's famous art. on Annu. appeared in the Supplement to the Ency. Brit., to which all subsequent writers on the subject, including ourselves, have become more or less indebted. In the same year there appeared in Thom. Ann. Phil. a paper On Annu., on Imaginary Cube Roots, Roots of Binomials, by Mr. W. J. Horner; and in No. 13 of the Pamphleteer, a paper by Mr. E. B. Sugden: Considerations on the rate of Int. and on redeemable Annuities.

In 1817, by 57 Geo. III. c. 26, some important modifications were made regarding the granting of Gov. L. Annu. By the previous Acts no annu. could be obtained except in exchange for Gov. Stocks, and none whatever on the lives of persons or nominees under the age of 35. By this Act annu. could be purchased for money, although the amount of the annu. was still made to depend upon the price of Consolidated or Reduced Bank Annu. (at the option of the purchaser). The age of annu. or nominees was reduced to 21; and £4 and 5 p.c. annu. stock was permitted to be exchanged for L. annu., the values of such stocks being first reduced to the values of 3 p.c. annu., in order to regulate the amount of the annu. to be granted. The Act also permitted the sale of deferred annu. We find it recorded that at the end of eleven years, or in 1828, the Commissioners had only sold annu. of this class involving a payment of £14,000 p.a.

In this year Mr. Fred. Blayney pub. A Practical Treatise on L. Annu., including the Annu. Acts of the 17th and 53rd Geo. III.; also a synopsis of all the principal adjudged cases under the first Act, together with select modern, and useful precedents, etc.

In 1818 a Com. of the H. of Commons sat on the Usury Laws, and various witnesses were examined. The Committee found in its resolutions (inter alia) that of late years the

constant excess of the market rate of int. above the rate limited by law, had added to the expense incurred by borrowers on real security, and that such borrowers had been compelled to resort to the mode of granting annu. on lives; a mode which has been made a cover for obtaining a higher rate of int. than the rate limited by law, and has further subjected the borrowers to enormous charges, or forced them to make very disadvantageous sales of their estates.

One of the witnesses called before the Committee was Mr. Sugden (now Lord St. Leonards). He stated that when the market-rate of int. was above the legal rate, the landed proprietor was compelled to resort to some shift to evade the Usury Laws. He had known annu. granted for three lives at 10 p. c. upon fee-simple estates unincumbered, and of great annual value, in a Register County. He had also known annu. granted for four lives, and more would have been added, but for the danger of Equity setting aside the transaction on account of the inadequacy of the consideration. Latterly, many annuities were granted for a term of years certain, not depending on lives. On being asked whether, were there no laws limiting the rate of int., better terms could or could not have been obtained, he answered: I am decidedly of opinion that better terms could have been obtained for there is a stigma which attaches to men who lend money upon annu. that drives all respectable men out of the market. Some leading men did latterly embark in such transactions, but I never knew a man of reputation in my own profession lend money in such a manner, although we have the best means of ascertaining the safest securities, and of obtaining the best terms.

In 1818 also Mr. John Clark, who was then engaged in founding the European (No. 1), wrote a pamphlet in support of the claims of that office, on the ground that it meant to conduct annuity transactions on more equitable terms than had formerly prevailed. He says:

Annu. at present are either certain or redeemable, at the option of the grantor: if certain, they pay the annu, amounting to 12, 14, 16, or 18 p.c., as long as the life or lives selected shall continue to exist; but if redeemable, it may be paid off at any period, by six months' notice, or six months' advance of the annu., in addition to the sum originally borrowed. In either case the terms are hard on the granter, who, perhaps, through some temporary want of a particular sum, is induced to grant an annu. at the high rate before stated, which he must either continue to pay as long as he lives, or return the sum originally borrowed, after having paid perhaps an excessive annu. for years.

It may be well here to state that the practice of dealing in annu. so far as ins. offices were concerned was almost the reverse of what it is now. The office, instead of receiving a principal sum of money, in consideration of which it was to grant an annu. for the life of some particular person, used to advance a sum of money, in respect of which the borrower agreed to pay a certain annuity-often varying from 12 to 18 p. c.-during the remainder of his life. This method of dealing in annu. originated, as we have already intimated, in the sixteenth or seventeenth cent. ; and was designed especially to evade the Usury Laws.

In 1819 there appeared in Dr. Rees' Cyclopædia, an art. on L. Annu. This was written by Mr. W. Morgan. In the same year there was pub. by Wm. Tate, The Calculations of L. Annu., and the Public Funds Simplified and Explained, etc.

In 1820 Mr. Wm. Hendry pub., The Method of Calculating the Values of Life Annu., Assu., Fines Payable on the Renewing of Leases, etc., etc.; with an appendix containing Tables of the Values of Life Annu. by Stat. 36 Geo. III. c. 52.

In 1821 the 2nd ed. of Mr. Morgan's Principles and Doctrine of Assu. and Annu, on Lives was pub. The formula for determining the values of contingent reversions, originally given by the author in the Phil. Trans., were in this ed. substituted for the approximations given in the 1st ed.; and it contained tables of the Values of Annu. on single and joint lives calculated from the Northampton and Swedish Tables, taken from Dr. Price's Observations, etc. Otherwise there was nothing new, except a T. showing the number of persons ins. in the Equitable So. who died of each disease in each decade of age from 10 years to 80, and above 80 years of age during the term of 20 years, commencing with 1801. The want of a proper explanation of the facts connected with the compilation of this T. led to some misunderstanding, of which we shall speak under EQUITABLE EXPERIENCE TABLE.

In 1821 Mr. J. B. Benwell pub. An Essay on Int. and Annu., chiefly respecting those cases when compounded by instalments intercepted within yearly, as half-yearly, quarterly, momently; embracing a summary of the ambiguities averred of the solutions on Dr. Price's and De Moivre's principle, with a critical examination into the source of them, etc. In 1822 an Act was passed, 3 Geo. IV. c. 92, to explain the Act of 1813 regarding the inrolment of memorials of grants of annu. There is nothing very special in it. An annu. deed, a memorial of which had been inrolled, was declared valid, though the deed itself had not been inrolled (sec. 2). This Act was not to give add. validity to any deed, nor to give effect to any deed declared void, or affect any proceedings at law commenced before 31 May, 1822.

In 1823 Mr. R. Thomas pub. Tables of the Values of Annu. and Assu.

In 1824 Mr. Francis Corbaux pub. An Inquiry into the State of the National Debt, in which was embodied a plan of finance for the redemption of the National Debt., upon the principle of Terminable Annu.; and an appendix on State Lotteries, with suggestions

respecting a perpetual lottery "upon a system equitable, productive, and unobjectionable," in aid of the plan of redemption.

In the same year Mr. Peter Watt pub. Comparative Tables of Rates of L. Assu. demanded in Scotland: with an exposition of the doctrine of Life Ins. and annu.: showing how the rates are calculated, and the present value ascertained, when claimed on a bankrupt estate or sold for their true value.

In 1825 Mr. Francis Corbaux pub. The Doctrine of Compound Int. illustrated and applied to Perpetual Annuities, to those for terms of years certain, to L. Annu., etc., with Tables giving the current values of annu. on single and joint lives. This, like Mr. Corbaux's other works, is ably written. The author says:

Annu. on single or on joint lives,

with other prospective transactions, equally founded upon the operation of compound int. combined with the chances affecting the duration of human life, collectively form a copious subject, already enlarged upon by able writers of this and other countries. The intention, here, is therefore to treat that subject with great brevity: merely stating the general principles upon which it rests, with so much of their application as will be sufficient for estab. the basis of calculations relative to the transactions above described; and superadding a few tables which, occasionally consulted, may so far guide the unpretending reader as at least to prevent his being betrayed into gross errors, upon a matter beset with difficulties, and involving considerations of a delicate and complicated nature.

In 1825 a Committee of the H. of Commons sat upon Friendly Sos., among the witnesses examined were Mr. Finlaison, Mr. W. Morgan. Mr. Joshua Milne, Mr. Frend, and others. The Committee pub. a report, in the appendix to which is contained a most valuable collection of Tables relating to sickness, annu., and the law of mort., as prepared by Dr. Price, Mr. Morgan, Mr. Glenny, Mr. Finlaison, and others. The remaining space at our command for the completion of the present art. will not allow us to dwell upon this. We shall, however, have occasion to notice these Tables in various parts of this work. [FRIENDLY SOS.] [SICKNESS.]

By the Bankruptcy Amendment Act, 6 Geo. IV. c. 16, sec. 54 (1825), it was provided that an annuitant might prove for value of annu. on bankrupt estate, regard being had to its original cost, and the depreciated value by lapse of time. No T. of mort. was specified.

In 1825 Mr. Geo. Thatcher pub. A Treatise on Annu. for fixed periods, particularly Gov. Long. Annu., showing a defect in theory, with its remedy; and when annu. are dear and cheap. To which was added a practical T. for calculating long annu.

In 1825, or early in 1826, Mr Griffith Davies pub. his Tables of Life Contingencies; and therein was contained a T. of the mort, which had prevailed among the lives ins. in the Equitable So. at all ages above 10, based upon the statement of Mr. Morgan, already referred to (1821). Mr. Davies gave Tables of the values of annu. on single and joint lives, calculated both from the Table he had constructed [EQUITABLE EXPERIENCE] and from the Northampton T., rather fuller and more complete than any that had been pub. previously except that those derived from the mort. of the Equitable necessarily included no ages under 10. The values according to the Northampton T. were given only at the rates of 3 and 4 p. c. int. ; but Mr. Davies, not content to take them on Dr. Price's authority, had, like Mr. Babbage, calculated them anew, and, as well as the other values of annu., has carried them to four places of decimals.-Milne. The Annuity Values as deduced by Mr. Davies from

the Equitable Experience are as annexed:

In comparing this table with others, it must be borne in mind that a great majority of ins. lives are males, on which account the values are somewhat lower, especially from 15 to 55 years of age, than they would have been had there been nearly equal numbers of both sexes.

In 1826 was passed another Act, 7 Geo. IV. c. 75, to further explain the Act of 1813 regarding the inrolment of memorials of grants of annu. It merely defines what witnesses are required.

Age.

TABLE-4 P.c.
Years'
Purchase.

Age.

Years' Purchase.

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In 1826 also Mr. Charles Babbage pub. his Comparative View of the various Institutions for the Assu. of Lives. In that work he also gave a T. of the mort. which had prevailed among the ins. lives in the Equitable, at all ages above 10 years, based upon Mr. Morgan's statement (1821); and a T. of the value of annu. based thereon. He also gave formule and Tables not materially differing from those of Mr. Barrett, for determining the values of temporary and deferred, as well as increasing or decreasing, annuities, and assu. on single lives: these T. being derived from his own T. of the EQUITABLE EXPERIENCE, and from the CARLISLE Table.

This work of Mr. Babbage's did much to draw popular attention to the subject of life annu. and life ins. It was reviewed in the Edinburgh and Quarterly Reviews; and it was also translated into the German. [BABBAGE, CHARLES.]

His Table of annu. values from the EQUITABLE EXPERIENCE is given on the next page. It must be remembered, in comparing it with others, that it is calculated at

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