investigated and explained; together with several useful Tables connected with the subject. We shall give an outline of his views upon L. annu. under date 1810.

The Provident Life was founded in 1806, and commenced at once to grant L. annu. At that date only one other ins. office had pub. its rates for life annu., and that was the Royal Exchange. The following table gives the "year's purchase" required by each of these offices for life annu. of £1. The Royal Exchange paid its annu. quarterly, the Provident half-yearly.

In 1806 also Mr. John Clark pub.: An Enquiry into the Nature and Value of Leasehold Property, Reversionary Int. in Estates, and Life Annu., with a variety of Tables, etc.

TABLE-4 P.c.

In the same year M. Duvillard pub. T. of Mort. for France, before the Revolution, based upon obs. extending over a considerable portion of the kingdom. The annu. values deduced from this table have been considered too small to be used with safety. The table is regarded in France much as the Northampton T. is regarded in England. We give the annn. values deduced from it for the purposes of comparison.

In the Morning Advertiser of 31st October, 1806, there appeared the following advertisements:

70

5.635

75

4'420

We have seen how in the early part of the last century life annu. were applied for the purpose of raising money for Trading Corp. A century later, and they were very constantly employed as a means of raising money for parish improvements, as building, lighting, repairing churches, etc., etc. The speculation in them also continued. If we take a turn at the newspapers of this period, we shall find numerous examples of each class. We will quote such as best illustrate the practice then prevailing.

Cash for good bills and annu. to any amount during bus. hours at Humphryes and Co's., Navy Agents, No. 1, Sion Gardens, Aldermanbury, where the most liberal price will be given for well-secured annu, and merchandize. N.B. Tradesmen of credit accommodated on their own security, but no money agent will be treated with; nor letter received, unless post paid. Money on Annuity.-Wanted immediately £100, for which an annu, of 10 guineas will be granted on the security of landed property of ample value. Letters from principals (post paid) appointing an interview addressed to K. R., at Peele's Coffee-house, Fleet-st., will be duly attended to and satisfactory references given.

Money-£127,000 ready to be advanced on good security. Messrs. Lucan and Co. beg leave to inform those who may be in want, and desirous of borrowing temporary or permanent sums of money, and possessed of any property that can be assigned, that any part of the above money will be lent in sums from £100 to £10,000, on paying a fair and equitable annu. int. for the same, etc., etc.

In the Times, 3rd July, 1807 :

Two thousand pounds will be given immediately for a well-secured annu. of £220-the grantor ins. his life. Address to S. D., Post-office, Grantham, Lincolnshire. More money to be laid out on the same terms. This is 11 p.c. for money, and 9 years' purchase nearly.

In the Morning Advertiser, 20th April, 1807, there was the following:

The Commissioners appointed to carry into execution an Act for better Paving, Lighting, and Watering the Parish of St. Nicholas, Deptford, in the County of Kent, will meet in the Vestry room of the said parish on Tuesday, the 28th April inst., at 6 o'clock in the evening, to receive proposals from such persons as are willing to purchase annu. to be paid quarterly during the natural life of the purchaser or any person to be nominated by him or them, out of the rates or assessments directed to be made by the said Act. No annu. will be granted to any person under 40 years of age, nor will more than £600 be taken for the purchase of any one annu. Proposals to be sent, sealed up, to the office of Mr. Parrell, solicitor, Slades place, Deptford, Kent.

In the Morning Advertiser, 8th June, 1807:

Annuities.-St. Mary at Hill, Lond. The vestry of this parish do hereby give notice that they are ready to receive proposals from such person or persons as may be willing to advance the said parish the sum of £700 upon one or more annuity or annuities to be secured for the life or lives of the person or persons advancing the same, but redeemable at the option of the said parish on six months' notice. Proposals in writing, sealed up, to be delivered at the office of Mr. Ludlow, No. 4 Monument yard, Lond., on or before the 18th June inst.

In the same year there appeared :

Life Annuities.-Greenwich, 7th August, 1807.-The parishioners of this parish being desirous to raise the sum of £1500 by annu. on lives, for the purpose of enlarging the Burial-ground of the said parish, do hereby give notice that all persons intending to propose for any part of the said annu. may leave their proposals (in writing, sealed up) with either of the churchwardens on any day (Sunday excepted) between 10 in the morning and two in the afternoon, setting forth the name and residence, the age, sum proposed for (which is not to be less than £50, nor more than £200 on any one life), the rate of int. required, and the day for the delivery of the proposal. Further particulars may be had by applying at the office of Messrs. Everett and Martyr, the Vestry Clerks, at Greenwich.

In the Times, 15th January, 1808, there was the following adv. :

Annuities for Lives.-Wanted to be borrowed by the united parishes of St. Mary-le-Bow, St. Pancras, Soper-lane, and Allhallows, Honey-lane, Lond., for the repairs of the parish church of St. Mary-le-Bow, in Cheapside, a further sum of money, not exceeding the sum of £600, upon annu. for

lives to be named by the lenders. No sum to be accepted less than the sum of £200. All persons willing to advance money for the purposes aforesaid are desired to send their proposals in writing, mentioning the sum they are willing to advance, the life or lives, and the terms upon which they are willing to advance the same, to Messrs. Nettleshipps, solicitors for the said parishes, at their office, at Grocers Hall, Poultry, of whom further particulars may be known.

In the Morning Advertiser, 5th March, 1808:

Parish of Woolwich, in the County of Kent.-The Commissioners under an Act of Parl. lately passed for improving the town of Woolwich, do hereby give notice that they will meet at the Poor House of the said Parish, on Friday next, the 19th February inst., at 6 o'clock in the evening, and every subsequent Friday evening at the same place and hour, for receiving the proposals of such person or persons who may be desirous of purchasing annu. directed to be raised by virtue of the said acts, and to be charged on the parish rates. And all persons making such proposals are desired to take notice that they will be required to produce a copy of the Register of his or her Baptism or Birth, to identify their respective ages, and also certificate of his or her residence, under the hands of the minister, churchwarden, and overseer of the parish or place where he or she shall dwell.

In the Morning Advertiser, 25th April, 1808:

Annuities on Lives.-St. Luke, Middlesex.-The Commissioners for paving the said parish will meet at the house known by the sign of the St. Luke, opposite the Church, in Old-st., on Wednesday, 27th April inst., at 4 o'clock in the afternoon precisely, to receive proposals for the absolute purchase of one or more annuity or annuities not exceeding in the whole the sum of £1000. The contributor or nominee must be of the age of 45 years or upwards. The annuity or annuities not to exceed £9 p.c. p.a., and to be paid quarterly out of the moneys to arise by or from the rates to be made on the houses situate in the streets called the Baltic-st., Honduras-st., Domingo-st., Memel-st., situate between Goswell-road and Golden-lane. No proposal will be received after half-past 5 o'clock.

Dale had said in reference to this class of security and the high annuities offered in common therewith, as early as 1772:

If parishes give at any time extraordinary int., it is on some emergency, such as building or repairing churches, workhouses, etc., and in such cases the annu. granted may perhaps be above the common rate, for the sake of obtaining ready-money to execute the work immediately.

Various other Corp. bodies of a trading character have permanent powers to grant money by means of life annu. We may mention two, the New River Co. and the Manchester Waterworks Co.

The exemption in favour of Corporate Bodies in the Annu. Act of 1777 only applied to those cos. having special charters of incorp., or which were empowered by Act of Parl. to transact annu. business, of which there were very few; and when early in the present century several new offices were estab., they found themselves unable to grant annu., as they could not inrol the names of all their proprietors. To obviate this difficulty, several of the cos., as the Globe, Albion, London Life, Pelican, and Provident, obtained in 1807 Acts allowing them to inrol the names of trustees only; and these Acts were very carefully worded to show that they conferred no really corporate privileges, this alone excepted. [LEGISLATION, ETC., FOR INS. Asso.]

In 1807 the Amicable So. was, by a new charter then obtained, authorized to grant life annu. in lieu. of payment of the sums secured to the representatives of deceased members. It was also authorized to grant annu. in exchange for policies of ins. in the event of members desiring to exchange. We believe the transactions of the So. under this power were very limited.

In 1808 it was provided by 48 Geo. III., c. 142, that from and after 1st August in that year, it should be lawful for the Commissioners for the Reduction of the National Debt to accept transfers of 3 p.c., consolidated or reduced, Bank annu. in exchange for the purchase of life annu. on single lives, or on two lives, or on the longest liver of two lives, subject to certain limitations and restrictions therein mentioned. Persons so desirous of exchanging might nominate other lives than their own, but such nominees were not to be under the age of 35 years, and must reside in Gt. Brit. or Ireland. Proof of age and certificate of identity were required; and no annuity or annuities on the life of any one nominee should exceed 1000, or for two nominees £1500. Extensive tables were appended to the Act, regulating the values of the annu. not only by reason of the age of the annuitant, but also by reason of the price of the stock at the time of transfer. The highest age in the tables is 75, the prices at that age counting for "75 and upwards." The following is an abstract of the Tables:

Age.

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

The

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

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 481, 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.

19.585

15

18.956

20

18.363

25

17.645

30

16.852

35

16.041

40

15074

45

14'104

50

12.869

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