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The borrowers grew tired of placing themselves entirely at the mercy of the lenders, and they devised the system of redeemable annuities. Again the Courts rebelled, but ultimately succumbed. We shall treat of these points more at large as we proceed.

In 1777 also Mr. Wm. Dale pub., A Supplement to Calculations of the Values of Annu. pub. for the Use of Sos. instituted for Benefit of Age. Containing various illustrations of the Doctrine of Annuities, and Compleat Tables of the value of £1 immediate Annu. (being the only ones extant by half-yearly Int. and payments). Together with investigations of the state of the LAUDABLE So. of Annuitants, showing what annu. each member hath purchased, and the Mort. therein from its institution, compared with Dr. Halley's table; also several Publications, Letters, and Anecdotes relative to the So., and explanatory of proceedings to the present year, etc. The writer in his opening para. shows pretty well what had been the consequence of the raid made by Dr. Price and himself upon the annu. asso. of which we have already spoken:

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Of all the deluding inst. for benefit of age, the writer knows of but three at present remaining. Of these only one (he believes) has attempted reformation, and that attempt has been frustrated merely because the intelligent and humane were in the minority. To prove this allegation true, the author of Calculations, etc., thinks it incumbent on himself to submit to inspection of an impartial and candid public, such calculations as he presumes may fully demonstrate it to the entire satisfaction of all who read with willingness to understand. For which purpose compleat Tables of £1 annu. by half-yearly int, and payments; Tables of what annu. each member in the Laudable So. of Annu. has purchased; and the actual state of mort. in that So. from its institution, are here subjoined. And these the writer deems himself called upon by both the contending parties to produce.

He then recounts many points of the controversy to which we have already specifically referred.

Contrasting the smaller Mort. which had been experienced in the Laudable So. of Annuitants against that which had been experienced by the Laudable So. for the Benefit of Widows, he offers a practical suggestion, which is now generally supposed to be the result of modern sagacity:

It may be that tables of mort, which include a mixture of healthy and ailing, would not agree with either of these sos. separately; for it might be expected beforehand that fewer would die in the first, and more in the last, than what the tables suppose. Such consideration would direct the application of tables which suppose the fewest deaths to the So. of Annuitants; and the contrary to the other So., as the most prob. means of approaching nearly to the real state of mort. in each So. Accordingly, comparison finds that real longevity in the Laudable So. of Annuitants exceeds that supposed even by BRESLAW BILLS; and perhaps comparison would find that real mort. in the other, and such like sos., would exceed that supposed by even Lond. Bills: were it not for the particular consideration which counter checks, by taking all possible precaution to admit no life suspected of unhealthiness, either in state of body or profession.

He then addresses the following remarks to the orig. founders and then managers of the Laudable So.

Do they not know that the inst. according to their plan is the direct reverse of “laudable"? Will they themselves presume to term it laudable to have seduced unwary believers to hope for £44 annu. by constant promise and formal agreement? Will they term it laudable to mock the deceived and disappointed, by telling them that" the Sec. always informed every member at entrance what the cap. was, and the number of members-it was for them to calculate? Will they term it laudable or humane to tell deluded age that the promised annu. cannot be paid; and even so much as has been purchased and might be received, shall not be paid them; for that they the first members having bought the least, and being the majority, have desire and intention, nay, have already resolved to be sharers in the stock equally with those who have purchased the very most, and depended on agreement, and on their promise, to receive it with addition; that is not less than £44 during life?

In this vol. was contained (p. 49) a table showing the value of life annu. by halfyearly payments, int. 3 p.c. according to Simpson's and Halley's Tables; the first time, we believe, that half-yearly values had been calculated.


In 1778 the Government raised a further sum of money by the sale of life annu. this year also the third Irish Tontine was set on foot; and the nominees, in each case, were included in Mr. Finlaison's Observations in 1829.

In 1778 also was pub., Articles of the Universal Inst. for Annu. and Assu. on Lives. In three parts. [HIST. OF LIFE INS.] And in the same year, by W. Backhouse, A Dissertation on the Value of Life Annu. deduced from general principles clearly demonstrated, and particularly applied to the Schemes of the Laudable and Amicable Sos. of Annu. for the benefit of age. Also, same year, at Vevey, by M. Fatio, an extensive collection of tables, embracing some on annuities.

In 1779, by 19 Geo. III. c. 18, the sum of £7,000,000 was authorized to be raised on Annu. ; and £490,000 by a Lottery. Every 100 sunk for an annu. was to produce a £3 p.c. annu. redeemable by Parl.; and also an annu. of £3 155. p.c. for 29 years, and then to cease. But every subs. might exchange the last-named annu. for a life annu. on intimating a desire to do so before a certain day named in the Act, and naming a nominee there being no restriction as to age of subs. or nominee. Persons who subs. a 1000 to the annu. fund were entitled to 7 tickets in the Lottery upon paying a further sum of £10 each for the same.

The Government of that period was driven to great extremities for raising money; and nearly every session one or two Annuity Acts were passed, generally accompanied by a

Lottery project. But most of the annu. granted were for terms of years or in perpetuity, and therefore do not require detailed notice here.

In 1779 Mr. Wm. Morgan, Actuary of the Equitable, pub. his Doctrine of Annu. and Assu. on Lives and Survivorships Stated and Explained. The particular degree of merit to be ascribed to this work has been the subject of some controversy. It appears to have been pub. very much at the instance of Dr. Price, who wrote the introduction, wherein he says:

The second chap. contains an explanation of the doctrine of life annu. in general, and of the principles on which their values are calculated. At the end of this chap. an account is given of the method of expediting all calculations of the values of life annu., which must, I think, be very acceptable to all who have ever employed themselves in making such calculations. In these two chap. Mr. Morgan has studied to render the subjects of which he treats as intelligible as possible to persons who may be unacquainted with mathematics.

Regarding the mort. table to be employed in the valuation of annuities, Mr. Morgan


The excellent Mr. Simpson has indeed given a table of the values of two joint lives agreeable to the London table of obs., but this table of obs. ought not to be much used, because representing the rate of mort. among the inhabitants of Lond. taken in the gross, it gives the values of lives much too low for the middling and the better sort of people in Lond. itself..


As by these methods the calculations are rendered pleasant as well as expeditious, I hope that ere long some person will undertake them, chusing for his guide the Northampton table of obs., which is perhaps better fitted for common use than any other.

There can be no doubt but that the work contained formulæ for the solving of questions in annuities, and in life contingencies generally, which were new and valuable; and as Dr. Price does not specifically claim these, Mr. Morgan is entitled to be regarded as the originator.

In 1779 M. de Saint-Cyran pub. his work, wherein the valuation of annu. on lives is treated algebraically, but in a manner much inferior in all respects to that of Mr. Simpson; and six tables are given of the values of annu.-on single lives, on the survivor of two lives, and on the last survivor of three, calculated from M. Kerseboom's table, Although the values in the cases of two and of three lives were only determined by approximation, these tables were just then a valuable acquisition to the science; but their use was entirely superseded only four years after by the pub. of others much more valuable.-Milne.

Table of Annu.
Values-5 p. c.









14 15



In 1780 Mr. Brand published an ed. of Smart's Tables, and therein was contained many problems in life annu., and also various tables of annu. values; all of which have been noticed here in their chronological order.

The accompanying column shows his annu. values on single lives at 5 p.c.



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In 1781 M. Antoine de Parcieux pub. in Paris, Traité des Annu., ou des Rentes à Terme, [DE PARCIEUX.] In the same year M. Flourencourt pub. a work on Political Economy, wherein was contained a T. of annu. for single lives, deduced from De Parcieux's T. of Mort., but making the annu. payable at the end of every year the life survived; with a table of proportionate parts for add. to be made according to the period the annu. survived the year. In 1783 Dr. Price pub. 4th ed. of his Observations, etc. This ed. was very much more comprehensive than the eds. which had preceded it; but it mainly demands notice from us here from the fact that it contained tables of money values deduced from the NORTHAMPTON T. of Mort. The author says hereon:

The 6th table, showing the mean prob. of the duration of life according to a register of mort. at Northampton, has been inserted in all the former eds.; but it is now given more correctly; and tables deduced from it have been added, of the expectation of life, and the values of single lives, and of any two joint lives at all ages, and for three rates of int. The labour of computing these tables was undertaken in order to set aside all occasion for using the defective valuation of lives founded on Mr. De Moivre's hypothesis; but not having been able to finish these computations till a great part of this treatise had been printed off, I have been obliged to continue the use of the old tables so far as to take from them many of the examples of the solutions of questions in the first and following chapters. The other distinguishing feature of this ed. was, that it contained the SWEDISH Mort. T., with expectations and money values deduced therefrom. The learned author says hereon:

With respect to the tables in particular deduced from the Swedish obs., I cannot hesitate to pronounce that they exceed in correctness everything of this kind which has been hitherto offered to the public; and that nothing is wanting to make our knowledge in this instance compleat, but similar obs. in other kingdoms. By these tables I have been enabled to state minutely the different rates of mort. at all ages among males and females; and to form tables of the values of single and joint lives for each sex, as well as for both sexes collectively; in consequence of which I have been further enabled to determine the increase of the values of annu, payable during survivorship, occasioned by the longer duration of life among females; and thus to furnish a direction of some importance to the various sos. in this kingdom and abroad, for providing annu, for widows.

Here are abstracts of life annu. values deduced from the two preceding tables :

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In 1783 the Baron Maseres pub. The Principles of the Doctrine of Life Annu. explained in a familiar manner, so as to be intelligible to persons not acquainted with the Doctrine of Chances; and accompanied with a variety of new tables of the values of such annu. at different rates of int., but for single lives, and for two joint lives; accurately computed from obs. In this work was contained a very lucid criticism upon the works of various writers already named by us in the course of the present art. The author was an amateur, and an enthusiast, and is entitled to the gratitude of succeeding generations. His work is very bulky, consisting indeed of more than 700 pages; but the preface contains a very good synopsis of the contents; and from that we take the following:

The principles of the whole doctrine are contained in the first 90 pages, which I would therefore recommend to the attentive perusal of every reader. Of these, the two first pages contain an explanation of the data, or grounds upon which the computations of the values of annu. for lives are built. These are, first, the decrease of the present value of a future sum of money arising from the mere distance of time at which it is to be paid, and the consequent discount that is to be allowed to the purchaser of it for prompt payment (the quantity of which discount it is evident will depend on the rate of int. of money), and secondly the chance which, when the payment of such future sum is not made certain, but is to depend upon the continuance of the life of a person of a given age, the grantor has of escaping the necessity of paying it at all by means of the death of the said person before it becomes due; in order to determine which chance it is necessary to have recourse to certain tables of the several prob. of the duration of human life at every different year of age, which have been formed from obs. of the numbers of persons who have died every year, in the course of a long series of years, at different ages, in divers cities and parishes, and other numerous bodies of men.

In pages 3-6, an account is given of two tables of these prob. that appear to me to be better grounded, and consequently fitter to be adopted, than any others: to wit, those of Mons. Kersseboom and Mons. de Parcieux; and the tables themselves are exhibited. And in p. 7-15, a comparison is made between these two tables, in order to discover which of them represents human life at several different ages, as the more durable, or makes the prob. of living greater than the other; and it is found upon the said comparison that till the age of 70 years, the prob. of living are rather greater according to Mons. de Parcieux's table than according to Mons. Kersseboom's; but that after the age of 70 years, or for persons above the age of 70 years, the prob, of living are greater according to M. Kersseboom's table than according to Mons. de Parcieux's.

We shall have occasion to speak of this work again under various heads. That it was calculated to help forward the science of life annu. to a considerable extent is admitted by all who speak of the work.

Professor Tetens, of Kiel, in his work on life annu. and rev., pub. 1785, says: "These annu. calculations have long been known in England. Halley, whom we have to thank for so many useful discoveries, came upon them already at the end of the preceding century. Huygens, before him, had taught how to compute prob. His principles Halley applied to the registers of death, when they were brought into order; and formed the method upon which to compute life and widows' annu. Again: "Of the more recent British authors on this matter, only Morgan and Price have come to my knowledge as having produced anything excellent or orig. In the general theory both agree with Simpson. Morgan has indicated a double method of computing annu., which has in all respects much value. Dr. Price, who with justice much recommends it, seems, however, to ascribe to it somewhat too great pre-eminence. I have not found it so easy or short as not to have had reasons for devising yet another, and for preferring this latter method. One can compare them and judge."

It is the columnar method, similar to that afterwards devised by Barrett, of which he speaks.

In 1785 also the 2nd vol. of the Opuscula Analytica was pub., after the death of its author, Euler; and therein the solution of a question relating to rev. annu. is given. "A much more arduous undertaking (observes Mr. W. T. Thomson) than in the present day, when so many auxilliary tables are ready to assist the actuary.

Sir John Sinclair, in his HIST. OF THE REVENUE, first pub. in 1785, enumerating the means which had been employed in raising the revenue, said:

Annuities for lives is another mode that has been frequently practised, and by some is accounted the

most advantageous. But it is hardly possible for a nation when it is in distress by any means to make a profitable bargain with a money-lender, particularly on the principle of granting temporary annu. Thus, when annu. for lives are granted, the creditor takes care to pitch upon the persons who are the most likely to live long, and who consequently will prove, for the longest period, a burden upon the State. Nor have all the flattering hopes which Tontines held forth to the avarice of mankind been able to procure money by life annu. on advantageous terms to the public.

In 1789 the Great English Tontine was set on foot under the authority of 29 Geo. III. c. 41. It was to raise the sum of £1,002,500 for the public service by way of Tontine. Every subs. for the sum of £100 55. was to be entitled to an annu. upon the life of his nominee at a rate proportioned to the age of the person of from £4 35. to £5 125., with benefit of increase arising from survivorship, till the annu. upon the orig. share should amount to 1000 a year, the excess then falling in to the public. The gentlemen who contracted with Government for the whole of the Tontine not being able to get it disposed of in time, an option was afterwards given, by 30 Geo. III. c. 45 (1790), to the subs. to convert it into terminable (long) annuities for 694 years. A considerable number of the orig. contributors held their subs,-to the number of 4129 out of 10,000 shares. were held upon 3495 lives. The mort. of this particular class was given in Mr. Finlaison's Obs. in 1829. [GOVERNMENT ANNUITY TABLES.]


In 1789 the Westminster So. for Granting and Purchasing Annu. and Ins. upon Lives and Survivorships applied to Parl. for a charter, and was refused. Three years later (1792) the asso. was founded under a Deed of Sett.

In 1792 Mr. Wm. Blewert pub. Perpetual and Determinable Annu. reduced to a level; or a comparative view of long and short annu., with 3 p.c. reduced, and 3 p.c. Consols at the Bank of England, etc. But neither in this, nor in his work in 1783, did he treat of life annu.

Dr. Waring, in a small pamp. On the Principles of translating Algebraic Quantities into probable relations, etc., pub. 1792, devoted about 30 pages to the consideration of the subject of annu. and assu. "His style and manner (says Francis Baily) will not be much admired by those who have read the works of preceding writers on this subject."

In 1793 the Royal Exchange Marine and Fire Corps. applied to Parl. for add. corporate powers to enable them to grant, purchase, and sell annuities for lives and on survivorship; and by the 33 Geo. III. c. 14, they were empowered so to deal in annuities under the name of the Royal Ex. Assu. Annuity Co. The preamble of this Act deserves particular


Whereas it would tend to public utility, if the said Corps. were empowered to grant, sell, or purchase annu, upon lives, or by or with survivorship, which no other Corps. now are; the granting and purchasing such annu. being in the hands of improper persons, who make an exorbitant gain thereby, to the great detriment of individuals and the public in general, which would be in a great measure (if not wholly) prevented if a known office, long estab., were empowered to do so. May it therefore, etc.

It is necessary also to see the precautions with which this power was fenced round. It is provided by the Act that, in order to render full security to the annuitants, the money received for the annuities should (as often as it should amount to £1000) be laid out in Gov. security; the interest or dividends on which the corp. might from time to time receive: but they were prohibited from touching any part of the principal until the extinction of the life on which the annuity was granted. And for the sake of preventing any fraud in this respect it was enacted that the time and place of the death and burial of each annuitant should be inserted twice at least in the Lond. Gazette, and that a certificate of such death or burial, with an account of the annuity depending, should be left at the office in London, to be inspected without fee or reward by any person interested in any annuity granted by virtue of that Act. And it was likewise further enacted that no agreement for the selling or purchasing of any annu. should be valid unless at the price stated in a table which was directed to be prepared and hung up in some conspicuous place in the office; and which table should be remaining in the office at the time of granting the annu.

In 1794 Rev. David Wilkie pub. The Theory of Int., Simple and Compound, derived from first principles, and applied to Annu. of all descriptions; of Tontines, etc., etc.

In 1796 a new Legacy Duty Act-36 Geo. III. c. 52-came into force. Previous Acts had imposed simply a stamp duty upon legacies of specific amounts, and had not reached annu. on lives. This Act therefore opened a new and large source of revenue; for it had become customary to bequeath annuities in order to escape the duty. Where an annu. was bequeathed for life or for years, it became necessary to value the same in order to assess the duty (sec. 8). A series of annu. tables was therefore appended to the Act, based upon the Northampton T. The use of these tables was superseded in 1853 by those appended to the Succession Duty Act of that year. [LEGACY DUTY.] [SUCCESSION DUTY.]

In 1796 Mr. Thomas Tremlet pub. Strictures on a proposed plan for adopting a Loan, with a view of instituting Rev. Annu., or Government Dividends payable at a future period. In the same year Mr. Wm. Hunt pub. A Collection of Cases on the Annuity Act; with an Epitome of the Practice relative to the Inrolment of Memorials.

In the same year also was pub. A Treatise upon Law of Usury and Annuities, by Francis Plowden.

In 1799 Sir Frederick M. Eden and several other persons of position in the City of Lond. having conceived the idea of founding a new Ins. Office with corp. powers, a Bill was introduced to the House of Commons and passed. The preamble of the Act recited, that "it would in many respects be greatly advantageous to the public if a corp. were estab. for making or effecting ins. on lives, and ins. against loss or damage by fire, and for granting, purchasing, or selling annuities for lives or on survivorship."

A draft-charter to incorp. a co. pursuant to the powers of this Act was prepared, and in due course submitted to the law officers of the Crown. The name to be the Globe Ins Co.; among its objects the granting of annuities.

In the report of the law officers upon the charter and its proposed powers, it was pointed out that there should be

Some restraint on the terms of the Co.'s dealings in annu., post obits, and other traffick of the same description in which they understood it was the intention of the Co. to adventure, and in which the example of a great co. authorized by Parl. and by Your Majesty's Charter might be highly injurious if their dealings should be for the same unconscientious advantages as were usually extorted by those who deal with necessitous persons in such trans.: which in general can only be carried on with necessitous persons, and most frequently with many persons subsisting on expectancies. In this view, it appeared to them that publicity in such transactions is highly important; and that all post obits to be granted to the Co. ought to be subject to provisions similar to those respecting annu. contained in the Act of Parl. of 17th year of Your Majesty's reign for registering grants of life annu., and for the better protection of infants against such frauds; but they conceived that could not be done without the aid of Parl.;

In consequence of this report, some modifications were made in the proposed charter ; and another set of law officers (in 1802) reported upon the amended charter-but having before them the objections of their predecessors in office just quoted—as follows:

We conceive that this objection applies principally to post obits and dealings of that description: so far as it so applies, it is wholly removed by an express renunciation on the part of the co. of all dealings of that kind, and a consent to be restrained therefrom by the terms of their Charter, as to the mere dealing in annu. if it had stood alone, as it now will do, we do not apprehend that it would have been objected to on the part of our predecessors; and so standing we do not ourselves feel it to be fairly objectionable.

The promoters of the Globe, after encountering a good deal more of this pre-precautionary legislative attention, determined upon the prudent course of commencing bus. under an ordinary deed of asso. and without a charter. [GLOBE Ins. Co.]

In 1800 Mr. Robert Withy pub. A Practical Treatise of the Law of Annu., wherein the different securities for annu. and the remedies for the recovery thereof were fully exemplified. Together with the determination of the Courts on the construction of the Annu. Act. To which was added a large collection of precedents.

In 1802 we reach a name that will require more prominent mention as we proceed. It is that of Mr. Francis Baily, author of various works bearing upon L. Annu. and L. Ins. In a work on Leases, pub. in this year, there was an appendix, containing besides analytical demonstrations, Some remarks on the method by Dr. Price and Mr. Morgan for finding the Value of Annu. Payable Half-yearly, Quarterly, etc., together with some formulæ for determining the rate of Int. in Annu. (see again 1805 and 1810.)

In 1803 the Globe Ins. Co. was founded. Its founders, as we have seen, contemplated making the grant of life annuities an important feature of its business. Hence one of the reasons for the security of a large capital. Its active projector, Sir F. M. Eden, said (1804):

With respect to annu. on lives and on survivorship, the creation of a new corp. with an adequate capital for this branch of bus., may afford great accommodation to the public. It is more wanted in this country, as the public funds do not in this respect furnish those facilities for the purchase of annu. which were formerly met with in France. The grant of an annu. is often a measure greatly beneficial to the seller, as well as the purchaser. Important family arrangements might in many instances be effected thro' the medium of life annu., if a new office were sanctioned by legislative authority on safe and equitable principles. The land-tax of a very considerable estate of a nobleman of high rank has been redeemed by means of a sum raised by the grant of life annu.

In 1803-4 Sir John Sinclair, Bart., pub. the 3rd ed. of his famous Hist. of the Revenue, and therein he offers the following remarks upon the granting of L. annuities as a scheme of national finance :

In time of war, when a State is immersed in difficulties, every idea of obtaining money to advantage upon contigent annu. is absurd: but during peace the same rule does not hold good. Were the public therefore to estab. regulations similar to those by which private sos. are enriched, considering that it may act on a much greater scale, the granting of such annu, might prove a very important resource, more particularly in a luxurious age like the present, when every individual aspires to rival his neighbour in expense, and would grasp at so desirable and certain a mode of increasing his income. But care should be taken to grant annu. only on the life of the person by whom the money is paid; nor should the creditor be suffered to search everywhere for the best lives, or for people who from the strength of their constitutions, or other circumstances in their favour, are likely to live beyond the usual short space of human existence.

In 1804 Mr. Newman pub. A Collection of Mercantile Tables upon a New and Improved Method; and among them were Annuity and Compound Int. Tables, "compiled from the best authorities."

In 1805 Mr. Francis Bailey pub. his work on the Docrine of Int. and Annu, analytically

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