N.B.-"This is the original Obs. by which all the T. on Life Annu. [for Females] hitherto computed for the service of the Gov. have been in fact constructed."-See 1823. [Mr. A. G. Finlaison adopted for the annu. portion of the Post Office Ins. scheme of 1864 rates deduced from this data and that of Obs. No. 20.]

14. On the Mort. of the Female Nominees of the Life Annu. of the Sinking Fund entirely by themselves-4815 lives; 3860 survivors in January, 1826.

15. On the Mort. of the whole of the Male Nominees in the 7 preceding Obs., taken by themselves--9347 lives; 4477 surviving in January, 1826. [See note on Obs. No. 8.] 16. On the Mort. of the Males of the Tontine of 1693, combined with the Males of the Exchequer Life Annu. of 1745, etc.-1522 lives; 36 survived in January, 1826.

17. On the Mort. of the Males of the Exchequer Life Annu., combined with the Males of the Three Irish Tontines-2414 lives; 611 survived in January, 1826.

18. On the Mort. of the Males of the Three Irish Tontines, combined with the Males of both Classes of the Tontine of 1789; and also with the Males of the Sinking Fund— 7825 lives; of whom 4441 survived in January, 1826.

19. On the Mort. of the Males of both Classes of the Tontines of 1789, combined with those of the Sinking Fund only-6339 lives; 3866 survivors in January, 1826.

20. On the Mort. of the Males of the Irish Tontines, of the Tontine of 1789, and of the Sinking Fund, as observed at the end of the year 1822; but the prob. of life corrected by a different method from that of the preceding Obs. [except No. 13].

"N.B.-This is the orig. Obs. by which all the T. of Life Annu. [for Males] hitherto computed for the service of the Gov. have been in fact constructed."-See 1823. [The Annu. rates for the Post Office Ins. scheme of 1864 were framed by Mr. A. G. Finlaison upon the data of this and No. 13 Obs.]

21. On the Mort. of the Male Nominees of the Life Annu. of the Sinking Fund, entirely by themselves-2077 lives; 1484 survived in January, 1826.

Mr. Hendriks states that the total number of lives brought under obs. in the preparation of this new T. brought into use in 1829 were the following (vide Fourn. of Statis. So. vol. xix. p. 346):

The new calculations which were made the basis of the rates intro. by this measure [Act of 1829] were not formed upon a larger number of complete obs. than 6679. By complete obs. is here meant lives entered upon the Gov. books as annuitants, and remaining on those books until the dates of their death-such dates of death being prior to the ultimate date to which the obs. extended. To the number just mentioned may be added 12,119 incomplete obs., by which is here implied lives entered upon the Gov. books as annuitants, and remaining on those books, as still living, at the ultimate date to which the obs. extend. The intro. of so many incomplete obs.-nearly two-thirds of the whole number of obs.-had the effect of very much marring the degree of reliability to be placed upon the deductions therefrom, at the more advanced periods of life; the result being to increase the liability to error, in under-estimation of the vitality at such periods, as practically indicated by comparatively high rates of annu.

It is to be noticed that none of these several Obs. were reduced into the form of Mort. T., as then and now understood. They were something more than merely elementary T.; but the col. of "expectation "--so valuable for the purpose of comparison of resultswas absent in every instance. It may have been, in part at least, this circumstance which induced Mr. Francis Corbaux, a well-known writer on Political Arithmetic, to present a petition to the House of Commons praying that money values deduced from these Obs. might not be sanctioned by that House until the results of Mr. Finlaison had received confirmation by some competent authority-a step which, however, the House did not take. This petition will be again referred to later.

The Rep. of Mr. Finlaison included some further T. illustrative of the Law of Sickness, and of the Law of Mort., not material to our present purpose the former in fact have already been given under FRIENLDY Sos., MORT. AND SICKNESS EXPERIENCE OF; the latter will be dealt with under MORT., LAW OF. There was also given (pp. 64, 65) a "T showing the value of a Life Annu. of £1000 a year, if purchased at each

under

mentioned ages, as deduced from the following obs. respectively [those mentioned in the head-lines of the T.], assuming in all cases the interest of money at 4 p.c."

The Obs. in the preceding summary which are of the most permanent interest are Nos. 8, 13, 15, and 20-but Nos. 13 and 20 are understood to be identical with those from which the Mort. T. we have given in abstract under date of 1823 is compiled; and from these alone were deduced the new scale of money values commenced to be charged in 1830. There is a general belief that Obs. No. 13 exaggerated the value of Female Life unduly. The difference between the value of Male and Female Life throughout these Obs. generally has been noted under FEMALE LIFE. The interest especially attaching to Obs. Nos. 8 and 15 is, that it is from these Mr. Jardine Henry has constructed his extensive T. pub. respectively in 1859 and 1873—to be hereafter spoken of in more detail. As a matter of convenient reference at this point we have compiled from Mr. Henry's T. issued in 1859 the following T. of Male and Female Life, as deduced from Obs. Nos. 15 and 8-which require to be read in the light of the following explanation given in the preface of vol. i. (1859), p. xviii :

In reference to T. I. and V. of Appendix-pages 756 and 762, being Obs. 15 and 8 of Mr. Finlaison's Rep. and forming the basis upon which the T. have been calculated-it may be remarked that a few trifling differences will be found on comparing them with the actual T. given in Mr. Finlaison's Rep. of March, 1829. The cause of these differences is the few unimportant corrections that were required to be made in the T. of Mr. Finlaison's Rep., arising from minute errors discovered by forming the T. in Obs. 15 and 8 anew, from the separate obs. of each Tontine given previously in the Rep., and by checking each separate obs, independently from the materials furnished by Mr. Finlaison. The very small errors existing in Obs. 15 and 8 were thus rectified, and the Radix T. formed from the Obs. were rendered accurate-a matter indispensable in T. forming the basis of extensive calculations. Mort. of Government Annuitants - MALE and FEMALE-deduced from Mr. Finlaison's data (1829)—Observations No. 15 (Male) and No. 8 (Female)—by Mr. Jardine Henry.

There is a note that the numbers of male and female children respectively newly born (of the age o) were derived from the English T. No. 1.

The amount of capital stock of various denominations trans, to and cancelled by the National Debt Commissioners on account of Life Annu. granted between the years 1808-29 was £10,919,000, which by additions of interest and other points of financial manipulation involved in the process was made up as a matter of account to £11,855,000. The loss on this dealing was about £3,124,000-being about 29 p.c. loss on all the cap. stock trans. or cancelled upon the purchase of Life Annu. ! This was in a period of 24 years and 4 months, up to 5th January, 1829. [We ought to add, the authorities at the National Debt Office do not recognize, much less admit the accuracy of the methods by which these results were arrived at.] But Mr. Hendriks, from whose investigations we obtain these figures [see 1856], adds this important remark thereon (p. 343):

In the absence of any publication, or of any data for the ascertainment of the Vital Statis. of the Gov. Life Annu., it is impossible to say how much of this loss arose from the errors in the calculation of the T. as regarded the value of life (taking into proper consideration the limits which to a certain extent existed in modification of those errors), or how much of the loss in question arose from the real defects in the principles upon which the Gov. has during the last half century embarked in the speculation of Life Annu. bus., without the power of conducting such a bus, on the principles which ordinarily regulate such a measure of finance when conducted by trading bodies or individuals. But that the loss has in a large measure arisen from those inherent defects in principle will the more clearly appear when we extend our obs. to what has taken place since 1829, and down to the present time.

The view here expressed is undoubtedly justified by the fact that the losses in connexion with Life Annu. by no means ceased on the adoption of the new T. this year (1829). See 1856. Mr. Hendriks further expresses a strong view that up to this date the loss had resulted upon young rather than the older annuitants (p. 332), thus:

The errors of the T. against the Gov., and the taxed public, and in favour of the annuitant who became a charge upon them, were thus in the inverse proportion to the age of the nominee: in other words, the younger the annuitant, the greater the loss. It is of some importance to keep this in mind, as it is a commonly received opinion that the contrary rule prevailed, and that the older the life, the greater was the loss.

Even Mr. McCulloch, in his Treatise on Taxation, had expressed the latter view. In the absence of adverse selection, Mr. Hendriks considers a profit might be made on the rates charged for annu. from 70 to 75 and upwards (p. 331).

It is historically interesting to be enabled to state that the Institute of France took considerable interest in the inquiries upon which Mr. Finlaison was engaged. The Academy of Sciences transmitted many questions on the subject for his consideration; and in return for the information contained in his answers, he received a letter of thanks.

Criticisms upon Mr. Finlaison's Obs.-We now propose to pass under review the criticisms which have been offered upon the Gov. T. as prepared by Mr. Finlaison, taking them in their chronological order.

Dr. Thomas Young, in a paper pub. in Phil. Trans. for 1826 (p. 287), on A Formula for expressing the Decrement of Human Life, reviewing various data relating to mort., said: Mr. Finlaison's T., therefore, although they may be extremely just and valuable for the purpose of setting a price upon Annu. to be granted on the lives of proposers, cannot with any prudence be adopted when the parties concerned have an interest in offering the worst lives that they can find, notwithstanding any partial security that might be afforded by the exercise of medical skill in their rejection; and if it is true that some of the Tontines were principally filled by lot (Rep. p. 16) with the children of country clergymen and magistrates, it must still be supposed that the families of such persons may have been more healthy than the average of the pop. of Lond. and the country taken together.

Sir John Lubbock, in his paper, On the Comparison of various T. of Annu., read before the Philosophical So. of Cambridge in 1829, says:

Mr. Finlaison has recently pub. extensive T. of Mort. formed from the Gov. Tontines and Annu., which are rendered equally valuable by the accuracy of the materials from which they have been deduced, and the very great care and attention which has been bestowed on them by the author.

Obs. such as those presented by Mr. Finlaison, where the deaths are given at every age, are particularly well calculated to determine delicate points, such as any small increase of the rate of mort. at different ages. A small increase of mort., according to Mr. Finlaison's T., takes place about 23; thus in Obs. 19 (p. 56) it appears that there is a minimum mort. at 13, a maximum at 23, and a minimum again at 33. This does not obtain in Mr. Finlaison's obs, on females. It is very remarkable that the same circumstance is to be observed in the Chester T., though here it is found equally in the T. for males and females.

However accurate the obs. be upon which Mr. Finlaison's results are founded, it must be recollected that the lives were selected from a selected class; and it remains to be shown that the mort. in the lower classes of society is the same as in the higher, and that selection produces no effect on the results. Mr. T. R. Edmonds, in his Life Tables, etc., 1832, says:

The value of this T. depends, in a great measure, on the truth of the assumption that selection produces no sensible effect; in other words, that there exist no means of distinguishing a good life from a bad one. My opinion is entirely opposed to such a position. When the admissions take place at all ages, and at various times, as is the case with Gov. Annuitants, no useful result is to be expected from a comparison in the gross of the number living and dying in any interval of age, without any regard to the time each individual has belonged to the So. The point on which the Gov. T. opposes my theory, as well as that of every other person, consists in declaring that, from the age of 20 to 45, the force of mort. does not increase with the age; it even goes so far as to show that a man's chance of living 1 year increases in that period. A T. of Mort. of French Annu. presents an appearance of the same anomaly, though less in degree. Possibly the cause of this anomaly may be found in

...

the falsification of ages, the above period being that in which people are most tempted to represent themselves as younger than they really are.

Mr. Francis Corbaux, in his work on Pop. pub. 1833 (p. 104), offers the following obs.: "It is not our purpose unnecessarily to dilate on the numerous Mort. T. of which the public is already in possession. In the number of those T. however, are two, constructed by Mr. Finlaison, and respectively referred to the discriminated sexes, as also understood applicable to the specific class of Life Annu. and Tontine nominees. They having been admitted, as a law of the land, to serve as regulators of the valuation of Life Annu. thenceforth to be granted by the Exchequer of this country; and the writer of these pages having conceived proper, at that time, to warn the legis. against blindly adopting a measure of such nature and importance, without previously obtaining the opinion of a plurality of persons competent on a matter of their department; it becomes the more imperative on him here to assign his principal objections to those T., as-in disregard of his petition hereafter transcribed-the ministerial influence obtained a Bill to pass sanctioning such a practical application of Mr. F.'s tables as they are unlikely to meet anywhere else.' The petition here referred to has already been mentioned. It is a document of great interest, and will be referred to in some detail under MORT., LAW OF. The reasons which, in his work now under notice, he assigns for repudiating the value of Mr. Finlaison's Obs. may be, in their essential points, summed up as follows:-1. Because the absolute intensity of female life is there exhibited in a very exaggerated excess of 57 years over that of male life; although the question is concerning a class of select lives, which admits only a minimum of superior intensity possessed by the former sex, or at the utmost an excess of 3 years. 2. Because the collective intensity, in regard to one and to the other sex, is exhibited as invariably decreasing from the very first year of existence; although an increase, during the first 5 or 6 years, at least, is an incontestable result of the vitality's rapidly progressive consolidation after that first year; but which progression has never failed to become manifest, according to experience, proved by every one of the Mort T. hitherto constructed, except these two only. 3. Because the specific intensity of life is there presented, regarding the males as even 9 times greater for the interval separating the second from the third year of existence, than it is for the immediately preceding interval, or that from the first year to the second; being a most unaccountable and utterly inadmissible disproportion, to whatsoever minima such intensity might by possibility be reduced for the first year of life-as also for the respective sexes-and to whatsoever maxima it might upon justifiable grounds be elevated for the second year, especially with reference to a select class. "It should, however, be remarked (continues Mr. Corbaux) that those T. have left entirely out of consideration every result concerning such first year of existence," etc. 4. Because, under the admission of those supplementary resultswithout which, and if more elevated intensities were introduced for that specific year, this fourth ground of objection would acquire but greater force-it is made to appear that onehalf of all females born, of the class referred to, attain the comparatively advanced age of 57 years, whilst a similar proportion of the males appeared to outlive the 48th year of their age only. . . . And so on until in the whole twelve objections are exhausted. The disparity between male and female life being the chief point at which the criticism is aimed. Mr. Milne, in his art. "Mort., Human," pub. in the Ency. Brit. 1837, says: "These, from the number and accuracy of the data, are more valuable than anything of the same kind that had previously been pub."

In this same year (1837) a number of the leading actuaries prepared a memorial to the H. of Commons, praying that orders be given for the pub. of all T. founded upon the same data as those upon which the Gov. now grant annu. on lives," etc. See EXPERIENCE T. OF MORT. (GENERALLY).

66

Mr. T. R. Edmonds this year contributed to the Lancet a paper: Defence of an Art. in the Brit. Medical Almanack" entitled National Statistics, which we shall notice in a later portion of the present art. [see 1830]. In another paper, also in the Lancet, On the Duration of Life in the English Peerage, there occurs the following passage:

In the English Gov. Annu. Office there prob. exists an abundance of materials, if properly classified, for determining the average mort. of persons in easy circumstances. The leading principle of such classification ought to be, the separation of the mort. of newly-admitted members from that of the anciently-admitted members. The mort. of all members or annu, of more than 20 years standing would prob. afford a good measure of the mort. in England among a part of the pop. in easy circum

stances.

Mr. Sang, in 1841, drew attention to the fact that the male lives selected from the Gov. Annu. were much worse than the average male pop. of the kingdom, particularly at ages under 25. Looking to the cause of this, he says, it may, no doubt, be attributed to the want of regular labour, and to the pampered style of living of the richer classes. The constitutional effect of early irregularities (he continues) seems to influence the remainder of life; for after age 30, when the mode of living may be supposed to have become sobered, the line still continues, though at less distance, below that for the average pop. Between ages 20 and 30, a great improvement may be remarked. The expec. of life by the females of the wealthier classes is, on the other hand, decidedly, though not much, greater than by the mass of the female pop. : a circumstance that seems to indicate that women enjoy prosperity much more moderately than men do, and that they use the advantages