MORTALITY. LAW OF. 



MORTALITY, LAW OF. 



UM Uw ot mortality as follow* : Suppose the register* of a year 

 showed that M,, died in their ftnt year, x, in their aeoond year, and 

 ao on. the equality of birUu and death* shows that M + II, + M, 4- . . . 

 oat bar* been born in that year, and the etitinnary character of the 

 Uw of mortality being assumed. it follow* that of u a M , + . . . perron* 

 born, it i* the law of the mortality that M,, die in their first year, or 

 that M, +M, + ...survive; aimilaily that M. + M,* ... survive two 

 years, and o on. But if the population be in a state of increase, and 

 if the annual ratio of increase be that of 1 : 1 + n, those who die at the 

 age x 1 and x cannot be incorporated in the same table, mnce the 

 first are a portion of a table beginning with a larger number of birth*. 

 The former then must be reduced, or the Utter increased, in the 

 proportion of 1 : 1 + p : so that if M,,. M,, Ac., be the death* in the 

 first, second, Ac. years of age by the register, the table must run 

 thus: of 



persona burn, M die in their first year, M, (1 + p) in their second, and 

 so on. 



A table of mortality may also be given in the form of n table of the 

 mean durations of life, calculated as in LICK, MI:AX DI/HATION OF. 

 Or the table of mean durations may be calculated from the table of 

 yearly rates, as follows : Let e m be the mean duration of the lives 

 aged , and m . the yearly rate at the same age : then 



.- 4 = (!-) (.+i + 4) 



by which, beginning from the end of life, the mean duration at each 

 age may be computed from that at the age next higher. 



Various tables of these several kinds have been constructed, begin- 

 ning with that made by Halley from the town of Breslau, and ending 

 with that formed by the Equitable Insurance Office from its own 

 materials, and with the Actuaries' Table presently mentioned. If we 

 were to look to the wants of the subject, whether as a physical imv- 

 tigation or a statistical one, we should find that it is everywhere in the 

 merest infancy. The fact of a difference of mortality between the 

 two sexes U established, and it also seem* to be known that where the 

 occupations of females are not above their strength, their mortality is 

 leas than that of males ; but no settled determination of the amount 

 of difference has been obtained. As to whether married or single life 

 is the longest, whether the age of the parents, or the relative age, 

 affect* the mortality of the children, whether the earlier children of a 

 marriage differ in their Uw of mortality from the later, &c.. we have 

 no trustworthy information at all. In some foreign countries, a* in 

 Sweden and Belgium, the attention paid by the government to 

 statistical subject* has produced some results which are worth a good 

 deal ; the reader may consult the article in the ' Encyclopicdia lint-tu- 

 nica,' already cited, for reference to them. We shall now give merely 

 the date* and titles of the most remarkable earlier tables connected 

 with the subject. 



1688. Pariah registers first kept in England. 



1540-41. The statute 32 Henry VIII., c. 28, enabling ecclesiastical 

 person* and corporations to grant leases for three lira, or licentij-one 

 ytart. From this permission springs, we think, much of the attention 

 which ha* been paid to the subject of life leases in England. It gave 

 rise to certain tables of the value of leases which were called ' .l>r,.idV 

 Table*,' and which were put together, a* was thought by Uter writers, 

 about the end of the reign of Henry VIII. They assume a rate of 

 jnterart greater than 11 per cent. After the Restoration, when the 

 interest of money had very much fallen, the ecclesiastical lessors 

 began to raise their fine*. ThU occasioned great dissatisfaction, and 

 frequent representations to the House of Commons, which, though it 

 passed no Uw, in several cases recommended to |>articular bishops, Ac , 

 an adherence to the old rule. Attention began to be turned towards 

 the actual value of life. In 1662 John Uraunt published his ' Natural 

 and Political Observations <>n the Bills of Mortality.' often reprinted. 

 In 1674, Sir William Petty, in a paper in the ' Philosophical Trans- 

 action*,' proposed a Uw of mortality of the following kind : the 

 probability of one life surviving another, after the age of 16, i* 

 inversely a* the *quare root* of the ages In 1685 were published the 

 well known ' Table* for renewing and purcharing the lease* of 

 Cathedral Churches and College*/ the method* of which were 

 certified to be correct by Newton, and which therefore have been 

 frequently called Newton* Tables. About 1720, if not before, a 

 letter called The Value of Church and College Leans considered,' 

 was ap|wnded to these tables, and a very sharp controversy took 

 place, which produced a great many pamphlet*; the party of the 

 le**eea appealing to custom, the lessors showing from the value of 

 life and interest of money that the church landlord dealt more 

 leniently with his tenant than the layman, as was indeed the 

 case. Among the writing* which an we out of this controversy was 

 The Gentleman's Steward instructed,' 1730, by John Richard*, 

 containing the most complete tables of annuities which had been 

 I ->! 



The work of Uraunt and the political essays of Sir William Petty 

 preceded, and probably utimulated the attempt of Halley to construct 

 (in 1W2) a table from the bills of mortality at Brmlau. which was 

 puSliahed in 13. In 16B came Dr. Davenanfs 'Eaiay,' Ac., con- 

 t ning extract* from some table* by Gregory King (afterwards pub- 



lished entire), which Mr. Milne state* to represent tables since made 

 with great accuracy. Kerseboom's tables of lives (constructed from 

 Dutch registers of annuitant*) appeared in 1738, 1740. and 171-' I ' 

 Moivre'* Treatise on Annuities,' containing hu celebrated hyi> 

 was published in 1724; and Thomas Simpson's work 011 tli> 

 subject, containing a table deduced from London obs rvatinn.-. m 17 I. 1 . 

 Deparcieux, in 1746. published his 'Treatise on Annuities,' con: 

 hi- 1 ililes deduced from the live* of Krrm-li annuitants, as well 

 monks and nuns. These were the first tables in which male and fenii tie 

 life were distinguished from each other. 



The works of Price, Baily, Hilne, Ac , contain altogether a large 

 number of tables, which we shall here no further notice than to give 

 references to the works in which they may be f mid. with other matters 

 connected with the same subject. 



Observations on Reversionary Payments,' by Richard Price, D.D., 

 .-vv.-nth edition, edited by William Morgan, London, Cadell and I ' 

 1812. 



'The Doctrine of Annuities and Assurances,' by Francis Bailr, 

 London, Richardson, 1816. Thin work, now out of print, has been 

 translated into French, under the title Thc'orie des Annuites Viageres," 

 traduit de 1' Anglais per Alfred de Courcy, Paris, Bachelier, 1838 Thci . 

 U also a spurious edition, issued ten or twelve year* ago, which is mi 

 imitation of the type, Ac , of the original. 



'A Treatise on the Valuation of Annuities and Assurance*,' by 

 Joshua Milne. London, Longman & Co., 1815. 



' On the Natural and Mathematical Laws concerning Population, 

 Vitality, and Mortality,' by Francis Corbaux, London, 1833. This work 

 contains a large number of tables. 



Reports (two in number) of Select Committees of the House of 

 Commons on the Laws respecting Friendly Societies. Ordered to be 

 printed, July 5, 1825, and June 29, 1827. 



' Report of John Finlaison, actuary of the national debt, on the 

 evidence and elementary facts on which the tables of life annuities arc 

 founded." Ordered by the House of Commons to be printed, Mau-h :'! . 



' Library of Useful Knowledge," treatise ' On Probability.' This 

 anonymous work is by Sir John Lubbock and Mr. Drink water (Bethuue), 

 but by some mistake many copies were issued with Mr. De Morgan's 

 name on the binding. 



' Treatise on Friendly Societies,' by Charles Ansell, Ac., London, 

 Baldwin A Cradock. 1835. 



' Tables showing the total number of persons insured in the Equitable 

 Society from 17t>2 to 1829,' Ac., by Arthur Morgan. London, 1831. 



Mr. Rickman's various Reports on the Population Census emit tin 

 tables de.luced from them. 



' Recherches sur U Reproduction et la Mortality," Ac., par MM. Q' 

 et Sniits, Bruxelles, 1832 ; and Sur 1'Homme, Ac., ou Kssai de Physique 

 Sociale," 2 vols., par A. Quetelet, Paris, Bachelier, 1835. These work- 

 exhibit for Belgium what we could wish to see imitated in England. 



' Tables of Mortality, deduced from the experience of the Amicable 

 .Society during 33 years, ending 1841.' Published in 1841. 



' Law of Mortality, deduced from the combined experience of 1 7 

 ofiices, embracing 83,905 policies, of which 40,616 are distinguished by 

 denoting the sex of the l.vee assured, and by classing them into town, 

 country, and Irish assurances.' Privately printed for the otlices in 

 1843. This table was constructed on pulicici, not untirei: a person 

 insured in two or more of the seventeen offices counted a* two or more 

 person*, all of whom were bound to die at the same moment. Perhaps 

 this would make little difference in the general results, though it 

 would be unsafe to assume as much. Again, though .-.-\vnt.Mi oincev 

 were combined, yet the Equitable and the Amicable put together make 

 up far the largest part of the whole. The distinctions pointed out 

 between male and female life (that is, amurcd life), are no doubt 

 correct, and are very remarkable. Female life, though better than 

 male life, appears worse among assured females than among assured 

 males. But the female difference and the Jrii'. difference are probably 

 to be explained by reasons which more cnc in thr uflices than the 

 student of the physical Uw of mortality. 



Tin- publications of the registrar-general commenced in 1839. It 

 would be- impossible to give any account of this valuable an<i 

 growing mas* of materials in any space which we could afford. And 

 there would be little satisfaction to the reader of a few years hence in 

 the perusal of what ho would know must be then very imperfect. We 

 h<i|>u that the registrar-general himself will soon |Vcl it hi* duty togive 

 the public a digest of results, with the proper references, and a com- 

 plete list of hi* publications. And when, speaking with <lu. 

 propriety, we mention the registrar-general, all who are conversant 

 with the sub ect will know that we mean Dr. Fair, who is as much tin 

 guiding spirit of the Registry Office as Sir Rowland Hill is of thr !' 

 Office. 



We shall now proceed to give some tables of mortality, namely, the 

 Northampton and Carlisle tables, those of the Kqnitable Insurance 

 Office, and Mr. Anscll'a Friendly Societies' table. We shall give a brief 

 description of each. 



1. Northampton Table. ThU table was formed by Dr. Price from 

 the burinl registers at Northampton, between 1741 and 1780. He has 

 not distinctly described the process by which he formed it. This table 

 was for a long time the only one used by the insurance offices. It i - 



