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bitants, the numbers of the living (the decrements continuing the same) should be dimi nished at every age by a number equal to the annual average of new-comers at and after that age. After this diminution, the table will exhibit the same probabilities of life atevery age with Table 46th; and if the sum of the remaining numbers is divided by the sum of the decrements, the quotient lessened by half unity will, agreeably to the rule in

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86 of this Volume, give the number which I have called the expectation at entrance, and consequently the true proportion of inhabitants dying annually. But there being no observations which make a subtraction of this kind, at every particular age practicable; it is necessary to be satisfied with such a subtraction at the beginning of mature life as, that directed in the 2d Essay, p: 84, &c. The Stockholm observations happily give a proof of the necessity and use of this subtraction, by informing us of the true probabilities of living at Stockholm, as exhibited in Table 46th; and at the same time furnishing us with the means of con structing a table (like the 13th for London of the probabilities of living in this town, on the supposition that all who die were born there. Let therefore, (since the excess of the burials above the births is nearly the same in both cities) the correction be applied

In nine years before 1764, the births at Stockholm, exclusive of the still-born, were 7,907, and the burials 11,344.

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to this last table which has been applied to Table 13th for London. That is; let it be supposed that one quarter of all males and females who die at Stockholm, begin their residence in their 20th year; and in conformity to this supposition, let 2500, or a quarter of the radix, be subtracted from all the numbers living at every age before 20, preserving the decrements the same. The result will be a table which, when compared with Table 46th, will appear to exhibit more nearly the true probabilities of living in all the stages of life. By giving them, however, too high, it will appear that the cor rection has not been sufficient and that, to vodami a bea or boilghlum od ot Ligno After this correction, the numbers in the notaj pt-253, will be flag for a jot od el Living.

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Living. Males at age 0 7,500 Females at age 0 7,500

J701 4,760 5 ob 12.4022oowood a histor 2 -4,148

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53,309

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20. 4,865

25 4,480

Audi 9 &c. &c.

Totals (including

the numbers omitted) after deducting 5000 J.JIVI.

>187,100

20 5,145

25 4,854

&c. &e:

297

230,367

Therefore the expectation at entrance of males is 18%, of females is 23 of both conjointly 20,; but these expectations are really (as appears from the observations) 16.8020.93, and 18.89 respectively.

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consequently

consequently, the expectation at entrance will come out, though much nearer, yet still above the truth,

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I have thought it worth while to make these observations, in order to shew, from an unquestionable fact, what judgment ought to be formed of the tables for London in the following collection; and it seems impossible not to be convinced by them that though these tables give the probabilities of the duration of life in London (and consequently the values of life-annuities) strikingly lower than in other situations, yet they do not give them low enough; and that, in particular, the number by which the annual deaths ought to be multiplied to find the number of inhabitants, and which Table 14th deter mines to be 204, is not probably so much

as 20.

In short. From the agreement in almost every particular between the London and Stockholm bills, and between two tables formed on the same principles from the deaths only in both towns, it seems a necessary conclusion that, since one of these tables (even after the correction explained in the fourth essay) gives certainly too favourable a representation of human life, the other must do the same.

The following fact has some tendency to confirm this conclusion.

It appears from the midwifery reports of the general Westminster Infirmary, that of

1618 married men, and 1618 married women, examined by Dr, Bland the physician to this Infirmary, only 329 of the men and 495 of the women, had been born in London; that is, a fifth of the men, and somewhat more than a quarter of the women. But the correction I have been considering implies, that a number equal to half of all turned of 20 in London, are natives of London; and therefore, if we may judge at all from this fact, it must be an insufficient correction.

See Dr. Bland's account in the Philosophical Transactions, Vol. 71st, Part II. p. 370.--Of the whole number (3236) four-sevenths, or 1870, were born in the different counties of England and Wales; 209 in Scotland; 280 in Ireland; and 53 were foreigners.

TABLE

3. TABLE I i

The present Value of £t to be received at the End of any Number of Years, not exceeding 100;

Years. 2per cent 2 per cent 3per cent 34 per cent 4per cent 43 per cent,

2

1934567

980392 .975609.970874 966184.961538 .956938 961168951814.942596 .933511.924556919730 942322.928599.915142 .901943-888996 .876297 .923845 .905950.888487 .871442 -854804 .838561 .905731,883854.862609 .841973-821927 802451 887971.862297.837484 813501-790315 .767896 .870560 .841265.813092 785991.759918 734828 8 853490 820746.789409 .759412.730690 .703185

9

10

11

.836755 .800728.766417 733731 702587800

.820348 781198.744094 .708919.675564 .643928 .804263 .762145.722421 .684946.649581] .616199 788493 .743556701380 661783.624597 589664 13773032 725420.680951 .639404600574) .564272

12

14

15

16

17

18

19

20

21

.757875 .707727661118 617782377475 .5399731 743015690465.641862 596891555265) 4516720 728446 .673625.623167 576706.533908494469 714162 .657195.605016 .557204.513373 .473176) 700159 .647166.587395 .538361.493628 .452800 |.686431 .625528.570286 .520156|.474642| .433302 .672971.610271.553676 .502566.456387 .414643 .659776 .595386.537549 .485571.438834 .396787 22 .646839 .580865.521893 .469151.421955 .379701 23 .634156 .566697..506692 .453286.405726 .363350 24 .621721 .552875.491934 .437957.390121 .347703 25.609531.539391.477606 .423147 .375117 .332731 26 .597579 .526235.463695 .408838.360689 .318402 27 .585862 .513399.450189 .395012.346817 .304691 28 .574374 .500878.437077 .381654.333477 .291571 29 .563112 .488661.424346 .368748.320651 .279015 30 .552071 .476743.411987 .356278.308319 .267000. .541246 465115.399987 .344230.296460 .255502 32 .530633 .453770.388337 332590.285058 .244500 33 .520229 442703.377026 .321343.27 4094 .233971 34 510028 .431905.366045 .310476.263552 .223896 35 .500028 .421371.355383 .299977.253415 .214254 36 .490223 .411093.345032 .289833.243669 .205028 37 .480611 .401067.334983 .280032.234297 .196199 471187 .391285.325226 .270562 .225285 .187750 39.461948 .381741.315754 .261413.216621 .179665 .452890 .372430.306557.252572.208289 .171929 41 444010 .363347.297628 .244031.200278 .164525

31

38

40

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