527 
expressive of the law of human mortality ^ &c. 
In the ingenious Mr. Morgan's sixth edition of Price's 
Annuities, p. 183, vol. i. it is stated, that in the Equitable Assu- 
rance Society, the deaths have differed from the Northampton 
tables ; and that from 10 to 20, 20 to 30, 30 to 40, 40 to 50, 
50 to 60, and 60 to 80, it appears that the deaths in the 
Northampton tables were in proportion to the deaths which 
would be given by the experience of that society respectively, 
in the ratios of 2 to 1 ; 2 to 1 ; 5 to 3 ; 7 to 5, and 5 to 4. 
According to this, the decrements in 10 years of those now 
living at the ages 10, 20, 30, and 40, will be the number 
living at those ages multiplied respectively by ,0478 ; ,0730 ; 
,1024 ; ,1284 ; and the deaths in twenty years of those now 
living at the age of 60, would be the number of those living 
multiplied by ,3163. And also, taking, according to the 
Northampton table, the living at the age of 10 years equal to 
5675, I form a table for the number of persons living at 
the ages . . 
10 
20 
30 
40 
50 
60 
70 
being . . . 
and the log. of"] 
the number of > 
persons living J 
5675 
5403.5 
5010 
4496 
3919 
3116 
* 
3,75612 
3,73268 
3,69984 
3.65283 
3 . 593*8 
3.49360 
* 
Consequently, if a== 20, r = 10, we have x 3,73268 ; 
(V) = ^ (^20) —m — mp = 3,65283 ; X ^ _ 
mp — mp"" — m = 3,493^0 ; m,i p — ,07985 ; and 
mp^ X 1 +/> = 3,65283 — 3,4936 o =,15923 ; hence X(/>)= 
ix = , 149875; and />=i, 412131; X(ot)=x(,07985) — 
X (2,41243) =2,519874; and ,033013 ; X (e) = ■ ~ ”* - 
^ X ' ,412131 
negative ; X (g ) is negative ; XX [g) — Kyn — X, 412131 — 
,0149875 X 20 = 2,6051 ; X{d)=zX — x( 6) = 3.73268 — 
,080302 = 3, 81s sufficiently near ; and our formula for the 
