524 
Mr. Gompertz on the nature of the function 
Here = 3.779°9i 
= 3,746868 to be assumed = \ — m 
^(^ 30 ) = 3»7032°S • . = X — m-^mp 
^(^4o) = 3A816S . . —■kQ^^^--m — mp~mp^ 
= 3,564192 . . = X — m — wzp — 7WJ5* — mj9^ 
Consequently m + mp = X (^lo) ^ (Ho) = ,075886, and 
X (L^o) — (^50) = />* X w + mp = ,139013 ; therefore 
^’ = lpS’ ’■‘314468; .•./>=1,3535; = 
X (m) = 2,5084775 ;>« = , 032344; a— 10; r—10; 
^ (<z)= .01314468 ; negative; XX {g) = x(m) 
—10 X{q) —X (,3535) =2,82861; X {d')= XL^— = 
3,779091 + 091218, = 3,8703; consequently this will give 
between the ages 10 and 50 of Swedish males, 
X or the logarithm of the living at the age of x = 
3,8703 — number, whose logarithm is (2,8286i+,oi3i45 .r). 
A table will also follow to show the proximity of this with 
Mr. Baily's table. 
Art. 10. For Mr. Milne's table of the Carlisle mortality 
we have, as given by that ingenious gentleman. 
X |LioJ = 3,81023 
^ (Ho) = 3,78462 
X (Lj^j = 3,75143 
X = 3,70544 
X = 3,64316 
^ (^60) ~ 3,56146 
And the difference of these will form a series nearly in 
geometrical progression, whose common ratio is and in 
consequence of this, the first method may be adopted for the 
