538 
Mr, Gompertz on the nature of the function 
ten years, for the age 20, calculated according to the Carlisle 
table upon the consideration of interest at' 5 per cent. Accord- 
1,05”' 
ing to the Carlisle tables, I find X i 5 L; that is, the logarithm 
of the annuity of one pound on a life of 20, for ten years, at 
5 per cent = ,87176, and putting = 105 -iS, by hypothesis 
X 
T a- J 
we shall have X io| ; that is the logarithm of + a®. . i. 
a^°) = ,87176 ; that is, x == ,87176 ; hence proceed- 
ing, as shown above, to find from General Table I. X(j*°) 
Having given . . ,87176 
a"— I 
We have next lessrr, 86842 corresponding to ... T.75 
,00334 difference 
,00302 proportional p art . . . ,006 
30 . . ditto ,0006 
2 . . ditto ,00004 
.87176 corresponds to . x(a‘°) 1.75664 
X (1,05 '”) c= ,21189 
1.96853 for the 
log. of the accommodated chance to Iwe 10 years at the Carlisle mortality. 
In the same way may the accommodated chance be found 
for any other term, when general tables for the term are 
constructed, and from any other base of interest. I may 
observe, that by using different rates of interest, as a base for 
determining the accommodated chances, different degrees of 
accuracy may be obtained. See Art. 5. Chap. II. 
Art. 8. Table VI. is the logarithm of the accommodated 
chances € at every age, b for living One year, where € is of 
such value that the sum of the geometrical progression 
— -j &c. ad infinitum, or, which is the same thing, 
