521 
expressive of the law of human mortality, &c. 
logarithms of mp, of mp^, of mp^ the values 2,8649? 2,9771, 
1,0892; the numbers corresponding to which are ,07327; 
,09486 ; ,1228 ; and consequently m, mp, mp^, and mp^ re- 
spectively equal to ,0566; ,07327; ,09486, and ,1228 which 
do not differ much from the proposed series ,0566 ; ,07327 ; 
,09486, and ,1228 ; and according to our form for interpola- 
tion, taking m = ,0566 and p = 1,2944 ; we have = 
— = —,1922 ; and agreeably to the Northampton 
tables, being = 3,7342 we have X (<^)= 3,7342 -f- ,1922 = 
3,9264, d == 8441, (7), that is to say, the logarithm of the 
logarithm of ^ = x (7^) — ^ ^ (jf) = 1,28375 — ,16819 = 
1,1156, x(g)==^ ,130949= 1,8695, the negative sign being 
taken because x (^) = X (e ) x 7^ . g and g = ,7404. 
And therefore x being taken between the limits, we are to 
examine the degree of proximity of the equation L^ = 
8441 X 7404/ * or that is, the logarithm of the 
number of living at the age :r ==3,9264 — number whose 
logarithm is (1,11556 -j-x x. 01121 3), as the logarithm of g 
is negative. The table constructed according to this formula, 
which I shall lay before the reader, will enable him to judge 
of the proximity it has to the Northampton table ; but pre- 
viously thereto shall show that the same formula, with dif- 
ferent constants, will serve for the interpolations of other 
tables. 
Art. 8. To this end let it be required to interpolate 
Deparcieux's tables, in Mr. Baily’s life annuities, between 
the ages 15 and 55. 
