519 
expressive of the law of human mortality, ^c. 
This equation between the number of the living, and the 
age, becomes deserving of attention, not in consequence of its 
hypothetical deduction, which in fact is congruous with many 
natural effects, as for instance, the exhaustions of the receiver 
of an air pump by strokes repeated at equal intervals of time, 
but it is deserving of attention, because it appears corrobo- 
rated during a long portion of life by experience ; as I derive 
the same equation from various published tables of mortality 
during a long period of man’s life, which experience there- 
fore proves that the hypothesis approximates to the law of 
mortality during the same portion of life ; and in fact the 
hypothesis itself was derived from an analysis of the expe- 
rience here alluded to. 
Art. 6 . But previously to the interpolating the law of mor- 
tality from tables of experience, I will premise that if, 
according to our notation, the number of living at the age x 
be denoted by L^. , and x be the characteristic of a logarithm, 
or such that x (Lj may denote the logarithm of that number, 
that if A (LJ — X (L, + ,) = «, (L^ + r ) — (k + 
^ {K + zr) — ^ (K + 3r) = m^p; and generally x — 
• P '' ' ; that by continual addition we shall 
n 
have x(L^) — x i-f/) + ♦'•••/>" ) = 
I- ^ - 
m . 7-3^; and therefore if p^ z=q, and e be put equal to the 
number whose common logarithm is , we shall have 
+ = x(i = +x (0-9”; 
L 
L^_j_ ^ — X ; and this equation, if for a + ?i we write 
J->a ^ * L 
.r, will give ^ ^ ^ consequently- if y be put 
I 
