expressive of the law of human mortality , f^c. 535 
riods of ten years; that is, for X corr^^ 
to a given value of X(a*®). N°. 2, for seven years, or for 
X ] , corresponding to X ), and the sd for five years, 
or for X , corresponding to X (a’) ; calculated (whether 
/) = 10, 7 or 5) for every value of x(a^), answering to 3,00 ; 
3,01 ; 3,02, &c 0. The first column containing the 
aforesaid value of X. [a% corresponding to which, in an hori- 
zontal line, is placed the log. of and between each suc- 
cessive value is placed the difference, retaining a decimal 
figure more ; at the head of the other columns for the pro- 
portional parts of the differences, are placed a column show- 
ing the number of cyphers to be prefixed to the differences 
entered in the column following, which are headed 
{98755} nearest under 1, 2, 3, 4 and 5, and opposite the 
number ; suppose 2,16 of table log. of stands 
2477.’ ziS 1926; '.65'.: ' 37 ®} . the upper, with the addition of the 
two cyphers, give the proportional parts for ,001, 002, 003, 
,004, 005; and the under, with the two cyphers, shows the 
proportional parts for ,009, 008, 007, 006 ; and the reason of 
choosing this arrangement, is the advantage which it offers 
of proof of correctness ; thus the sum of the higher an 
lower numbers of each of the above row with the two 
cyphers = 002752, which is double ,001376, and equal to 
the whole difference between the successive terms. 
( 1 — Ct \ 
— j, corres- 
ponding to log. of = 1.7954-. In the General Table I, 
Opposite to T.79 we have . . ,88868 
For ,005 we have proportional part . 256 
For ,0004 . ditto . , .20 
The sum . ,89144 is the answer. 
