532 Mr. Gompertz on the nature of the Junction 
for any degree of accuracy the given table of mortality will 
admit of, but then the labour will be increased in. proportion. 
Art. 4. There are different modes of obviating, in a great 
measure, this inconvenience, by assuming an accommodated 
ratio for the given age, instead of the real ratio, from amongst 
which I shall only for the present select a few. The first is 
.V 
is, the log. of + 
"x+3 
1 
1 
V 
Lx 
L 
x-\.p ^ 
that 
L "T L L • • • • L 
XXX X 
this value in the general table, which will give the corres- 
ponding value of the log. of ; and construct a table of such 
values for every value of x, and adopt these values for log. 
of a instead of the abovenamed values of the log. of -7-^ > 
for the determination of the values of the limited periods : the 
preference of this to the first proposed method consists in 
this ; that if the series rx (L^^, 
f-j-£’+C'+&c. . . . the series &c. being nearly 
in geometrical progression, and-iii — €= s^, _£±f.«gs— ^ ^ 
&c. e^, &c.will be small, and g^-|- 0, and there- 
fore, if the series > "T^ Ac. 
formed accurately geometrical progressions, and the value of 
L X L 
d^i value of the annuity for the term. 
c + l 
would be accurately equal tow£-}-m*C® 
+ m *1+ w’ £j+ + but because in 
