542 
Mr. Gompertz on the nature of the function 
i = lO 
b—20 
6=30 
0 
II 
6=50 
b= 6 o 
0 
II 
6=80 
Log. of accom. ratio ) 1,9768 
forioyears = 37.9685 
X(i,03"‘°)=: T.8716 
7.9685 
1.9552 
1.8716 
1.9552 
*•9383 
1 .8716 
1*9383 
I .9292 
7,8716 
7,9292 
7,8318 
7.8716 
7,8318 
7 .6689 
7.8716 
1 .6689 
1*3134 
1.8716 
7.31347 from Tab.VIIL 
2.6695 3 Carlisle. 
1.8716 
sum . . = 7,8169 
1*7953 
7.7651 
i* 739 i 
7.6326 
1*3723 
2.8539 
3*8545 
No* corresponding ( 
to sum in Table I. 3 
.89139 
.87604 
.86295 
.81067 
.69156 
.48781 
.19146 
Log. of ratios for 1 0 years = | 
M, 03 -*o . . = 
7.97438 
I .96681 
7.87163 
7,94120 
7,92082 
1*74325 
7.89520 
7.85854 
1.61488 
7.83292 
7.77684 
7.48651 
7*75123 
^•S 9 S 77 
1*35814 
7.57016 
I . 1 9448 
7.22977 
7.16886 
2.36767 
1.10139 
The log. of the present 7 
worth of each portion 3 ” 
.70421 
.48131 
*23157 
7,90694 
7.39670 
2.48222 
4*82938 
And the present worth of each, or the numbers correspond- 
ing to the last logarithms are arranged below. 
For first 10 years 
7.9886 
2nd 
ditto 
5.0607 
3 d 
d'* 
3.0291 
4th 
d° 
1*7044 
5th 
d° 
.8071 
6th 
do 
.2492 
7 th 
d° 
.0303 
8th 
do 
.0007 
sum 
18,8701 
which 
differs 
but ii 
As the method by which the logarithms of the present worth of 
the diflFerent portions are found, may not be seen by every reader, I 
will explain the operation in the third portion ; that is, when the 
logarithm of the portion first found is anticipated for 20 years. 
Resume ..... .87604 
Table VII. log. of real chance for age ) - _ 
10 living 20 years . . .3 
Ditto 20 years living . . T. 92082 
^(I, 03 -*°) .... 1.74325 
.48131 
which gives 18.873. In a similar way, I find the value of 
the joint lives for ages 20 and 30, at 3 per cent, and Carlisle 
mortality to be 16.745 ; which, according to Mr. Milne's 
table, should be 16.749 ; which appears to be an insignificant 
difference. 
Example 4. To find, when particular accuracy is not 
.required, according to the formula for the whole of life, 
1,03 
1 
I 
—I 
Q + at the Carlisle mor- 
the approximate value of 
tality, when a = 10, 20, 30, &c. call the logarithm of accom- 
modated ratios for an unlimited time at the age a, standing 
for the accommodated ratio in Table VI. at the age a. 
