206 
Proceedings of the Royal Society 
is remarkably regular ; in fact so regular, that, notwithstanding the 
comparatively small numbers observed, we shall be justified in 
believing that we have here an indication of a law of nature, upon 
which we may safely base our calculations. 
In order to make our conclusions practically serviceable, it is 
necessary to calculate from them the probability for every age from 
40 onwards, or, in technical language, to graduate the probabilities. 
This I do by a graphic method. In the appended figure I take the 
abscissa to represent the age, and the ordinate the probability that a 
marriage entered into at that age will be unfruitful. Thus, for age 
42, being the middle of the five ages 40-44, the probability is *285, 
and this is represented by the point A. In the same way the points 
B, C, D, E, E, G, H, represent the probabilities for the ages 47, 52, 
57, 62, 67, 72, 77. Then, joining these points by straight lines, I 
draw a curve which shall follow the general course of the points as 
faithfully as is consistent with the avoidance of irregularities in its 
form. Then, by estimating the ordinates of the points where the 
curve cuts the vertical lines in the diagram, I obtain a first approxi- 
mation to the adjusted probability for each age, and this is after- 
wards corrected by a process which it seems unnecessary to describe 
on the present occasion. The following are the values which I thus 
obtained : — 
Probability that a Marriage entered into by a Man of any Age 
from 40 onwards will be Unfruitful. 
A ge. 
Proba- 
bility. 
Age. 
Proba- 
bility. 
Age. 
Proba- 
bility. 
Age. 
Proba- 
bility. 
40 
•284 
51 
•295 
62 
•702 
73 
•882 
41 
•284 
52 
•315 
63 
•720 
74 
•896 
42 
•285 
53 
•365 
64 
•738 
75 
•910 
43 
•285 
54 
•430 
65 
•755 
76 
•924 
44 
•286 
55 
■500 
66 
•772 
77 
•937 
45 
'286 
56 
•562 
67 
•789 
78 
•950 
46 
•287 
57 
■600 
68 
•805 
79 
•963 
47 
•287 
58 
•626 
69 
•821 
80 
•976 
48 
•288 
59 
•646 
70 
•837 
81 
•988 
49 
•288 
60 
•665 
71 
•852 
82 
1-000 
50 
•290 
61 
•684 
72 
•867 
If we now multiply the number of marriages entered into at any 
age, by the probability in this table, the product will be the number 
