CHOICE AND CHANCE. 45 
until it finally ceases. Fig. 5 represents an actual experiment. The time in min- 
utes is laid off on the horizontal line, while the velocity of evolution of the gas at 
various moments is represented by the distances from the base line to the curve. 
Hinrichs has shown from the experiments of Guldberg and Wage, that the proba- 
bility curve represents this case very closely. Operations based upon heat con- 
form more closely to this law, as there all the particles have a more equal chance 
of being acted upon—an essential condition. In society there are manifold oper- 
ations which closely resemble this. Almost every year society is agitated by some 
idea, which at first interests very few people, but the interest gradually grows, 
and apparently with considerable regularity, reaching finally a culminating point, 
and then gradually dying out. The base-ball and blue-glass fever and the zig-zag 
puzzle may be mentioned as cases of this kind, and other cases will readily suggest 
themselves. Movements in society which are properly classed as reforms, usually 
make slow progress at first. The case is, however, advocated by a few tireless 
enthusiasts, like Wm. Lloyd Garrison, and after dragging along for years, the 
matter suddenly makes rapid progress, and is abruptly settled. 
In other movements of less momen, tlike the adoption of some fashion in 
dress, the matter makes great headway at first, rapidly receiving the assent and 
adoption of the great mass cf people, a few laggards bringing up the rear. 
These cases, which are symmetrically related to each other, would be repre- 
sented by the chances in drawing balls from afy urn containing unequal numbers 
of white and black balls. 
Another well-known case lies at the base of all life insurance. We can pre- 
dict with great confidence how many persons out of 1000 who are 10, 20, 30 or 
40 years of age will live through the next year. ‘This case is so well known, that 
we will discuss a somewhat more interesting one, which has been investigated by 
Dr. Granville. I refer to the probability of marriage. Dr. Granville determined 
In some manner the age at which 876 English women were married. ‘The 
values thus determined are given in the following table, where the number marry- 
ing at the various ages from 13 to 4o is given: 
re A CS Ni ee ne a eee 
Age. | malay es uo ins | Pronaonl an sia iy 2a0(iion attain 
por a aa | rei) 43 45 | 76 | tts | 118.) 86 | 85 | 59 153 | 36 
Age. | 26 | 27 | 28 | 24 | 30 | 31 | 32 | 33.1 341 35 | 36 137 | 38 | 39 | 40 - 
ees ez itr) ol 7 shale 2lvel 2) ol tl o.. 
From such values, extended to a greater number of cases, we might easily 
‘deduce the probability of marriage at various ages. In this table, those who do 
not marry at all, are not included. These facts are represented in Fig. 6 of the 
plate. 
This operation reminds us very strongly of the chemical re-action. The 
hydrogen is liberated, at first slowly, the velocity increasing for a time, and grad- 
ually diminishing to zero. If we consider the velocity of marriage, the same 
