e
offices rely not merely on statistics of life and death in general, but
collect special evidence in respect of different ages and sexes, and
make further allowance for teetotalism, inherited disease, etc.
Similarly with individual cases: the average expectation for a class,
whether general or special, is only applicable to any particular case if
that case is adequately described by the class characters. In England,
for example, the average expectation of life for males at 20 years of
age is 39.40; but at 60 it is still 13.14, and at 73 it is 7.07; at 100
it's 1.61. Of men 20 years old those who live more or less than 39.40
years are deviations or errors; but there are a great many of them. To
insure the life of a single man at 20, in the expectation of his dying
at 60, would be a mere bet, if we had no special knowledge of him; the
safety of an insurance office lies in having so many clients that
opposite deviations cancel one another: the more clients the safer the
business. It is quite possible that a hundred men aged 20 should be
insured in one week and all of them die before 25; this would be
ruinous, if others did not live to be 80 or 90.

Not only in such a practical affair as insurance, but in matters purely
scientific, the minute and subtle peculiarities of individuals have
important consequences. Each man has a certain cast of mind, character,
physique, giving a distinctive turn to all his actions even when he
tries to be normal. In every employment this determines his Personal
Equation, or average deviation from the normal. The term Personal
Equation is used chiefly in connection with scientific observation, as
in Astronomy. Each observer is liable to be a little wrong, and this
error has to be allowed for and his observations corrected accordingly.

The use of the term 'expectation,' and of examples drawn from insurance
and gambling, may convey the notion that probability relates entirely to
future events; but if based on laws and causes, it can have no reference
to point of time. As long as conditions are the same, events will be the
same, whether we consider uniformities or averages. We may therefore
draw probable inferences concerning the past as well as the future,
subject to the same hypothesis, that the causes affecting the events in
question were the same and similarly combined. On the other hand, if we
know that conditions bearing on the subject of investigation, have
changed since statistics were