376 THE FACTORS OF THE MIND

approach, he is not hoping to discover another set of factors,
but merely to arrive at the same result by a more service-
able route. And, in proposing the alternative procedure, I
expressly made what seemed to me the natural assumption
that the factors reached by classifying the persons according
to their traits would be virtually the same as those reached
by classifying the traits according to the differences shown
by the persons. But such an assumption should be sus-
ceptible of formal proof or at least of verification when
challenged. Accordingly, my previous article went on to
factorize the covariances and correlations between the
several persons; and I sought to prove, by a concrete
arithmetical illustration,1 that the main resemblances and
differences between them could be explained by precisely
the same c bipolar factors? as were discovered when the
more familiar procedure of correlating traits had been
adopted.

To exhibit the exact equivalence between these two
modes of approach, somewhat stringent conditions had to
be imposed : first, that the group of persons to be compared
should be as homogeneous as possible in regard to all relevant
qualities except those producing the temperamental types ;
and, secondly, that the mathematical analysis employed
should be one which would give the best possible fit to the
empirical measurements actually obtained. The first con-
dition was secured by making up a batch in which the
average or total measurement of every person was identical;
the second, by applying the method of least squares—a
device well recognized in almost every branch of science.

Those who have been good enough to comment on my
arguments have rightly urged that it is scarcely practicable
for these two conditions to be rigidly observed in ordinary
inquiries. Nor are they altogether convinced that what
holds good within a group of nervous or delinquent children
will be equally true of adults or of the child population as
a whole. In what follows, therefore, my first object will
be to demonstrate that the same results are obtained even
under rougher conditions of clinical investigation and
with the simplest methods of statistical analysis. I shall

1 A general algebraic demonstration had already been offered in [101].