386 THE FACTORS OF THE MIND

led to inquire whether the arduous arithmetic imposed by the
full P- and Q-techniques cannot be legitimately abridged.
Suppose, for instance, that, having determined what the
types are, we propose to examine their frequency-distribu-
tions : we shall require to ' measure for their approximation
to the type' not ' fifty to a hundred persons as variables,'
([92], p. 18), but several hundreds ; and to work out the
intercorrelations between all these persons, and then
factorize the figures, would require the assistance of a full-
time computer and scarcely seem justifiable for the crude
observational measurements at our command. The ideal
procedure, I must still insist, would be to correlate and
factorize, not the persons (who may run into thousands)
but the traits (which can be reduced to about a dozen).
That, however, is precisely the procedure to which my
critics now take exception as committing us at the outset
to a denial of discrete types. Accordingly, one of the minor
objects of this paper will be to show how the essential
figures can be reached (at any rate within the limits of
approximation accepted by those who adopt the summation
method) by a far quicker and more direct approach.