124 THE FACTORS OF THE MIND

we should merely have to devise some way of counting or estimating
the number possessed by each. Nor is the proposal so far-fetched
as it might seem : for, even if we cannot count unitary elements of
ability or emotion, we can count the number of unitary reactions ;
e.g. the number of words Tom spells correctly in a uniform list of 50,
or the number of times he loses his temper within a specified proba-
tionary period.

Many writers, indeed, have explicitly assumed that the usual
correlation formulae and factor can only be applied upon some such
atomic postulate. Critics and defenders of factorial methods alike
apparently believe that the methods are illegitimate, unless the
measurements to be factorized are * extensive' measurements.
Cattell and Vernon in their recent controversy, for instance, argue
as if the issue turned essentially on the question, whether qualities
of personality can be measured in the same way as length and
weight. " Clearly," says Vernon, " our attempts at measurement,
whether with tests or with ratings, inevitably disrupt the personality
into separate bits, such as can be handled by our quantitative
techniques ; and naturally lead to the theory that personality
consists of such bits." l

Now, I have argued above that measurement is not necessarily a
physical process, and that wholes may be measured without imply-
ing that those wholes are divisible into separate parts. Even the
measurements of the physicist do not always involve direct counting
or direct superposition. To measure density we need not count the
number of molecules; nor do we estimate temperature by putting
one heated body on top of another or adding the component tempera-
tures. Nevertheless, although our correlation formula do not
require us to sum separable elements, they require us to sum differ-
ences. That is true even when we correlate orders or ranks ; and I
should agree that, unless the rank-differences can be treated as
approximately equal, the ordinary formula for rank correlation is
strictly inapplicable.2

1 Character and Personality, loc. cit, sup., p. 2.

2 Thomson seems to assume that, in general, correlating persons is only
valid " where each person can put the * tests' " (i.e. items to be judged—
pictures, subjects preferred, emotional traits of otlier persons) " in an order
of preference, according to some criterion or judgment." But, when we
come to subtract the rank-numbers and add the differences, we are going
beyond the postulates of mere order or ranking. We are making assumptions
about the spacing of the rank-numbers; and, if there is any reason to believe
—even the slender reason of subjective impression—that the spacing is much
wider at some parts than at others, then I should hold that the rank-formulas
are strictly speaking invalid.