CLASSIFICATION OF METHODS 267

merely as empirical principles of classification, then, though logical
rigour requires such principles to be independent, practical exi-
gencies will still impose a compromise. The classifications of the
school psychologist, for example, have often to be made in terms of
partly correlated factors. When he explains that his theoretical
factors classify children according to verbal, arithmetical, and
manual abilities or disabilities, teachers inevitably assume that he is
referring to the more concrete classifications of pupils into schools or
forms according to what he would regard as c mixed factors,' not
(pure9 or independent. Rarely if ever does the teacher think of
differentiating (say) between a child whose disability in verbal
subjects is due mainly to his inferiority in general intelligence and
one whose disability is due to inferiority in what may be loosely
termed pure verbal capacity, i.e. an inferiority which affects solely
his power to understand or manipulate words.

In my educational work, therefore, I have found it necessary to
distinguish between what I have called ' mixed' or * joint' factors
(e.g. * concrete abilities *) and ' independent * factors (e.g. * pure' or
abstract capacities), or sometimes (adopting the phraseology of
Binet) * compound 7 and c partial aptitudes.'x Other writers have
recognized a similar distinction. Alexander, for example, uses the
terms * functional abilities * and i independent factors * to express it.
" The so-called functional abilities," he writes, " are not independent
traits; they are resultants. . . . Verbal and practical abilities can
be resolved into three (independent) factors—g and v, and g and F "
([82], pp. 117 et seq^). Rotation will often recombine independent
factors into what Thurstone calls * oblique reference vectors'
([84], p. 154). Eysenck, for instance, has endeavoured to show that
in Thurstone's recent work on Primary Abilities many of the rotated
factors, e.g. V, P, and W (verbal relations, perceptual functions, and
verbal fluency [122], Table 4) are positively correlated, and that
each includes a common factor, similar to Spearman's g, in addition
to some pure or independent factor peculiar to itself (cf. [133],
p. 272). The repeated application of Spearman's two-factor proce-
dure to submatrices of residuals successively obtained from the
same initial table of correlations has also led in the past to factors
which would seem to be correlated rather than independent. From

1 L'Annee Psychohgique, XIV, p. 32. Cf. also Tht Backward Child,
pp. 459 et seq. In my earlier Notes, the physicist's terms * spectral analysis'
and * fractional analysis * were used to indicate the evident analogy, but (as
indicated below) it would seem a little unwise to introduce into psychological
nomenclature a rather puzzling pair of terms for a distinction that is already
designated in half a dozen different ways,