io8 THE FACTORS OF THE MIND

total variance as possible, the next for as much, as possible of the
remaining variance, and so on, .and their purpose is not fulfilled
unless all the significant variance is ultimately accounted for.

These two changes introduce both order and comprehensiveness
into the description of the data ; and it is these that are the essential
merits of a sound scientific classification, not the fact that the
classes reached shall be necessarily fewer than the specimens to be
classified. Select a representative sample of all the plants in Kew
Gardens ; set a botanist to classify them : he begins with a compre-
hensive specification that will distinguish plants from other living
things—the general factor ; he then divides the whole lot into seed-
bearing and non-seed-bearing—a division which, as we have seen, is
chosen because it carries with it larger and more numerous differences
than any other ; then he redivides the former into flowering and
non-flowering, for precisely the same reason ; the flowering in their
turn into two contrasted classes, the one-seed-leaved and the two-
seed-leaved ; and these again into orders, and the orders into
varieties. Is it an objection that the varieties he ultimately names
may be as numerous as the specimens he has been given ? Give him
yet another plant, different from all the rest; and he will invent yet
another pigeon-hole to receive it.1 Economy is achieved^ not by

for a given set of correlations in such a way that the residual or partial
correlations remaining would be as small as possible. This phrase seems to
convey the notion best to those familiar only with elementary algebra. In
more technical discussions it would seem better to substitute the term
' dominant factor,' which is used to mean the factor corresponding to the
highest latent root of the correlation or covariance matrix, i.e. to the leading
element in the diagonal matrix of factor-variances. This is in keeping with
customary terminology in matrix algebra. In the latter the phrase ' highest
common factor ' would probably suggest the leading element in the diagonal
matrix obtained in Smith's reduction of a lambda-matrix to a canonical form
(a related and suggestive conception, but not quite identical).

1 Or, to use the technical language of the logician, I should argue that
infinite species are still species, and therefore in theory possess each its own
factor. When we come to correlate persons, however, the problem takes a
more disputable form. If each person is to have his own specific factor, does
that factor represent his principium individuationis, or his proprium (his
necessary properties), or merely his * inseparable accidents * ? (see below,
p. in). In practice the question will rarely arise. Usually there are fewer
traits than persons; and in such cases, in virtue of the lowered rank of the
matrix, there will not be a specific factor for each person. When, on the
other hand, there are fewer persons than traits, the persons will usually be
chosen for their representative character ; and hence, once again, the person's
* specific factor ' will not really be peculiar to him individually ; it will be
peculiar to him only as representing a particular class or type.