84 THE FACTORS OF THE MIND

more rigid mathematical basis. By examining the relations
and resemblances of visual sensations, obtained not from
mere introspective comparisons but from quantitative
experiments on the effects of mixing lights of varying hue,
it is possible to secure a series of colour-equations; and it is
then not difficult to show that these equations are reducible
to terms of three independent variables only—the so-called
primary colours, three colour-factors that can be repre-
sented by the three dimensions of the familiar double colour
pyramid. We may even determine what three primary
colours will best fit the actual data.1 But whether there
are really three separate retinal substances or processes
corresponding precisely to these theoretical primaries is a
question that cannot be decided from the colour equations
alone.

The mental c factors' with which recent factor-analysis
is more commonly concerned—the ' primary abilities'
deduced from tests applied to school children or adults—
have precisely the same abstract nature. Like the primary
colours deduced from the colour equations, they are postu-
lated to provide a standard frame of reference. They are,
in short, as the schoolboy is taught to say, * component
vectors' into which c resultants ' may be ideally ' resolved.'

Analogy between Factor-analysis and the Resolution of
Forces.—The foregoing illustrations, however, bring to the
fore an important point of difference between factor-analysis
in psychology 'and analogous methods of solving geometric
problems in the simpler physical sciences. The dimensions
with which the navigator or the aeronaut is primarily con-
cerned are directions in actual space : the dimensions with
which the psychologist deals are directions in a diagram only,
and the lines of which he speaks represent changes in non-
spatial variables, not differences in actual length or actual

1 In our own laboratory, Mr, P. H. Chatterji has recently been working
over the problem of colour-vision afresh from this point of view, applying
a more up-to-date factorial technique both to his own data and to that
recorded in the literature. I may add that many of the time-honoured
problems in sensation, hitherto attacked by so-called psycho-physical methods
only, could be fruitfully taken up anew from the standpoint of the analysis
of variance or covariance,