8o THE FACTORS OF THE MIND

better fitted for permanent reference, which usually means
reference to a standard system of orthogonal axes, at once
independent of each other and of the accidental circum-
stances of the observations.

Although the introduction of the idea of resolving
observed tendencies into independent components seems
to have struck the psychological worker as something wholly
novel—so novel in fact that he often supposes the whole
procedure to be an invention peculiar to psychology, and
to a special school of psychology at that—nevertheless there
is scarcely a branch of science, pure or applied, into which
such transformations do not constantly enter. I have
already cited one instance from geography. Let us
glance at another, almost equally familiar and far more
instructive. The theoretical psychologist who dismisses the
introduction of mathematics as far-fetched, and the applied
psychologist who regards arithmetical computations as an
unpractical hobby of the faddist, will do well to consider
how similar mathematical and arithmetical devices have
become part of the everyday tasks, not only of scientific
investigators, but of practical workers in numerous other
fields.

A navigating officer on the high seas will measure the * altitude'
and the * bearing ' of a particular star, i.e. its apparent height above
his horizon and its apparent distance east or west of Ids meridian.
If another observer measured the apparent position of the same
star simultaneously from another spot, he would obtain a different
set of measurements ; yet, if compared, the two sets of measure-
ments would evidently be related to each other in a way which
would not have arisen had each observer measured a different star.
The navigating officer therefore performs a routine calculation, and
converts his measurements into standard terms, namely, the dis-
tance of the star above or below the celestial equator (or equinoctial)
and the distance east or west of the vernal equinox (first point of
Aries), thus finding its celestial latitude and longitude-, or, as he would
call it, its ' declination ? and * right ascension ?; these will be the
same at all times and places, and will have the further advantage
' that, for different stars, the specifications will now be quite inde-
pendent of each other.

A navigator of the Spearman school* more interested in theory
than in practice, might perhaps prefer to express his results in terms