NATURE OF THE FACTORIAL TECHNIQUE 87

from Dover to Calais. Now, we have seen that it is desir-
able to refer such movements and such forces to a standard
frame of reference ; and, as every schoolboy learns in the
* parallelogram of forces/ mechanical force may always in
theory be resolved, in accordance with the cosine law, into
independent components represented by lines at right
angles : e.g. if the vessel is moving south-east at x miles per
hour, this may be due to a wind blowing east at (x cos 45°)
miles per hour and a current running south at (x cos 45°)
miles per hour, or perhaps to what we call (summing up an
implied resolution in a phrase) a south-east wind.

(ii) The next step is to use similar points to mark differ-
ences in physical state other than those of mere difference of
position—e.g. differences in heat, pressure, volume, chemical
composition, electric potential, and the like. The lengths
of the lines will then be proportional to the amount of
change, and the differences of direction will mark differences
in the quality of the change, not differences of direction
in actual space. Thus, one line may represent increase in
pressure and another increase in volume, and we may seek
to explain these as the inevitable accompaniments of a con-
comitant rise in temperature. With this further extension
in the significance of the symbolic lines, there is no longer
any need to restrict ourselves to three independent dimen-
sions : we can have as many as we like, though, of course, it
will then be impossible to represent all of them at once on
flat paper or by a model. At the same time, however, the
whole system of quantitative changes may be regarded as
the result of a transfer, or rather of a transformation, of one
underlying capacity, constant in amount, but capable of
being applied in many different directions—namely, energy.

(iii) Having generalized so far, the transition from
physical processes to mental is easy. We may think of the
application of a test to a testee as the disturbance in the
equilibrium of a mental system, leading to a progressive
change of state in that mental system—such and such an
extent of change being visibly registered during a unit of
time, provided the conditions are kept constant. In every
case the essential nature of the process can be described
by saying (with a natural expansion of the strict meaning