402 THE FACTORS OF THE MIND

But, however applied in actual practice, the underlying principle,
it will be noted, is to estimate resemblances between individuals
and the * type' first of all, and deduce the ' type ' afterwards.
With the method described in the previous paragraphs the order of
procedure is reversed : we first determine the * type/ and deduce
the degree of resemblance to it afterwards. Moreover, with this
method we use measurements from all the persons to determine the
coefficients for the type, and give to each person an equal weight.
At first sight this seems far better than using one person, or even one
small group of persons picked out by simple inspection. Yet the
method itself demonstrates in the end how widely the various per-
sons differ in their resemblance to the hypothetical types. Does
it not therefore follow that the principle of equal weighting was
after all very inadequate ? Would it not be better to weight the
several persons differently according to their saturation coefficients
as now obtained ? We may readily agree. But, if we go on to
revise the whole of our computations on this basis, we shall find that
the correlations with the type as thus recalculated will not be the
same as those with which we started out. We must therefore begin
again with these revised saturation coefficients. Thus we shall be
continually led to fresh coefficients and fresh weights : in short, to
a spiral process of successive approximation. If we keep on we
shall ultimately discover that, having started with saturations
determined by simple summation, we are gradually approximating
towards the saturations determined by least squares. That being
so, would it not be much quicker to seek from the very outset a
direct determination of the type by correlating traits instead of
persons ? For, with the method of least squares, the saturation
coefficients for persons are really the correlations of those persons'
measurements with the saturation coefficients for traits ([114],
p. 178); and to reach the latter we must begin by correlating traits.

C. CORRELATIONS BETWEEN TRAITS

But this brings us back to our central problem. Can we
still assume that the factors obtained by correlating traits
will be identifiable with those already obtained by corre-
lating persons, even under the more general conditions that
we have here laid down ? For the ordinary reader, the
most convincing way to answer this question will be to
examine calculations for a small table of figures such as that
given above, and then note how the principles involved
are perfectly general.