x PREFACE

different procedures in turn on some small table of measure-
ments.

As regards the second problem, I have always held that the
methods of factor-analysis might be applied quite as
legitimately to correlations between persons as to correla-
tions between traits, and that the same factors would be
reached by either approach. This I have regarded as
almost self-evident : yet it has also become the subject
of recent attack. Until an agreement on this issue is
achieved, the very nature of mental factors must remain in
doubt. In defending my own position, it seemed that the
most convincing line was, even at the risk of appearing
polemical, to examine one by one the various criticisms
advanced, and then, adopting the critic's own procedure, to
show how the results achieved are virtually the same. This
is the aim of the concluding Part. The upshot, I think, is
to demonstrate that for practical work a very much simpler
arithmetical technique will suffice than is described in the
usual books on the subject.

My acknowledgments are too numerous to record in full.
I owe most, I fancy, to the writings of those who are not
psychologists at all, but have been concerned primarily with
the general methodology of the more complex sciences—-
particularly Keynes, Johnson, and Fisher, and, among mathe-
maticians, Cullis, Sheppard, Russell, and Weyl. To English
psychologists, who have engaged in factorial work-
Spearman, William Brown, Godfrey Thomson, and my own
students—my indebtedness will be manifest at almost every
point. To my teacher, William McDougall, I shall never
be able to express my thanks: though his own approach
to psychological problems was along very different lines,
my first factorial research was carried out over thirty years
ago under his immediate supervision. Spearman's pre-
eminence is acknowledged by every factorist, even by
those who at one time differed from Mm most strongly.
My own obligation is a personal one as well: the generosity
that he showed in encouraging and criticizing my early work
has continued to the present day. The last two Parts of
this volume were completed before the appearance of
Thomson's admirable work on The Factorial Analysis of