PREFACE ix

essential formulae, on the lines of my published Memorandum
drawn up at the request of the International Examinations
Inquiry Committee. But the recent publications of
Thurstone and Thomson—both remarkable for the lucidity
and thoroughness with which they have covered these more
technical aspects—have rendered my own attempt not only
superfluous but largely out-of-date. Accordingly, I have
merely retained an Appendix on working methods which I
hope may be of service to the practical investigator, not
only in psychology, but also in many other sciences—
medicine, agriculture, biology, economics, and the various
branches of social science—where, as I believe, factor-
analysis might often be applied with ease and advantage.

Parts II and III were actually written before Part I.
The second was accepted for publication by the editor
of the British Journal of Psychology a year or more
ago; the third was submitted to the editor of the British
Journal of Medical Psychology as a sequel to an earlier
article printed in its pages. To the editors themselves I
am much indebted for permission to include them here
instead of in those journals. As they stand, they form a
natural continuation of the earlier chapters. The im-
portance of the two issues with which they deal became
evident at the symposium on * Factor-analysis' arranged
by the British Psychological Society at the beginning of
1939 ; and the interest aroused by these special aspects
showed the need for a fuller discussion in a more widely
accessible form.

As regards the first of these issues, I myself have always
held that the different methods of factorizing a given set of
data were merely variants of the same underlying principle—
alternative ways of reaching the same essential results with
a greater or less degree of ease and approximation. This
view has encountered strong criticism, and therefore re-
quires more adequate support. Proofs and illustrations are
supplied in Part II; and, if they win assent, should do
much to reconcile conflicting points of view. Let me add
that every student should test the issue for himself. What-
ever conclusion he reaches, there can be no better way of
understanding general principles than by trying all the