292 THE FACTORS OF THE MIND

figures ; but he is " of opinion that his (Burt's) is a very
narrow case, and that the factors considered by Burt are
not typical of those in actual use " (p. 213) ; and he ends
his account of the method by affirming that " it would be
wrong to conclude in general that loadings and factors are
reciprocal in persons and tests," since " most of what we
call association or resemblance between either tests or
persons is due to something over and above the very special
kind of residual association " shown in " Burt's doubly
centred matrix'5 (pp. 218-9). With this latter argument
as worded I fully agree : for " most of the association or
resemblance (i.e. most of the correlation or covariance)
between either tests or persons " is due to the first or domi-
nant factor (c the general factor' for tests or for persons
respectively). This by definition is the factor that accounts
for the greatest amount of the total variance ; and such
factors are by hypothesis excluded from my ' reciprocity
principle.' But, although he does not say so, the context
seems to imply a belief that even the non-general (the
secondary or bipolar) factors are not, as a rule, c reciprocal'
or equivalent. With that I cannot agree, unless by reci-
procity we mean an exact reciprocity, regardless of the
inexactitude which tests * in actual use ' always entail.

His chief criticisms of my argument may be summarized as
follows. First, discussing my fictitious example ([101], pp. 90-4),
he points out that " we could write down an infinity of possible raw
matrices from which Burt's doubly centred matrix might have
come " (p. 219). Thus, " to the rows of the matrix we can add any
quantities we like, without altering the correlations between the
tests, but making enormous changes in the correlations between
persons." But, if that were done, we should be disturbing the
relative difficulty of the tests: for in the rows the measurements
are entered as deviations about the average for each test (or trait),
and this implies that the tests are presumed to be of equal difficulty.
This is a presumption common to nearly all current factorial work :
(the only important exceptions are those cases in which the relative
difficulty of the tests itself becomes an object of investigation, as,
for example, in my investigation of the Binet-Simon scale, where the
relative difficulty of the tests was studied by correlating persons).
Again, he says, " we can add any quantities we like to the columns
of the matrix of marks." But that would introduce differences in