358 THE FACTORS OF THE MIND

TABLE VII
CONTRIBUTIONS OF FACTORS TO TOTAL VARIANCE

Theoretical Values.
Thurstone's Data.

Factors.

!*
, __^t
a __ i _

n
n
*Vi

Before
After
Before
After

Rotation.
Rotation.
Rotation.
Rotation.

I
•30 to -50
•339
•072
•487
•104

II
•08 to -15
•082
•061
•118
•087

III
•03 to -06
•050
•071
•071
•103

IV
•oi to -03
•035
•084
•050
•121

V
<-OI
•033
•048
*°47
•069

VI \

•027
•050
•040
•072

VII

•025
•046
•°35
•066

VIII

•021
•072
•030
•104

IX .
<*oo5
•020
•049
•029
•069

X

•021
•046
•031
•066

XI

•024
•049
•034
•070

xii ;

•019
•048
•028
•069

Total
•42 to -75 • +
•696
•696
I -000
I '000

tendency." * I have ventured to suggest that a truer description of
the facts is not that the correlation tables tend to have a rank of
one, i.e. only a single latent root, but that their latent roots, though
numerous, are widely separated and exhibit much the same
diminishing proportions — one being nearly always three or four
times as large as any other and usually accounting, not, indeed, for
all the variance, but for at least half the total significant variance.
Given certain specifiable conditions, these proportions, and their
mode of diminution, could, I think, be predicted on theoretical
grounds.2 Hence it may be of interest to compare these general
values with those actually obtained in the latest and most extensive
research in which factor-analysis has been employed — Thurstone's
work on Primary Mental Abilities [17]. From the saturation co-

P- 139 f- ;. P7l P- 9i ; [132], pp. 5> 3i6- The tendency is not
peculiar to -psychological data, as these writers imply (v. pp. 357 and 486).

2 Since analysis by multiple factors is a process of averaging deviations
about preceding averages, the range of the correlations is reduced to rather
more than half at each step : the treatment of the first factor as exclusively
positive, instead of bipolar, produces the effect of missing a step.