NATURE OF THE FACTORIAL TECHNIQUE 73 Hotelling,1 and Kelley2 all begin with a similar equation. Thurstone writes it in more general terms, s^ = % #lt- + a& XM + • - • + an Xgh where s^ is z's score in test j9 x is i's measurements in the * q statistically independent reference abilities/ and a the c factor loadings' or saturation coefficients. Using matrix notation,3 we might express it still more succinctly as M = FP, where M denotes the empirical measurements, F the factor loadings, and P the hypothetical factor-measurements for the popula- tion tested. Now the form of all these equations suggests that the observable capacity, as empirically tested and measured, is composed of four or more fundamentalc abilities' or c fac- tors ? added together, just as the value of lo dollars can be obtained by adding ^ pounds to 2 shillings, 7 pence, and one halfpenny. I myself, however, have argued that " to begin with an equation like M = FP, when P is not given and M is, seems highly illogical: it is far more natural to start from the equation P = WM"i.t. deduce the hypothetical factor-measurements as a weighted average of the observed test-measurements instead of vice «w#([ioi], p. 84). This would emphasize from the very outset the literal truth, namely, that the factors, not the test-performances, are the hypothetical quantities to be obtained by algebraic sum- mation. After all, almost every factorist, who gets so far as to tell us how he would calculate his factor-measure- ments, writes out a regression equation conforming to this second type,4 though, instead of making it the starting- point of his exposition, he usually appends it as an after- thought. Factors as Averages.—This alternative equation, express- ing the hypothetical factors in terms of the empirical obser- method * for those who feel unequal to the fuller and more technical pre- sentation in Vectors of the Mind I 1 [79l» P* 4l8> e