492 APPENDIX II columns, persons or tests : I leave the reader to calculate unit hierarchies from Table IK, and so verify this statement. The sum of all such contributions should obviously yield the original measurement matrix (as shown at the foot of Table IVi), If Pt were already known, we could obtain the same detailed and total result by first multiplying the rows of factor-measurements by the appropriate factor-loadings, and then adding the products, according to the familiar equation M = Ft Pt (cf. Table IK above). But since Pt is not given and M is, it seems more logical to exhibit the direct analysis of M than its resynthcsis from Pt. Such a series of unit hierarchies is analogous to what is termed in quantum theory a * spectral set of selective operators ' ; each < selects ? the contribution of its factor, and so ' analyses a mixed aggregate into its pure constituents.' Thus, the mental performance measured by a given test is in effect conceived as the sum of a number of contributory reactions, mixed and heterogeneous : the selective operators sort these reactions into a few mutually exclusive classes, such as would popularly be attributed to distinct elementary TABLE III Results of Factorizing Covariances between PERSONS : I\I --* Lp (a) Covariance matrix M' M == Rp =a Fp F'p. R* b Total* Pi fa fa fa fa 54 — 18 o -36 1 08 fa — 18 14 -4 8 36 fa o -4 2 2 0 fa -36 8 2 26 72 Total* 1 08 36 o 72 z,6=3v< V6 0 2-V/6 0 Squares 54 6 o 24 84 s=s ist factor-variance f 7 caIculatW tjie total, the persons that are to receive a negative factor-loading (here person i) have their signs reversed.