326 THE FACTORS OF THE MIND The weighting and summing is repeated again and again, until, after 9 or 10 repetitions, the final results yield no change, at any rate so far as the sixth digit in each number (Table VI) ; it will be noted that the differences between corresponding numbers in the successive lines become smaller and smaller, and that approximately -415804— -398374 __ -419210— -415804 __ __ 175782 ^ •419210 — -415804 ~~~ -419869 — -419210 " " " 0-33950 ~" v% and similarly for the second and third column. Moreover, the figures thus obtained by table-by-column multiplication will be found identical with those obtained by table-by-table multiplication CM, P- 185). In the present example, since the determinants of the correlation matrix are small, a check is procurable by undertaking a direct solution. The figures so obtained are inserted in the last line but one, and coincide with the values that would be reached by increas- ing the index of R indefinitely, as estimated by summing the three geometrical progressions. TABLE VI Stage of Approximation. Saturation Coefficients. (Proportionate Values for Successive Approximations) . Factor Variance. Summing R (Thurstone) •398374 •386179 •215447 1-742923 R* -415804 •381779 •202397 1-754932 R* •419210 •380921 •199870 1-757263 £* •419869 •380751 •199380 I7577I3 R* •419997 •380717 •199285 1757800 R6 •420022 •380711 •199267 1757816 £7 •420025 •380710 •199264 1757820 R8 •420026 •380710 •199263 1757820 + R9 •420027 •380710 •199263 I75782I ™ » r •42002715 •38070993 •19926295 1-75782072 By successive rotations (Kelley) •420273 •380669 •199058 175783 The first line of the table is identical with the figures cal- culated according to Thurstone's centroid method ; the last line but one gives figures we should reach by Kelley*$ method or Hotelling's, if their rotations or iterations were continued indefinitely. The results obtained by Kelley himself with, his * new method of analysis5 are appended in the last line