THE general theory of the probable errors of the constants of skew frequency distributions was originally given with illustrationis by Pearson and Filon, Phil. Trans. Vol. 191, A (1898), pp. 229-311. The values there deduced depend on the form of special frequency cturve adopted, and involve considerable arithmetical work for each individual case. In these frequency investigations the fundamental constants are the well-known /,3 and /2. Every frequency character expressible in terrns of A, and 2 can have its probable error determined, provided we know the probable errors of 8, and 12 and the correlation in deviations between 8 and 32. General expressions for the probable errors (or the S.D.'s Qpl,, Yp) of A3 and 2 as well as the correlation R,plp2 of deviationrs in /3l and /2, together with the probable error of the criterion (or its S.D. = >IK) were first given by Pearson, Phil. Trans. Vol. 198, A (1902). These involve a knowledge of 36, /35, /4 anid /3*, further constants of the distribution which can only be found if the numerical values of /at, A6, p, and bt8 have been in some way determined. Now it has been shown that with the total frequencies usual in practice these high moments are subject to very large percentage errorst, rendering their use extremely undesirable, even if we could overcome our natural repugnance to the great labour of calculating them.