Page:Proceedings of the Royal Society of London Vol 60.djvu/251

230 Centroid = 11*504888. 12*483682. = 3*533226. ^ = 1*936527. yu4 = 451*998740. A = 0*001927. A = 2*900359. r = 55*546793. Skewness = 0*023589.

The critical function 2/32—3/3t—6 = —0*205063 is negative, and so the theoretical curve has a limited range. This range is 53*325; in the actual statistics it is 24, and so here as in the case of the R. antero-lateral it much exceeds any conceivable limit that may exist for the crab.

L. Dentary Margin.—The trend and range of the mean resemble those of the R. dentary. The total observed range of deviation is 417—524 thousandths. In groups 6—12 the range is 425—524, giving 24 units. Centroid = 14*071229. = 12*061035. o = 3*472903. —4*649576. H = 438*990665. A = 0*012322. A = 3*017770. r — 8438*070126. Skewness = 0*055527.

The critical function 2A—3A — 0 = —0*001426. From this we see that the. theoretical curve has a limited range; but this range would be enormous, and the curve would closely resemble a normal curve.

Correlation of the Organs.—Out of the six organs discussed, the frequency curves of three of them (total breadth, frontal breadth, and L. antero-lateral) give theoretical curves of unlimited range, while the other three (R. antero-lateral, R. and L. dentary margins) give curves of limited range. In every case the amount of skewness is Small, and the diagrams show that the generalised probability curves do not give very obviously better fits than the normal curve. The fact of the R. antero-lateral giving a strictly limited range while the L. antero-lateral gives an unlimited one, demonstrates that little stress can be placed upon the type of curve which a series of observations may yield.

In the present case the curves would appear to be sufficiently normal to allow us to find Galton’s function (known as r) for pairs of organs. For this purpose we shall employ the modified formula

^ _ 2 Deviation A x Deviation B w <ta <7B