Page:Proceedings of the Royal Society of London Vol 60.djvu/530

Rh Breadth of skull :* mx= 150*47, <rx = 5*8488, vx — 3*8871. H eight of sk u ll: m2 — 133 78, <x2 = 4*6761, V2 = 3*4954. Length of sk u ll: m3 = 180*58, ff3 — 5*8441, v3= 3*2363. Cephalic index, B /L : in = 83*41, 2 l3 = 3*5794, V is = 4*2913. Cephalic index, H /L : i 23 = 74'23, S23 = 3*6305, V 23 = 4*8909. Cephalic index, H /B : 1^1 = 89*12, S21 = 4*1752, V 2l = 4*6849.

The coefficients of correlation may at once be deduced: Breadth and length : r13 = (vx + v3 V13~)/(2r2r3) = 0'2849. Height and length : r23 = (v2 + v3—V232) /(2 v2v3) = —0*0543. Height and breadth : r2j = (v22 Jr v 2—V2i2) /(2 vyv2) = O'1243.

This is the first table, so far as I am aware, that has been published of the variation and correlation of the three chief cephalic lengths.! It shows us that there is not at all a close correlation between these chief dimensions of the skull, and that a small compensating factor for size is to be sought in the correlation of height and length, ., while a broad skull is probably a long skull and also a high skull, a high skull will probably be a short skull, and a low skull a long skull.

Without substituting the values of vu r13, r23 in (v), we can find p, or the correlation between breadth/length and height/length indices from : p = ( V132+ V232—V122) / (2 Y13V 23).

This follows at once from the general theorem given in my memoir on “ Regression, Panmixia, and Heredity,” ‘ Phil. Trans.,’ vol. 187, A, p. 279, or by substitution of the above values of r12, r13, in (v), we find: p = 0-4857.

If we calculate from (vi) the correlation between the same cephalic indices on the hypothesis that their heights, breadths and lengths are distributed at random, i.e., that our “ imp ” has constructed a number of arbitrary and spurious skulls from Professor Ranke’s measurements, we find: p 0 = 0-4008.

It seems to me that a quite erroneous impression would be formed of the organic correlation of the human skull, did we judge it by the magnitude of the correlation coefficient (04857) for the two chief

variation are percentage variations, i.e., they must be divided by 100 before being used in formula; (i), (ii), and (iii). t I hope later to treat correlation in man with reference to race, sex, and organ, as I have treated variation.
 * All the absolute measures given are in millimetres, and the coefficients of