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
- All the absolute measures given are in millimetres, and the coefficients of
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.
