W. R. Macdonbll 
189 
We will next give the coefficient of variation, which is defined as the per- 
centage variation in the mean, the standard deviation being treated as the total 
variation in the mean {Phil. Trans. Vol. 187, A., p. 277). 
TABLE 12. 
Coejfficients of Variation. 1000 Cambridge Men and 3000 Criminals. 
1000 Cambridge Men 
3000 Criminals 
Head Length 
Head Breadth 
Height 
3-1839 + -0481 
3-2836 + -0496 
3-6958 + -0558 
3-1544 + -0275 
3-3332 + -0291 
3-8773 + -0338 
The probable error of the coefficient of variation, v, is calculated from the 
formula : 
probable error = '6745 
J2n 
where n is the number of measurements. (See Pearson, Proceedings of the Royal 
Society, Vol. 61, p. 345.) 
From an examination of these results it appears that there is but little 
difference in variability or correlation between the criminal and the educated 
classes, but a most noteworthy difference in means. It is also to be noted that 
there is practically no difference in variability whether measured absolutely or by 
coefficients of variation. 
Finally, we will compare the cephalic index in Cambridge men and criminals. 
In calculating the index it is to be noted (i) that 11 millimetres are deducted 
from the head measurements, in accordance with Dr Alice Lee's memoir "A First 
Study of the Correlation of the Human Skull " {Phil. Trans. Vol. 196, A., p. 252) ; 
and (ii) that we know only the mean Head Breadth and mean Head Length, and 
therefore in calculating the mean of the Cephalic Index, which is 100 times the 
ratio of Head Breadth and Head Length, we must apply the formulae given in 
Professor Pearson's paper in the Proceedings of the Royal Society, Vol. 60, p. 492. 
He there shows that if ;r, , a-o, be the absolute sizes of any two correlated organs, 
mi, m.2, their means, a^, o-.,, their standard deviations, r^., their coefficient of 
correlation, i^^ the mean value of Sjo the standard deviation of ~, then 
■«12 = (1 + - TjoWiV.^), 
where 
Si, = ?io {v^- + v.? - 2r,.2ViV.^K 
Wi = o-i/?/ii, V2 = ai/m^. 
