146 Biometric Constants of English Brain-weights 
product and horizontal circumference together (^without age and stature), and on 
each of these alone, are also added. 
Prediction Formulae. 
(i) a !« = -1987/'+-8644f^-l-1910/l + l-7508,S' + 36-8559. 
Probable error of prediction: 48-5 grs. Mean en-or: 57'4 grs. 
(if ?: ir=-2195P+-5067/7-l-2395/l + l-072l6'+191-8298. 
Probable error of prediction : 43'2 grs. Mean error: STO grs. 
(ii) a M, = -2136/' + -8486t^+47'9443. 
Probable error of prediction: 49'6 grs. Mean error: 587 grs. 
(ii)'' ?: ;v = -2466P+ -3893 172-2420. 
Probable error of prediction: 44-7 grs. Mean error: 52-8 grs. 
(inf ■er=-2519P + 374-7628. 
Probable error of prediction: 49-9 grs. Mean error: 59-0 grs. 
(iii) ^ ?: «(; = -2653P + 315-8281. 
Probable error of prediction : 44-7 grs. I\[ean error : 52-9 grs. 
(iv) '' $: ?v = 4-0895 f/- 945-1 785. 
Probable error of prediction: 549 grs. Mean error: 64-9 grs. 
(iv)b $: = 3-7344^7- 766-4563. 
Probable error of prediction : 53-0 grs. Mean error : 62-8 grs. 
We see from these results : first, that owing to the higher correlations it is 
possible to predict female brain-weights somewhat more accurately than male 
brain-weights from external measurements of the head. Secondly, that the funda- 
mental character is the product of the three diameters. A comparison of (iii) and 
(iv) shows that it is woith a good deal more than the circumference, and further 
comparing (iii) with (i) we see that if we predict from the diametral product alone, 
we shall only make 2 grs. worse mean error than if we predict from all four characters. 
From this standpoint it is clear that age and stature allowances are not nearly as 
important matters as head diameters if we wish to predict brain-weights from 
physical measurements. 
The formulae were then applied to 24 ^ and 24 % cases selected at random, 
being every fourth or fifth case in the observation book. It does not seem needful 
to reproduce the individual results, but the general conclusions are given in 
Table XX. 
Our actual I'esults are therefore somewhat in defect of the mean errors to be 
expected by theory, especially in the case of (i), (ii), and (iii) for the males. In the 
case of the females the defect is very little, and the theoretical and observed mean 
errors are close. We think it quite safe to say that the brain-weight of a living 
individual can be predicted with a mean error of not more than 50 grs. It is 
