336 /- '/<'///" J'rofifi in <>f Ei-v'utivn in .1. 



anatomical institutes.* Accordingly it is an investigation of con- 

 siderable interest to compare the pribabU capacity of the skulls of living 

 persons with their roughly appreciable intellectual grade. It is only 

 by such a comparison that we can hope to discover whether the size 

 and shape of the skull is to any extent correlated with brain power. 



In the course of the memoir it is shown that the auricular height 

 of the skull is a better measurement for determining skull capacity 

 than the total height ; that the circumferences of the skull, while 

 highly correlated with its capacity, give regression equations which 

 vary widely from one to another closely-allied race ; that linear 

 regression equations involving length, breadth, and auricular height, 

 while giving fairly good results for individuals within the local race, 

 have very divergent coefficients as we pass from local race to local race ; 

 that the cephalic index has very little correlation with capacity at all 

 (as a rule what there is may be summed up in the words : In a brachy- 

 cephalic race the rounder the skull the greater the capacity, in a 

 dolichocephalic race the narrower the skull the greater the capacity 

 the greater capacity following the emphasis of the racial character) ; 

 finally, that the correlation of capacity with the triple product of 

 length, breadth, and height gives a regression equation which is fairly 

 constant from local race to local race, and is accordingly the best 

 available. 



From this and other equations individual and racial reconstructions 

 are made, and the deviations between the actual and predicted capacities 

 in randomly chosen series of skulls are tabulated. The mean error 

 made in the reconstruction of the individual capacity by the best 

 formulae is 3 to 4 per cent., the maximum error, although of course 

 infrequent, may even be 10 per cent. For the reconstruction of the 

 mean capacity of a race, the mean error is about 1*2 per cent., with a 

 maximum error of 2*5 per cent. If these errors appear large to the 

 craniologist, we would remind him that his search for an absolutely 

 correct formula giving cranial capacity from external measurements is 

 the pursuit of a Will-o'-the-wisp. The theory of probability shows us 

 exactly the sort of errors such formulae are liable to, and teaches us 

 how to select the best. The whole basis of the theory of evolution, the 

 variability of one character, even with fixed values for a number of 

 others, would be upset if any such absolute formula were forthcoming. 

 What we have to do is to select a few organs as highly correlated as 

 possible, but, having done this, it has been shown elsewhere that we 

 shall not sensibly decrease the error of our prediction by increasing the 

 number of organs upon which the estimate is based, t Accordingly we 

 do not believe that sensibly better reconstruction formulae than those 



* This argument applies also, in even an intensified degree, to the determinations 

 of brain weight. 



t ' Phil. Trans.,' A., vol. UK), p. 466. 



