948 



SCIENCE. 



[N. S. Vol. XII. No. 312. 



tance may be indicated by the following 

 considerations : 



(a) Many, especially of the more ancient 

 and accordingly of the more interesting 

 skulls, are too fragile or too fragmentary to 

 allow of their capacity being directly deter- 

 mined. 



(6) The methods for directlj' determin- 

 ing capacity are still not only very diverse, 

 but divergent in result, and from the phys- 

 ical standpoint, crude and inexact. In the 

 concordat of the German craniologists — the 

 Frankfurter Verstdndigung — the point was 

 left for future consideration, and so it has 

 remained for many years. The capacities 

 of series of skulls determined during the 

 past forty years in France, England and 

 . Germany are, we are convinced, not com- 

 parable, at least if the argument from the 

 comparison is to depend on a difference of 

 30 to 40 cm.' While the same observer 

 using different methods may be trained to 

 get results within 4 to 6 cm.' for the same 

 skull, different observers, equally careful, 

 using the same method, will easily get re- 

 sults for the same series diverging by 20 to 

 30 and even more cubic centimeters. 

 Shortly, the personal equation — involved 

 in the packing in the skull and in the 

 measuring vessel — is very large. 



Accordingly a regression equation for the 

 capacity as based on external measurements 

 may, if deduced from a sufficiently large 

 range of series measured by careful inde- 

 pendent observers, give results fairly free 

 from the error of personal equation and 

 this sensibly as correct as, or more correct 

 than, direct measurement when we require 

 the mean capacity of a series. 



(c) It is impossible to obtain a large 

 series of skulls belonging to known indi- 

 viduals with a classified measure of intel- 

 lectual ability. Actually we have only a 

 few skulls of men of great intellectual 

 power, sometimes preserved because they 

 were large, and to compare with these the 



skulls of the unknown and often the ill- 

 nourished, which reach the anatomical in- 

 stitutes.* Accordingly it is an investiga- 

 tion of considerable interest to compare the 

 probable capacity of the skulls of living 

 persons with their roughly appreciable in- 

 tellectual 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 capacitj', give regression 

 equations which varj' 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 coeffi- 

 cients as we pass from local race to local 

 race ; that the cephalic index has very lit- 

 tle correlation with capacitj' at all ; as a 

 rule what there is may be summed up in 

 the words : In a brachycephalic 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 correla- 

 tion of capacity with the triple product of 

 length, breadth and height gives a regres- 

 sion equation which is fairlj' 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 pre- 

 dicted capacities in randomly chosen series 

 of skulls are tabulated. The mean error 

 made in the reconstruction of the individ- 

 ual capacity by the best formulae is 3 to 4 



* This argument applies also, in even an intensified 

 degree, to the determinations of brain weight. 



