Data for the Problem of Evolution in Man. 335 



vertical circumferences of the skull. The present memoir deals in the 

 main with the problem of the reconstruction of the capacity from these 

 characters. 



Three fundamental problems arise in the theory of reconstruction, 

 i.e., the determination of the probable value of an unknown character 

 from a known and measurable one, or from several such. Namely : 



I. The reconstruction of the individual from data for his own 



race. 

 II. The reconstruction of the average value of [a character in one 



local race from data determined for a second local race. 

 III. The determination of the probable value in an individual of 

 characters not measurable during life from characters which 

 are measurable. 



These three problems are all dealt with for the special character 

 capacity of the skull in the present paper. Their importance may be 

 indicated by the following considerations : 



(a.) Many, especially of the more ancient and accordingly more 

 interesting skulls, are too fragile or too fragmentary to allow of their 

 capacity being directly determined. 



(ft.) The methods for directly determining capacity are still not only 

 very diverse, but divergent in result, and from the physical stand- 

 point crude and inexact. In the concordat of the German craniologists 

 the Frankfurter Verstiindigung the point was left for future con- 

 sideration, 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 comparable, at least 

 if the argument from the comparison is to depend on a difference of 

 30 to 40 cm. 3 While the same observer using different methods may 

 be trained to get results within 4 to 6 cm. 3 for the same skull, 

 different observers, equally careful, using the same method, will easily 

 get results for the same series diverging by 20 to 30 and even more 

 cubic centimetres. 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 independent 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 individuals with a classified measure of intellectual 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 



