DATA FOR THE PROBLEM OF EYOLUTTON IN MAN. 
245 
In Table XIX. a more elaborate investigation is made of formnla (9) only, using 
the four forms given in Table XVII, and tabulating the errors made. We see that 
the maximum error of the mean formula is under 2 per cent,, and the average error 
under 1 per cent. These errors appear to me less than the personal ecpration of two 
observers, measuring the same series of skulls. In fact, I am inclined to think that 
the errors of the mean formulae may be as much due to the dilferent observers 
who have determined the “actual” values as to defects in the formulae them¬ 
selves. The close association of the Aino and German results is specially note¬ 
worthy. 
The results for the correlation and i-egression, not only of the skull, but of the 
long bones of the Ainos, show a relation much closer to modern Europeans (French 
and German) than the latter bear to the Naqadas. The })rimitive Aino race appears 
to be in some manner much more closely related to the evolutionary source of the 
Aryan races than either are to the Naqada. 
On the other hand, it will be seen that the Naqada formula while giving bad 
results for German and Aino gives much better results than they do for both the 
ancient and modern Egyptians. Its maximum error as applied to the Egyptian 
races is only slightly over 1 per cent., while its average error as applied to all three 
Egyjjtian races is under ‘4 per cent. 
The mean formula over-estimates the Aino and German, and under-estimates the 
Egyptian races.* 
The general rule for deducing the best result, would clearly be to work with the 
formula for the most closely associated race. But if no association can be predicted, 
then we shall hardly have an error as large as 2 per cent, if we use the mean 
formula. As this error is less than that frequently obtained by diherent observers 
for the same series, I conclude that a fairly satisfactory formula has been reached for 
the reconstruction of skull capacity from external measurements, 
(11.) At this point it seems desirable to say a few words about the errors made 
hy different observers in estimating skull capacity. I believe the differences of the 
same observer using different methods on the same skidl can be reduced to a very 
few cubic centimetres, but the personal equation of two observers using different or 
even nominally the same methods on the same skulls will be very considerable. When 
the observers have been trained in different schools and use different methods the 
divergences may be very great. The value of the capacity depends so largely on 
the amount of “ packing” both in the skull and in the measuring glass. Thus I found 
with two very careful investigators measuring about fifty skulls, their averages 
differed by about 30 cubic centlms., and this difference was approximately constant for 
each skull. Three measurers using the same process with great care got results for 
individual skulls occasionally differing by even as much as 40 cubic centims. ! On the 
* It should be noticed that the German formulae give better re.sults than the Aino for the Naqadas, 
although in cephalic index the Aino is much closer to the Naqada than the German is. 
