DATA FOR THE PROBLEM OF EVOLUTION IN MAN. 
of method. Again Mr. Herbert Thompson found for the ca23acities of 39 d and 55 $ 
Naqada skulls, 1339 and 1243 cid^ic centims. respectively, hut Miss C. D. Fawcett 
using a diftereut method on 69 d and 98 ? skulls obtained 1387 and 1279 cid). centims. 
respectively. Something here is due to the difference of the samples, 1jut as in tlie 
previous case the personal equation is the chief source of difference. Now if 
differences of sample, of observer and of method will lead to determinations of racial 
capacity differing by 3 to 6 per cent., is not a great deal to be said for a formida 
Avhich when applied to a series of results of a uniform character (like those of the best 
German determinations given above) leads to an error of only 2*5 per cent, as a 
maximum ? I should personally feel as content with the results in Table XXL of my 
mean regression formulm and of the least square formulm of}). 247, as with the average 
found for a ]‘ace after days of laborious determination of ca})acity l)y aid of shot, 
seed, or sand. If the reader be not content rvith tliis degree of a}3})roximation, 
then I think no formula will satisfy him ; for nature being inherently variable, the 
caypacity is no elefinite function of any dimensions of the skull, it is only moderately 
correlated ivith these dimensions, and the probable error of the determination cannot 
be reduced beyond (pate sensible limits. 
The alternative to a formula is, of course, to make direct determination more 
uniform and exact. Now I believe two observers may l^e trained to get fairly 
accordant results, but will these results be the reed ca}3acity of the skull ? May 
not the reality lie more nearly in the mean of the determinations of a number of 
careful observers measuring inde})endently ? Their errors may fall on eitlier side of 
the truth, whereas a systematised })rocedure may give their errors a common l)ias. 
Hence a formula based upon a fairly vdde set of results by different, but careful, 
observers may after all be more trustworthy than direct determination Ijy a conven¬ 
tional method. It might, of course, Ije jjossible to reduce the conventional method to 
physical exactness; but I do not think this exactness is reached Ijy the construction 
of control skulls {Normalschadel, Crane Cedon), which cannot cover all tyjies ; it 
might }30ssil3ly Ije done by o}3ening each skull (allowing for the thickness of tlie saw 
cut), and then tilling either half But such a })rocess is laljorious, it destroys the 
skull for some other })urposes, and when the true ca})acity has been found we should 
have only the average of a sample. With the size of cranial sam})les at })resent 
available, the mean errors of the means amount to aljout 12 cubic centims., or are 
of the order of the errors of a good formula. Hence }3hysical exactness (whicli would 
also im}3rove the constants of the formula) is not all that is wanted. 
(13.) Accepting the }3roduct formula as a working result, a further question may 
still arise as to whether it is needful to form the mean })i'oduct of L X B X H or 
whether we may content ourselves with the }3roduct of the mean values of L, B, 
and H for the race. 
The following table indicates the order of error made by using the }3roduct of 
means for the mean product 
VOL. cxcvi. —A. 2 K 
