Eaymond Pearl 
11 
have attempted to apply to the individual results gained by somewhat doubtful 
statistical analysis of mass data, and vice versa, what is much worse, have argued 
that the relations found to hold in a single individual might be considered to hold 
for the mass. As an example here might be cited Marshall's* attempt to correct 
the brain-weights of De Morgan, Thackeray, and others for stature and age. The 
results detailed in this paper will indicate to the biometriciau at least how 
dangerous both of these methods of procedure are with such material as brain- 
weight statistics. Of course both disregard fundamental canons of general 
statistical theory, but the chance of grave error becomes very much greater when 
the character under consideration shows on the one hand definite and clearly 
marked types in different races, and on the other hand low correlations f- With 
the application of adequate statistical methods it is possible to reach definite and 
significant results regarding the weight of the brain. When we have biometric 
constants for a considerable number of long series of brain-weight statistics from 
different races we sliall be able to advance our knowledge greatly with reference 
to the general problems of the evolution of man's brain. 
While the discussion of such problems can at the present time admittedly lead 
to only tentative results, still I think it will be worth while to examine for 
a moment the bearing of our results on a single evolution problem. Progressive 
evolution through natural selection may be brought about in any character either 
by the direct selection of that particular character or by the indirect selection of 
other characters correlated with it. As we proceed in the analysis of the problem 
the proportional effect of each of these two sets of factors must be quantitatively 
determined. A first approximation to such a determination has been here made 
* Loc. cit., supra, p. 18. 
t In this connection Weigner's recent paper "Ein Beitrag zur Bedeutung des Gehirngewichts beim 
Menschen," Anatomische Hefte, Bd. 23, pp. 69 — 109 is decidedly open to criticism. But when one, after 
very briefly analyzing the weighings of 69 male and 66 female brains (sic) from individuals ranging in 
age from 1| to 82 years, by the most superficial of statistical methods, feels justified in drawing the 
following sweeping conclusions inter alia, what can biometry offer that will be in any way effective? 
Weigner's three principal conclusions as to fact are (loc. cit. p. 108) ; 
1. " Das Gehirngewicht steht in keinem direkten Zusammenhang mit dem Alter, und wenn auch 
die angegebenen Zahlen sich zu Gunsten dieses Zusammenhanges verwerten einen, verlieren diesclben 
an der Bedeutung, da durch dieselben nicht der Beweis gefiihrt werden kann, wie sich Gehirngewicht 
bei einem und demselben Individuum in verschiedenen Altersperiodeu verhalt ; 
2. zwischen dem Gehirngewichte und der Kurperliinge lasst sich keine bestimmte Proportion 
feststellen ; 
3. die Durchschnittszahl hat bloss einen relativen Wert, und zwar deshalb, weil die das 
Gehirngewicht reprasentierenden Zahlen durch die Wagung eines zufallig uns gerade zur Verfiigung 
steheuden Materials gewonnen sind und das aus demselben bestimmte arithmetische Mittel keine 
konstante Grosse, sondern eine frei bewegliche Eeihe von Zahlen uns darstellt." 
It should be said that the material on which these conclusions are based is apparently within the 
limits of its probable errors entirely normal, and shows an approximately linear regression of 
brain-weight on age during adult life. This being the case the very positive conclusions seem to take 
on the character of extreme dogmatism. If 1. were true, by the same token no life insurance company 
could fix upon a premium rate for the insurance of lives of individuals, aged 21 say, which would enable 
it to carry on its business justly and fairly, because no life insurance company knows when any one 
individual aged 21 will die. Yet life insurance companies seem to be struggling on ! 
