Craniologk'al Notes 345 



coiiiciilc in l'roli'.ssor v. 'I'oi'ük'.s iliit.i witliiii tlie orror.s of raiidom sampling.s. The arithmetic 

 incaii call lio frcod IVdiii tlic cliargos ho liriiig.s agaiiist it. C'aii hc solve tlie "Problom einer 

 Tyi>u«liestiininung" on thcsc lines ? IVrsoiially 1 tliink not. "Der Kampf iiiii ilie Walirheit" 

 in tlic fi'aniology has for its sololy \oi^itnmiU: /mn Hu in salimu thc rcuognition tliat oraniology i» 

 a branch of hioniotry, auil caii only bc l'ollowed protitably wlion thc muderii tlieory of .sUvtistics 

 Las boon properly studieil. 



II. llüinogeneity and Ileterogeneity in Collectioiis of Craiiia. 

 By Karl Pearson, F.R.S. 



In a roviow* by Mr C S. Myers of a nieinuir by Miss C. D. Fawcettt, one of thc liidiuetric 

 \v()rlc<'r.s at Univcrsity College, London, exception is takon to the argnnicnt.s adduced in favour 

 of the homogeiicity of tho Naqada prehistoric crania. Thero are mauy statoinents in Mr Myera' 

 review which it woiild be ea.sy to traver.sc, but as the wiitcr expresses himself as in synipathy 

 with what ho i.s ploased to term tho " ncw path," a consideration of onc of thein will suffico 

 to show to what extent he appears to l.io fit at pre.sent to enter upon it. 



The .Statement is as follows : 



The question, moreover, arises, are we entitled to consider eitbor the Naqaila or the above English 

 skuUs as belonging to people of a single race? The authors think that we are " justified in troating our 

 material as homogeneous and iu speaking of a Naqada race and not merely of the Naqada crania " 

 (p. 424). " If the [Naqada] material were markedly heterogeneous the variability in length and breadth 

 of skull ought to be large as compared with admittedly homogeneous material" (p. 424). The Standard 

 deviations ot the male Naqada skuUs and of Bavarian, Aino, French, and English male series as 

 regards skuU-length are 5-722, (i'üSS, 5-93G, 7'202, 0-440 respectively, and as regards skull-breadth are 

 4-012, 5-H4U, 3-897, 0-008, 4-'.)70 respectively. These deviations (aud the "eoeöicients of variability" 

 derived therefrora) are oonsidered by the authors to be small enough to Warrant the conclusion that the 

 Naqada crania, the old Bavarian crania ot Professor Bänke, aud the Whitechapel English crania of 

 Professor Thane coustitute each a homogeneous series. They have left neglected the questiou whether 

 a much larger Standard deviation would result, were we to consider a series, say, of forty-niue male 

 skuUs of most diverse ethnic types, eomposed, e.g., of fifteeu Australians, seven Guauches, fifteen 

 Eskimos, and twelve Chinese. This is the material which the reviewer set himself to work out, taking 

 the data haphazard from Flower's well-kuowu catalogue of skuUs in the Royal College of Surgeons' 

 Museum. The results gave him a Standard deviation of 8-389 for the skull-Iength, and of 7-002 for the 

 .skull-breadth. We see, then, how small is the difference of Variation bctween the Naqada skuUs of 

 Professor Pearson's series (which are ot a "homogeneous character") and a series which is as 

 heterogeneous as it could well be. Are we, then, not justified in considering the Naqada skuUs and the 

 others of Professor Pearson's series as if they had Sprung from a mixture of races? If not, at least the 

 Problem is less simple than the writcrs appear to tliink. 



The mean of tho variabilities of the skull Icngths given in the above paragraph is 6-2788 and 

 of the skull breadths is 5-0804. ;\Ir Myers mixing Australians, Guanches, E.skimos and Chinese 

 finds a variability of .skull length =8-389 and of skull breadth =7-002. He then points to tho 

 difterences (2-1102 and 1-9216) and triumphantly asks how such small ditltn-ences can be of any 

 importance ! But had Mr Myers had a mathomatical training he would know that nothing 

 is "small" absolutely, but only relatively to something eise, and had ho had a Statistical 

 training he would havo known that ho must compare it with tho variability of the.so variabilities 

 i.e. the Standard deviaticin of the Standard deviations of the skull mcasurcments. Now the 

 Standard deviation of the above series of skull length variabilities =-5185 and that of the 



♦ Man, February, 1903, p. 13. 

 + Ilinvu'trik,:, Vol. i. pp. 408—407. 

 Biometrika ii 44 



