348 MlsceUavea 



sliow that cnrrclation varias from racc to raoe, and thit only for certaiii special organs (related 

 in a imrtioular way to tlie inannor in wliicli .selection has dift'erentiated the two i-aces from 

 a commou stock) will the regression coetficients on which prediction deiwnds reniain the same 

 for the two races. Only hy an extensive tabulation of the differeuces bctween regression 

 coefficients shall we be aVile ultimately to predict the evolution of racial differences, and 

 accordiugly there mnst always he danger in extonding intraracial results from one race to 

 a second ; we arc le;vping over the very fence we have oui-selves erected when we classitied them 

 aa separate races, for the soiirce of that Separation is writtcn from the evolutionary side in 

 the very difl'erences of regression coefficients which we disregard when we predict from one race 

 to a second. But it is not only in predicting from one race to an individual of a second that we 

 need caution. How fp.r may we even assert that what holds witliin one racc holds for the races 

 of the World taken as a whole ? A long-headed Aino is i)r<)bal)ly tall-hea<lcd ; arc the long-headed 

 races of the world tall-hcaded races ? A platyrrliine N'aqada was cb.amaeconchic. Is racial 

 platyrrhiny usuallj' associated with racial chamaoconchy / Thore are many such problems which 

 can only be answered when a much more ample tabulation of racial types than we have at 

 prcsent has bcen provided. Still there is an obvious and correct method of approaching and 

 solving such problems ; we must correlate the type values of the characters for as many races 

 as possible. Sucli correlation coefBcionts have becn tormcd interracird coefficients of correlation, 

 and their discovcry must form the basis of an exact theory of race for any species, in particiüar 

 of a theory of race in man. Tlie present note is only preliminarj'. Its chief function is by an 

 illiLstration or two to serve as a caution against the extension of intraracial results to interracial 

 conclusions, or against the application of intraracial results to reasoning on individual organisms 

 belonging to dift'crent or possibly quite unkuown races. Wc confinc our attention for the 

 present to characters of the hmnan liead. 



(2) Ilbutration I. Correlation of Breadths on the Living Head. As material we took 

 the niean values of 57 castes or tribes from Risley's Ti-ihes and Castes of Dengal, selecting 

 those which contaiued the data for 50 to 100 iudividuals each. lu all instances where 

 Risley's means looked suspteious new aveniges were Struck, and several rather serious errors 

 were in some cases foiuid. Six non-siispicious cjises takeu at random and tested were found 

 to be sensibly in agreement with Risley's results. The threo measurements dealt with were the 

 cephalic brciidth, the miniuium froutivl breadth, and maximum bizygomatic breadth. Let us 

 term these Bc, By, and B^ respectively ; let J/^., J/,-, J/^ be the corresponding means of the 

 racial means and o-,., a-r, <tz, the Standard deviations of the respective racial means. The 

 coiTelations will be reprcsented by >•„, »•„, and r,-2 for the interracial relatit)n8 between 

 cephalic breadth and niininnun frontal breadth, between cephalic breadth and maximum 

 bizygomatic bre;idth, and between niininium frontal breadth and maximum bizygomatic bi-eadth 

 respecti\ely. 



apparently splendid material, 2Ü0U Hnngariaii skulls ; they deal with four characters, tlic maximum 

 and iniuinium skull breadths, and the maximum and mininmm forehead breadths, and tboir object is to 

 deduce the probable value of one of these breadths from one, two, or three of the others. The direct 

 Statistical mctliod was to form six correlation tables, and determine the six coeflicicnts ; the multiple 

 regression formulae would theu have given the most probable viiUie of any cliaracter for given values of 

 the other three. The authors, iiowcvur, deal at very i^reat length with the arrays and subarrays of the 

 frequoncy surface for the multiple characters, whereas the correct Statistical proccdure would have given 

 the type and variability of any subarray at oncc. Had this been done it would havo bcen possible, for 

 eiamplc, to have at once predicted from tlie least forohead breadth and grcatest skull breadth the 

 probable grcatest forehead breadth of any Huugarian skull. But beyoud this we could not venture to 

 go until we had shown that the regression coellicieuts calcidated for Hungarians closcly huld for other 

 races. Professor von Türük's application of bis Hungarian data to au individual skull of a totally 

 difTerent race, the Neanderthal skull, may givc a near result or not, but the application is quite 

 unwananted by otir present kuowlcdge and is füll of dnngers. 



