.") K I Miscellanea 



but only to the iwpulation aa a whole. Yet thcy lielp to fix its tyi» in precisely thc same way 

 JUS the arithnietic mean does. Wliy should we deniand of the hitter, any moro than of thc two 

 foniier statisticivl " populatioii-constjint^s " tliat tliey slioiild be characteristic of the grcjit majority 

 of a poimlatioii ? It apjiears to nie that there is still lingeriiig in Professor von Tüi-ok's miud 

 something of the old confnscd notion of type, when he demands that any Statistical constant 

 which helps to describe the type shall be characteristic of the great majority of a population. 



For the himnetrician the type of any group (or " population " in the l>ionietric sense) is fixed 

 by the whole coniplex of st;itistical consfcmts — mcans, Standard deviations, correlations, skew- 

 uesses, etc., which suffice to diftereiitiate it sonsibly from other groups or {xipulations. Very 

 frequently the arithmetic nieans of a numV)er of characters will suffice, if so they fix the tyi^e. 

 Often we have to use a nuniber of other constants — correlations or what not — and the question 

 of whether two groups are differont in type l)ecomc8 an extreiiiely delicate one, only solved by a 

 Ciireful consideration of the prubabilities coiniotcd by thc probable errors of diöerences. 



I am aware that the conception of 'type' thus given is not that of many anthropologists, but 

 bionietry is essentially a science of exact quantitative definition, and if it is to lic of Service in 

 reiidei-ing anthroi)olog_v an exact branch of science, it niust replace vague ideas by nuuierically 

 detinite conceptions. If any anthropologist reiilios that : "'Type' is something to be judged by 

 general appreciation," then 1 persoually have no reply to luake. He spwvks like the anatomical 

 crauiologist in the language of an esoteric science and I do not pretend to criticise his conclu- 

 sions. All I demaud is that he should not use, what are to the mathematician hopelessly 

 inadequatc and faulty Statistical niethods to justify Ins "type" appreciations. If on the other 

 band he says : "There is a definite quantitative charaoter I understand by tyjx;, which is not 

 involved in your definition above,'' then bionietricians are perfectly prepared to try and under- 

 stand what it is, and will endeavour to give it a significant biometric definition and quanti- 

 tative measure. When Professor von Török teils nie that the type is something which is 

 characteristic of the great majority of a j)opulation, group or Gesammtheit, I am at a loss, for 

 although I have exaniined the characters of niany groups, I have never found this something, 

 to which I cüuld attach the name tyjic, except where the smallncss of the variability rendered it 

 IHjssible on merc inspcction to differentiate one population from a secoiid, — iis a black man from 

 a white, a dark haircd from a light-haired {»ople and so forth. Here, however, the unreasoued 

 differentiation rcally depends on the biometric conceptions of difterent means and small varia- 

 bilitics. But bccauso these conceiitions are not thc conscious soui\e of the Classification, the 

 anthropologist appears to hold that the bionietrician ai)[)lies a wlioUy difterent proccss wheu he 

 Uüos means and varial)ilities to distinguish the types of groups which in part ovcrlap, as far 

 as mere individuals are concerned. I am inclined to think that it is these cases of widely 

 divergent means with small variabilities where difi'erentiation is a matter of inspection only, that 

 really lead to the confused notion of many anthropologists that the "type" is something 

 characteristic of the great majority of a gnnip. 



Almost equally vague with the conception of type is the current conception of race in man. 

 I am wholly in accoi-dance with Professor von Török when he sjvys that the problera of race is 

 insciiarablv unitcd with the question of descent, but if he thinks that biometric niethods cAnnot 

 apply to this problein I niust venture to difter, and refer him for the sort of lines on which I 

 think the probloni will one day be solved to niy nieiiioir on the Inßin-nce of Natural Selection cm 

 Variation and Correlation*. Turning to the special problem lus concerns man, I hold that the 

 whole evolutionary evidence is in favour of descent from very few groups, i)erhaps a single group. 

 Hence Professor von Torök's Statement that it is impossible to settle by mathematical niethods 

 the problem of whether a given "Menschengruppe (Ras.se) 'blutrein' oder 'blutvermischt' ist," 

 understanding by "blutrciii" that "die betreft'eiide Menschengrui)pe niemals einer irgendwelchen 

 Blutmischung unterworfen war" has no meaniug at all for me, because his definition of "blutrein" 



* Phil. Tram. Vol. 200, \<\\ l-C.fi. See especially p. 22. 



