MISCELLANEA. 



Craniological Notes. 



Explanatory 338 



I. Professor von Török's Attack oii tlie Aritkmeüc Mean. By K. Pearsox . . 339 



II. Homogcneitij and Hcterogeneity m Collections of Crania. By K. Pearson . 345 

 111. Preliminary Note on Interracial Characlers and tlusir Correlation in Man. By 



S. Jacob, A. Lee, and K. Pear.son 347 



Explajiatory. 



The conclasions drawn by anatoniists and anthropologist.s from examinatious of series of 

 crania are at prcsent ba,sed upoii two ty[)cs of judgmcut. The tii-«t type of judgnient is wliat 

 we may term the niethod of appreciatiou ; tbe auatoniist examincs tbe cranial series and by 

 a proces.s of gcneral apprcciation cliusses the series as belonging to a cortain race, or tlirows out 

 certain individiials as belonging to a different race. Sonietinies the appreciative inspcction will 

 Icad the craniologist to classify a serie.s in tliis way into five or six typcs or races, — two or three 

 pure types and two or three niixed typcs. The bases of these appreciative jndgnients are 

 qualitative, thcy cainiot be criticised by the biometrician, they belong to the arcana of tbe 

 anatomist's training. The biometrician cjin only place alongside such judgments the results of 

 quantitiitive investigatious, which are deduced by difficult and often very laborions Statistical 

 thcory. The stati.stical ruethod in craniology i.s difficult and laborious bccau.sc tho series dealt 

 with are u.sually so .sniall that conclu.sions can only be drawn a.s the balance of a vcrj' fine 

 weighing of probable error.s, and accordingly the .stati.stician c;in frequently only .say : "This 

 I thiuk i.s tho balance of probabilities." llc is coiupelled to stand in wonder and admiratiou 

 before the definite facta which the method of appreciation appears to elicit. 



Now qualitative apiircciation doos not adniit of exact statcnient of tbe whcrefore of the 

 judgmcnt in print ; accordingly anatoniical craniologists have bccn in the habit of Publishing 

 measurements and dealing with a few stiitisticfil argumenta based on mcans or graphical 

 polygons of frequency or even rough tables of correlation. Hcrc the biometrician is at liberty to 

 Step in and exprcss a perfectly definite judgnient on the Statistical processes adopted and the 

 conclusions deduced. In nine cascs out of ten he can conlidently iussert that tlic anatoniical 

 apprcciation is only ob.scured by the st;itisticiil aigunients used in its favour. The data are 

 cither iusiifticicnt for any st;vtistical conclusiou whatcver ; or thcy are uuaccompanied by any 

 dctcrniiiiation of their probable errors on which alono a judgnient could often be based ; or the 

 \CTj principia of the theory of statistics are clearly unknown to the handlers of the data. It is 

 idle to deny tho obvioiLs fact that the numerical argunients used by such authoritics as 



