Crainological Notes 353 



Fi.r the Pithrcaiithropus (l)uboi.s) we h;ivc 



F= 87 mm., C'= I .'!:! mihi., 



and tlio refonstruoted valucs of (' from /' ai'C fi'om tlic iiitoiTacial Itengal fornmla 127, if 

 l)rcilictod fi-iim tlio üraoii trilie 12(5, i:{5 if prcdicted from either tlie English or Tlieliaii formula, 

 and if predirtcd IVoni tlic Kanada crania 133. 



Cleai'ly tlie at-curacy of sucli predictions varics imniensely vvitli the race used in mal<ing the 

 prcdiction. It is not safe to lay very much strc.s.s on the predictiou of an individiial fmui its 

 own rauial formula ; it is quite unsafo to judgc what will happen in an individvial case from the 

 correlation con.stants of a sccond and very divoi'se raco. Profe.ssor v. Török, without graduating 

 his data — as is actually doue in the nmltiple regres.sion formulae — but Ijy simply arguing on the 

 modes of .subarrays of multiple correlation serie.s, ha.s drawn conclasions and comparisons 

 as to Skulls of other races*. Uutil he has shown oonstancy of regi'ession coefficients for the given 

 breadtlis for all races of man, auy argiunent from one race to a .second is quite invalid. The 

 results alrcady proveii and those about to be given show how dangerous i.s the reasoning 

 by which iutraracial results are extended from one raco to a second, or by wliich intraracial and 

 inteiTacial results are interchanged the one witli the other. 



(3) lUustnuion II. Correlation of Cephalic and Nasal Indices. \\'e havc dealt with 

 this for two sets of living races in the male. Taking the same series of 57 tribes and oastes of 

 Bengal we find : 



J/,,,= 7.5-804, J/lv, = 81 -282, 



o-„ = 2-9195, (r,v, = 6-255G, 

 »V.v= - -äOlGO. 



Taking 51 races from an appendix to Dennikor's rccent work on the races of man, Dr Alice 

 Lee found + : 



i)/,., = 77-961, J/,v, = 75-y49, 



o-,., = 3-8231, o-.v, =11-0081, 



r,,.v= - -32639. 



We have accordingly the following reconstruction fornmlae, whcre / denotes a probable, /an 

 observed indes : 



Living Head from Bengal Data. 



Cephalic Index from Nasal Index: ?;.= 83-452 - -09409 7;v, 

 Na.sal Index from Cephalic Index; /v= 114-027 - -43197 ic. 



* loc. cit. pp. .584-8. Profes.sor v. Török tries to predict from the minimum foreliead aud 

 maximum cephalic breaJths of the Neanderthal skull its maximum forehead breadth, using tlie un- 

 graduated sub-arrays of the Hungariau correlation data. His process is fallacious («) from the 

 Standpoint of the theory of probabihty, for he ougbt to have graduated his material by calculating 

 the multiple regressiou coeßieients, aud (h) from the fact that he extends intraracial couclusions for 

 modern Hungarians to a very different race — that of the Neanderthal man. It would be a most 

 valuable bit of craniological work to deduce the accurate correlatious for Hungarian crania from 

 Professor v. Török's material. 



t These results give a scieutific Classification of cephalic index and nasal iudex. Half the races lie 

 above, half below 78, say. Hence 78 shoidd be the boundary betweeu brachycepbaly and dolicho- 

 cepbaly in liviiuj races. A quarter of the variations are below 75-38 and a quarter above 80- 54. Hence 

 indices of 75-5 and 80-5, say, should be taken as the bouudaries of hyperdolichocephaly and hyper- 

 hracbycephaly. Similarly for the nasal index in liviwj races we have tlie divisions : Below 08-5 

 hyperleptorrbiiiy, from 08-5 to 70 leptorrhiny, from 7ü to 83-5 platyrrhiny, above 83-5 hyperplatyrrbiny. 



Tbe Bengal results are for less wide racial langes aud we do not tbink it desirable to classify the 

 living head indices on their basis. Tbe systematic clussitication of races will be dealt witb at length 

 later wheu more ample data have been worked out. 



Bioiuetrika ii 45 



