340 Miscdlanca 



skull bieaiith varlaWlities is •"096. The first "siiiall" diftbrcncc is thcrefore 407 times its 

 staiulaid deviation, thc sccond is 2'40 tinies it-s staiularil deviation. In othcr words whatever 

 sort of gi-oiip the Xaqada, Bavarian, Aino, French, and Englisli male cranial series makc, 

 thc odds are ■12,.'J52 to 1 against such an cxcess of variability as Mr Mjcrs fouud for his mixed 

 scries of skull lengths belonging to a number of that series, and 121 to 1 agaiust such an excess 

 as ho found for tho skull brcjidths occurring in such a series ! It is such odds as these the 

 combination of which can hardly fall sbort of 4,000,000 to 1 and which uo saue man in practical 

 conduct could disregard, that amount to "sniall" difl'ercnces froin the standpoint of the old 

 school of craniologists ! But the whole matter deserves further consideration from a wider 

 stivudpoint. What fairly homogoneous dat<i have we for variability of skull length and breadth ? 

 In the first place the list above contains the variability of 860 French male skulls from the 

 Paris catacombs ; I have dealt with this series in previous papers and expressed doubts as 

 to its homogeneity, I have pulilished too othcr cascs of variability for niuch niore homogeneous 

 French series, — Parisians* and French peasants. The firet of these is tho largcr of the two 

 series, and though both have nuich less v.ariability than the catacomb skulls I take the Parisians 

 as the better series. We have then the following series, to which I have added three cascs 

 of measurcments on the living head : 



Scries. 

 Ainos 

 Bavarians 

 Parisians 

 Naqadas 

 English t 



Cambridge Undcrgraduatcs 

 English Criminals 

 Oraons of Chota Nagpur 



In this series of eight thc Xaqada crania stand casily fii-st for least variability iii leugth, and 

 third in the order of Iciist variability for breadth. 



Now it is impossiblc to regard these data, which cover, so far as I am aware, practicjiUy 

 all the availablo data for Variation in skull or head lengths hithcrto workcd out, without secing 

 (i) that Variation in head length is practically the same as Variation in skull length, and (ii) that 

 both for very differeut cranial series are extremely nearly six. This corrcsponds with the coefficient 

 of Variation about threo, which I have used in this case for many years. Anything that differs 

 much from six — like thc Parisian catacomb series — I should it priori susiwct of hetcrogeneity. 

 Xow if wo take the above series we find for tho mean variability of head length .5-987 and 

 of head breadth 4877, and for the Standard deviations of these variabilities ■1292 and •54.54 

 res|5ectively. In this case the deviations of Mr Myers' heterogeneous series are 2'402 and 2^125, 

 or respectively 18^6 and 3^90 times their staudaixi deviations. In othcr words, thc odds against 

 such a highly variable series being of thc samc character as thosc we have given above are 

 6 X 10"" to 1 and 20,832 to 1 respectively ! The correlation between length and breadth variations 

 as given by thc above data is - •0197 or negative. Tho combiiicd odds are thcrcfure greater 

 than if thc events werc indepcndcnt. In othcr words the odds against JIr Myers' mixture 

 belonging to the class of cranial series wo have grouped togethcr above as homogeneous aro 

 more than : 



12 X IQSO to 1 ! 



* Data providcd for nie by the courtcsy of M. Manonvrier. The other crania wcre brought to the 

 catacombs from grave-yards which had been in usc for sevural ccnturies. 



t Using tho rusults for thc glabclla luaximum leiiRth, for which I have to thaiik Dr W. 11. Macdonell, 

 who i« at work oii these crauia. The value cited by Mr Myors is tho horizontal leugth, all that was 

 availablo for Miss Fawcott's purposo at the time of her mcmoir. 



