72 
Variation and Correlation in Brain- Weight 
Now the condition under which we shall make a smaller standard error in 
estimating a\ from the two variables j:, and x.^ than in estimating it from x„ only, 
is evidently that 
(i-i?r)<(i-7y) 
or that > r^^. 
Now in the case noted above R{- < rj/, the figures being "2534 < "3005. 
Returning to the main line of the discussion, the results as to the correlation 
of brain-weight with skull characters are not altogether satisfactory, as they are 
apparently not entirely in accord with themselves. One of the points here on 
which information is most desired is whether brain -weight is more closely 
correlated with length or breadth of skull. According to our results brain-weight 
is more closely correlated with length of skull in the male and breadth of skull in 
the female. This seems a somewhat anomalous result as there is no apparent 
reason why one should not expect the sexes to show the same relation in the 
matter. However, Macdonell's (loc. cit.) figures for the correlation of skull capacity 
with length and breadth show a similar relation but in the opposite direction. 
He finds for the Whitechapel English skulls that the correlation between capacity 
and length is lower than the correlation between capacity and breadth in the 
males, and higher in the females. Other skull series do not, however, show this 
reversed relationship between the sexes. With the data at present available one 
cannot reach any general conclusion as to the relative closeness of correlation 
between brain-weight and skull length and breadth. It is very much to be hoped 
that future collectors of brain-weight statistics will include in their returns such 
head measurements as length, breadth, height and circumference taken before the 
cranial cavity is opened, and by standard anthropometrical methods. 
A comparison of the values of the coefficients of correlation between brain- 
weight and skull length and breadth and between skull capacity and these 
characters is of interest. I have adapted the following table from Macdonell's* 
Table XHI. 
Eace 
Brain-weight and Skull Length 
Brain-weight and Skull Breadth 
? 
$ 
? 
Bohemians . . . 
•5482 ±-0273 
■3604 ± ^0465 
•4655 ±^0306 
•5041 ± ^0399 
Skull Capacity and Length 
Skull Capacity and Breadth 
English* ... 
Naqada t ... 
German | ... 
Aino| 
•597 + -051 
•501 + ^054 
•515-1- -050 
•893+ •016 
•691 + ^040 
•599+ -039 
•687+ '037 
•663 + ^053 
•631 + ^048 
•434 + •OSS 
•672+^037 
•561 + •053 
•646 + ^044 
•532 + ^044 
•706+^034 
•502 + ^070 
* Macdonell, loc. cit. p. 235. t Fawcett, loc. cit. % Lee, loc. cit. 
