434 Variation and Correlation of Skull Measurements 
safe to say that according to this test the degree of correlation is nearly 
the same in both sexes. It is interesting to note that the cranial capacity 
is best correlated with the width (male and female) and the height (male) 
of the cranium. Therefore a prediction of brain weight based on the 
cranial measurements would give least error when based on the width. 
The length of the entire skull gives the lowest degree of correlation in 
both sexes. This is of course what one would expect since the length of 
the entire skull is least correlated with both the height and width of the 
cranium, especially in the case of the female. The product of the height, 
length, and width of the cranium is highly correlated with the cranial 
capacity and the correlation, although a trifle higher in the female, is 
nearly the same in the two sexes. This is also an anticipated result 
since roughly speaking the capacity should be closely related to the 
product of three diameters. In this case one might expect to find the 
correlation almost unity, but remembering that the cranial cavity has an 
irregular shape and is bounded by curved surfaces, the value shown in 
the table can be considered satisfactory. 
(d) Correlation between cranial capacity and body-weight.—Despite 
the fact that in the human subject the coefficient of correlation between 
brain and body-weight is extremely low (0.167 in male and 0.226 in 
female, Pearl, 06,) an intimate relation between these two characters 
found in the rat (Donaldson) suggests that in the rat at least it would be 
higher. 
As a matter of fact the following coefficients ~ of correlation have been 
obtained : 
TABLE VIII. 
Male. Female. Difference. 
Body weight and cranial capacity... .516 + .074 .692 + .058 176 + .094 
Assuming that the regression between the body and brain weights can 
be expressed by a straight line with a given angle, the following equations 
were formulated and used to determine the correspondence between the 
predicted and observed values. 
(1) Brain-weight, male = (0.0072 X (body-weight, male) + 9.349) + 
5.980. 
(2) Brain-weight, female = (0.0251  (body-weight, female) +6.168) 
— 6.009. 
? Unfortunately in this series, several rats which were found dead are 
included and thus the correlation here obtained may be slightly less than 
it should normally be. It is however true that the normal fluctuation in 
body-weight is rather wide and therefore the including of several self-dead 
rats should not affect the results to any great extent. 
