Raymond Pearl 
63 
practically fixed at the end of the growth period. After that time the relation 
undergoes no marked change throughout the remainder of life, since both stature 
and brain-weight regress on age at not far from the same rate. 
Finally, the combined effect of stature and age on the weight of the brain may 
be examined. This relationship can best be examined through the medium of 
multiple regression equations of the form : 
in which /Sj, and /^is are the partial regression coefficients of x^ on its associated 
variables x^ and x.^, it being understood that x^, x., and x^ here stand for deviations 
from the means of the respective variables. For our material these equations, 
when reduced to absolute magnitudes, take the following forms, the significance of 
the letters being the same as in the regression equations given before. 
(19) 
Swediyli 
6 
w= 
1091 -021 + 2-288 <S' - 
1-755 J, 
2 = 
101-819 
(20) 
c? 
w= 
1080-715 + 2-362 « - 
l-856a , 
2=- 
106-477 
(21) 
51 
? 
w= 
561 -433 + 4-679 -S' - 
1-078 J, 
2 = 
93-066 
(22) 
? 
w= 
533-407 + 4-854 s - 
l-092a , 
2 = 
98-923 
(23) 
Hessian 
6 
w= 
942-154 + 2-989 .S' - 
1-181 A, 
2 = 
108-992 
(24) 
11 
6 
w= 
926-586 + 3-107 s - 
l-318a, 
2 = 
108-889 
(25) 
11 
? 
ir= 
1005-607 + 2-244 ,S' - 
2-173 4, 
2 = 
94-261 
(26) 
11 
? 
Tr= 
974-382 + 2-.345S - 
1-829 a, 
2 = 
98-883 
These equations give the probable mean brain-weight of an array of adult 
individuals of either sex, having any given age (in years) and mean stature (in 
centimetres). They are, I believe, the first multiple regression equations relating 
brain-weight to stature, age and sex, to be published. They are of interest from 
several points of view. Examples of their practical use have been given earlier in 
the paper (pp. 25 and 48) in connection with the discussion of racial differences in 
mean brain-weight and later in connection with the sex differences. They afford 
a means whereby it is possible to make scientific comparisons of the mean brain- 
weight of different races, since by their use the probable brain-weight of a group 
of Swedes or Hessians having the same mean stature and age as the sample of the 
race with which comparison is to be made can be ascertained. We can in effect 
reduce both races to the same stature-aoe base and then examine the brain-weight 
differences. ,It would seem that these equations ought to prove very useful to 
anthropologists, who frequently wish to make comparisons of this kind. They are 
based on the two sets of brain-weighings which I believe to be on the whole the 
most reliable and trustworthy at present available. These equations also make it 
possible to determine the effect of indirect selection of stature and age on brain- 
weight. 
As a practical example of this last use of these equations let us consider the 
following problem : By how much would it be necessary to modify the stature of a 
group of Swedish males, having a mean age of 4.5 years, in order that they might 
have the same mean brain-weight as a group of Bohemian males of the same mean 
