56 
Variation and Correlation in Brain-Weight 
Diagram IX. Probable Braiu-weight for given Age. 
Hessian $ Young. 
I I I I I I I I 
17-5 22-5 27-5 32 5 375 42-5 47 5 
Age ( = f) in years. 
These diagrams show clearly, I tliink, that the regression of brain-weight on 
age in these cases is sensibly linear within the ages 15 to 80, so far as can be 
judged on the material available. The regression diagrams for the other two 
racial groups show the same relation. Obviously no simple curve will represent 
the systems of points shown in these diagrams II to IX better than the straight 
line does. So then, until we have very much larger samples of material to work 
with, we shall be justified in assuming for practical purposes linearity of regression 
between brain-weight and age, and in considering the deviations of the means of 
the arrays from the regression line to be due to errors incident to sampling in lots 
of less than 500 individuals. 
The equations to the regression lines for these diagrams may now be given. 
For convenience in practical use I have put these equations in the form of 
" characteristic " equations. The significance of the letters used is as follows : 
W denotes the probable brain-weight in grams of an array of individuals of age 
type A or a. The ages included by A are 15 or 20 to 80; by a 15 or 20 to 50, 
or in other words the equations containing A are deduced from the " total " series 
and those containing a, from the " young " series. 2 is the standard deviation of 
the array having the probable W as its mean. 
(1) 
Swedish 
i 
w= 
1487-783 - 
1-939 J, 
2 = 
102-972 
(2) 
51 
6 
w= 
1501-411- 
2-372 a, 
2 = 
107-582 
(3) 
51 
9 
w= 
1326-475- 
1-549.4, 
2 = 
97-969 
(4) 
55 
? 
Tr= 
1340-438- 
1-988 «, 
2 = 
104-329 
(5) 
Hessian 
o 
w= 
1439-734- 
1-119 J, 
2 = 
111-087 
(6) 
55 
6 
w= 
1432-497- 
-847 a , 
2 = 
111-014 
(7) 
55 
? 
w= 
1361-067- 
2-259 A, 
2 = 
95-512 
(8) 
55 
? 
w= 
1339-298- 
1-735 a, 
2 = 
100-445 
The foregoing constants bring out a number of interesting and important facts 
regarding the relation of brain-weight to age. In the first place it is clear that 
diminution in brain-weight with advancing years takes place very slowly. In 
10 years the Swedish males lose 19 39 grs. and the Hessian males 11-19 gTS.* 
* In order to economize space I have not tabulated the regression coefficients separately. It will be 
understood of course by anyone wishing to refer to or use these regression coefficients that the number 
prefixing a letter in the second member of any of the characteristic equations 1 to 36 is the regression 
coefficient (either gross or partial) of brain- weight on the character indicated by the letter. 
