Raymond Pearl 
37 
the brain-weight series and the other two is rather curious. There is no parallelism 
between the variability columns of the brain-weight series and the other two, but the 
variability columns of the stature series together with the females of the age series 
exactly agree (with the exception of the transposition of the Hessians and Swedes) 
with the columns of means of brain-weight. In other words in those series showing 
the greatest variability in stature (and in the females of age also) we have the 
highest mean brain-weight, and vice versa. No reason for this curious parallelism 
is apparent, and it may be purely accidental, but it seems worth noting. 
The questions of the relative variability of the sexes in brain-weight and the 
racial differences as affected by sex will be discussed in a later section of the paper. 
6. On the Nature of the Frequency Distribution. 
In this section the variability in brain-weight will be discussed analytically, 
according to the methods and nomenclature of Pearson's fundamental memoir on 
Skew Variation* and its supplement f. My purpose in considering these curves 
analytically is not primarily that data may be furnished so that the material may 
be fitted with appropriate curves, but rather in order that definite knowledge may 
be had as to whether the variation in this character obeys the "normal" law of the 
deviation of errors. Both Miss Fawcettj and Macdonell§ have reached the conclu- 
sion that, for practical purposes at least, the majority of skull characters may be 
considered to conform to this law in their variation. It is of prime importance to 
determine in how far the same is true of the weiglit of the brain. Since this was 
my chief object in analyzing the data, I shall not at this time deal graphically 
with the curves, but instead shall merely present the chief analytical constants 
arranged in tabular form. Furthermore, from considerations of the time involved 
in computation, I have not determined the analytical constants for all the brain- 
weight frequency distributions given in this pajjer. Instead, after examining all 
the data, I decided to confine myself to the " total " series for both sexes of the 
four races. 
The analytical constants for the selected series are exhibited in Table VIII. In 
the second column is given the number of brains on which the calculation in each 
case is based. The third column gives the unit in terms of which the second, 
third and fourth moments about the mean (/Xa, yu-3, and /Aj) are calculated : the next 
two columns give /3i and and the two following, fBn and 3 — /S.,. Following 
this are given in order the "criterion" (ati = 2/3o — 3;8i — 6)||, the mean, mode and 
skewness. The skewness was calculated from the moments directly by the formula 
, VA(/3. + 3) 
and from this the distance from mean to mode was obtained by multiplying by a. 
* Phil. Trans. Vol. 180, A, pp. 343—414. + Ibid. Vol. 197, A, pp. 443—459. 
+ Biometrika, Vol. i. p. 443. § Ibid. Vol. iii. p. 227. 
II Phil. Trans. Vol. 197, A, p. 444. 
II Pearson, K. : ."On the Mathematical Theory of Errors of Judgment and on the Personal Equation," 
Phil. Trans. Vol. 198, A, pp. 235—299. Page 277. 
