40 
Variation and Correlation in Brain-Weight 
as very probably insignificant. In two cases (•.3682 and •3026) the difference is 
less than thrice the probable error and hence may be considered possibly, or even 
perhaps, probably insignificant. The Bavarian $ series, both " total" and " young," 
give certainly significant values for 3 — Considering finally the criterion it is 
seen that in all cases except the two Bavarian $ the criterion differs from zero 
by a certainly or very probably insignificant amount. These two Bavarian $ 
series differed so greatly from the normal curve in most of the analytical constants 
that it was thought desirable to determine their position precisely by means of 
another constant k.,*. For the " total " series I found k.> = "0032, and for the " young " 
series k.2 = '0816. By the scheme given by Pearson {loc. cit p. 445) we see that 
the "total" series, when the probable errors of the constants are considered, comes 
very close to the condition demanding a curve of Type II {k.^ = 0, /Si = 0, ^.^ not = 3). 
The "young" series clearly demands a curve of Type IV (/C2>0 and < 1). The 
deviation of these Bavarian female curves from the normal type I believe to be 
due to an undue accumulation of individuals in one brain-weight class ; viz., that 
from 1250 — 1300 gr. It seems altogether probable that some of the individuals 
which should have gone into the next higher class (represented in the " total " 
series by a frequency of only 26 as against 69 in the class next lower) have by 
some error been entered in Bischoff's lists with too low brain-weights. What the 
source of error was it is, of course, impossible now to determine. The abnormality 
of the Bavarian females has already been noted in the discussion of the means 
and variabilities. Leaving these two series out of account I think that on the 
whole we may safely conclude, as Miss Fawcett and Macdonell {loo. cit. p. 443, and 
p. 227 resp.) have for skull characters, that : 
With series of hrain weighings such as are considered in this paper we shall 
reach for most practical purposes adequate graphical representations of the frequency 
by using the normal curve of deviation: y = yf,e~^^'l'^'''^. 
It should always be kept in mind, however, that our series, both on the brain- 
weight and skull sides, are too small to fix absolutely the normality or non-normality 
of the variation in these characters. Some of the distributions certainly differ from 
normality. The conclusion stated above is to be considered simply as a py^actical 
result, rather than as a theoretical generalization. 
This result seems to be of considerable importance as indicating the worth of 
brain-weight statistics. It shows that such statistics justify careful study and 
analysis, and that, contrary to the statements of certain recent writers on the 
subject, there is no general fallacy inherent in the data themselves which renders 
abortive any attempt to reach through them the truth regarding the mass 
relations of the brain. 
In order to test exactly how well the normal curve represents the data in a 
single case I have fitted the Swedish male "total "series with a normal curve. 
The frequency histogram and its fitted curve are shown graphically in the 
