An Experimental Study of Somatic Modifications etc. 331 
A table has been prepared (preceding page) showing the like- 
lihood of the > accidental « occurrence of such majorities for each of 
the characters singly and for all of them combined i). It will be seen 
that the cumulative improbability of the occurrence of all these 
majorities in the same direction is very high indeed, being about 
one in 2,400 in the case of the figures for the sexes combined. 
When we consider the sex-groups separately, it will be seen that 
the chances for the purely » accidental* occurrence of such majori- 
ties are even slighter. Those for the preponderance of the >warm« 
figure in 43 cases out of 57 (with one case of equality) are but a 
little over one in 20,000. 
It must here be granted that those figures which express the 
cumulative improbability of a similar preponderance being manifested 
in all three of the characters measured are subject to one important 
qualification. They are accurate only upon the assumption that these 
characters vary quite independently of one another. In reality, there 
is probably a certain degree of correlation, the extent of which has 
not been determined. This correlation would, of course, considerably 
increase the chances here stated. But in any case they would remain 
so slight that in most of the practical atfairs of life we should reject 
them as not worth considering. 
The fact is worth noting that it is among the females that the 
preponderance of the >warm« over the »cold« figures is shown with 
the greatest approach to unanimity. For example we find among 
the 57 pairs of figures which admit of a comparison between two 
averages for the same sex, the following distribution of cases: 
1) It will be found that these figures differ throughout from those given 
in my preliminary paper in the American Naturalist (Jan. 1910). In most cases 
the probabilities here stated are just half as great as those which I had previ- 
ously allowed. My earlier figures indicated the probabilities for the occurrence 
of such majorities in either direction. We are, however, only concerned with 
the probabilities for a preponderance in one direction, i. e. in favor of the warm- 
room descendants. 
Another source of discrepancy between the present figures and the earlier 
ones results from the treatment of those cases in which the two averages for 
a given character are equal. In the present computations, I have divided each 
instance of equality between the plus and minus groups. For example, to take 
the case of the ear measurements in the accompanying table (first-part , I have 
regarded the »warm< figure as being larger in 9V2 of the size-groups, smaller 
in IV2 of these. The probability given is the mean of the figures for 9 out of 
11 and 10 out of 11. This seems a fairer procedure than that of throwing the 
case of equality out of consideration as I had earlier done. 
