An Experimental Study of Somatic Modifications etc. 
329 
From this earlier series of measurements the following gross 
averages were obtained: 
Weight Tail Foot Ear 
(grams) (mm] (mm] (mm) 
Cold-room descendants .... 10.897 71.04 17.833 12.434 
Warm-room descendants . . . 10.631 71.19 17.960 12.536 
It will be seen at once that, although the offspring of the warm- 
room mice average slightly less in weight, they have slightly longer 
tails, feet and ears than the offspring of the cold-room mice. These 
differences are exactly such as were noted, on a larger scale, in the 
parent generation. But such gross averages do not, in themselves 
mean very much. In each of the contrasted lots were comprized 
individuals of widely different size (the extremes were 6.5 and 19.3 
grams). Our material, therefore is not at all homogeneous. 
Accordingly I have divided the animals into groups, each com- 
prising individuals of approximately the same weight. These groups 
have further been subdivided according to sex, the averages for the 
males and the females being determined separately. Herewith are 
appended in tabular form the results of such an analysis (Table A). 
Considering first the averages for the two contrasted sets of 
individuals within each size group as a whole (i. e. the sexes being 
combined), it will be seen that there are 11 groups in which such 
a comparison between warm -room and cold -room descendants is 
possible. The mean tail length for the former animals is greater 
in eight of these eleven cases (exceptions starred); the mean foot 
length is greater in nine of the eleven cases; while the mean ear 
length is greater in nine cases and equal in one case. Let us consider 
the likelihood that such results have been obtained through »chance«, 
i. e. that they are the result of a multitude of independent causes 
having no relation to the conditions of the experiment. 
Our method of procedure is the same as that employed in deter- 
mining the probability that a given number of » heads « or » tails « 
shall be thrown in the course of tossing a coin^). We here resort 
to the well-known formula of the binomial theorem: (a-j- b)" = W + 
, , n(n — 1) ^ . n(n — 1) (n — 2) 
Ma"-i b -\ ^-g — ^ b^ + — 'a"-^ b^ -\- etc. 
1) Apology is perhaps due for this excursion unto elementary mathematics. 
It is safe to say, however, that most of us allow our knowledge of even such 
elementary principles as these to lapse through years of disuse. 
