CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
179 
all the coefficients of correlation and adl the variations of the long bones have already 
been calculated. 
I owe to Miss Alice Lee the knowledge of the additional constants required for 
this further investigation, and embodied in Tables I. and II. below, which embrace 
all that is needed to fully determine the correlation of stature and long bones. 
The treatment of Dr. Lollet’s material was not to be briefly settled. He had 
measured only 50 bodies of each sex, and this number included a great variety of 
ages. M. Manouvrier in determining his table of statures has at once excluded 
from his calculations all the males but 24 as senile, and all the females but 25. Now, 
although the correlations between stature and long bones are high, it would be quite 
hopeless to attempt to calculate them from 25 cases ; 50 cases are hardly sufficient, 
25 impossible. It seemed, therefore, necessary to include all Dr. Dollet’s cases, and 
the question now arises how far the inclusion of the senile ones will affect our results. 
Taking 50 as the age at which stature begins to decrease, we notice that of the 25 
lowest statures recorded by Dollet, 18 are of men over 50, and of the 25 highest 
statures, 17 are of men over 50. In other words, there appear sensibly as many 
senile statures above as below the median stature. Of women there are 16 over 50 
years old with a stature greater than the median, and only 14 women over 50 under 
the median stature. Turning to means, we notice that 24 males under 60 years had 
for mean stature 167T7 centims., and 26 males over 59 years had 165'4 centims., 
25 females under 60 had for mean stature 154'04 centims., and 25 females over 59 
had 154*00 centims. 37 females under 70 had a stature 153‘94 centims., and 13 over 
70 gave 154'23 centims., an absolutely greater stature. 24 years was the minimum 
age. From this it would appear that whatever shrinkage may be due to old age, 
it is not of a very marked character in these data, or largely disappears when a 
body is measured after death on a flat table ; the senile stoop may then be largely 
eliminated. 
But there is another point to be noted ; we shall not directly make use of the 
mean stature as obtained from Bollet’s data, except to test how far our formulse 
will reproduce Bollet’s results. What we shall make use of from Bollet’s data 
are the standard-deviations and coefficients of correlation, and these will hardly have 
their values sensibly influenced by such comparatively small senile changes as are to 
be found indicated in Bollet’s measurements.''" Accordingly our constants are 
calculated by including all Bollet’s measurements, namely, on 50 of each sex. 
The following results were found :—■ 
* If llie bones shrink with old age, like the stature, the correlation would not be altered. The length 
of a bone varies with the amount of moisture in it (see below), and such shrinkage is itself a possibility. 
The bones of tke aged will of course be included among those of extinct races, and cannot easily be 
eliminated. 
2 A 2 
