No. 2.] THE STUDY OF VARIATION. 461 
toward the larger specimens at the right, and of course with a 
constantly increasing altitude! It will now be profitable for us 
to draw upon Plate C a line which shall represent the mean of 
the very irregular curve of length in terms of vertebree. If the 
specimens having a larger number of vertebre are irregularly 
distributed, this line will lie horizontally, but if numerical 
vertebral increase tends to occur in larger animals, the line 
will tend to rise from left to right. Suppose now we take the 
means used in Section I for the several blocks of twenty speci- 
mens, and, using them for our ordinates, we plot the curve of 
mean numerical vertebral variation. We will find it to lie 
between the abscissas of 45 and 48 (see dotted line on Plate C). 
The curve shows a vegu/ar rise from left to right, following the 
flowing curve of absolute lengths in millimeters, there being an 
increase of about three vertebrze in the entire series. The 
question at the beginning of this section is answered, then, in 
the affirmative. 
But the simple addition of three vertebrze, each less than one 
millimeter in length, at the caudal end of the animal, cannot 
account for the increase of over one hundred millimeters in the 
total length of the larger specimens. The increase in length 
is not then to be explained by the addition of new seg- 
ments behind, after the method of growth of developing 
arthropods and worms, but is interstitial, the individual verte- 
bre increasing in length with age ; though of course it does 
not follow that length is an absolute criterion of age. Under 
varying conditions growth may be more or may be less rapid. 
Whether the slightly increased number of vertebrze is due 
to multiplication of vertebrz after sexual maturity, or is an 
index of unusual embryonic vitality, or is predetermined in the 
egg, I will not now attempt to answer, though the application 
of the X-rays to the developing young will definitely settle the 
first of these, vzz., the question of vertebral multiplication 
after sexual maturity, and the frequent occurrence of smaller 
and average specimens possessed of nearly the maximum 
number of vertebrz might indicate early extraordinary vitality, 
predetermination, or both. 
1 The red figures on the right of the plate indicate millimeters. 
