840 THE AMERICAN NATURALIST. [Vor. XXXVI. 
and to this end by biometric methods, the actual stages in the 
development of the paired fins in accordance with their physi- 
cal requirements. Assuming, for example, a complete series 
of a form in which the limb characters can be favorably exam- 
ined, say a shark,’ in stages ranging from adult to embryos in 
which the paired limbs are just appearing as distinct structures, 
we can then determine by measurement what change occurs 
from stage to stage in the position of the gravity center (with 
reference to the total length of the animal), and by similar 
measurement of the fins in similar terms we can ascertain what 
ratio these measurements bear to the possible shifting of this 
center. For all will admit that the fins themselves, as light 
and delicate structures, can in their growth play little direct 
part as a cause of the changing position of the center of gravity, 
and that their migration, forward or backward, is rather 
an outcome of the shifting of bulkier organs, — muscles, 
brain, viscera, sense organs. We can therefore conclude that 
by such a system of measurements one can obtain evidence as 
to whether the ventral fins migrate backward, z.e., in terms 
of the total length of the individual, and show the correla- 
tion in growth with the pectorals which the Gegenbaurian 
theory demands; or whether, on the other hand, it is the 
ventrals which are constant, and resemble the dorsal fins, 
while pectorals play the part of the mobile and specializing 
members. 
The following notes are based upon a cestraciont shark,? a 
form particularly interesting from the standpoint of morpho- 
logical conservatism, since there is reason to believe that it 
has been little modified since Carboniferous times. And the 
measurements are recorded of sixty individuals ranging in 
length from 330 mm. to 14.5 mm. For this careful and labo- 
rious computation I am much indebted to my former student, 
Prof. C. H. Brookover, who made it the beginning of a research 
1 Better, of course, would be sets of many genera and species; but as long as 
these are lacking, we may base conclusions as to essential characters upon the 
NEUF of a single form. 
? Heterodontus japonicus Macleay. The embryos were collected during the 
writer’s visit to Japan, 1901, thanks to the many — which he enjoyed at 
Misaki as guest of the Im mperial University of Tokyo 
