86 
Scientific Proceedings (43). 
In frogs from one to four years old, the body weight more than 
doubles during each active season, although the precise form of 
the curve representing this body growth is not known. 
The growth of the central nervous system is precocious in 
relation to that of the body, but in the absence of direct obser- 
vations on the growth of the body, the form of the curve can only 
be indirectly determined. 
During the active season, the percentage of water in the entire 
frog falls slightly from spring to summer and rises again from 
summer to autumn. These changes seem to be due to the com- 
bined effects of advancing age and varying food supply. 
5i (576) 
An interpretation of growth curves from a dynamical stand- 
point. 
By S. HATAI. 
[From the Wistar Institute of Anatomy and Biology.] 
The growth phenomena may be considered as a gradual trans- 
formation of growth energy to the work done in forming the mass 
which composes the body. The present writer wishes to de- 
termine "what law, if there is any, governs in any individual the 
rate of transforming the growth energy into the work done." 
In order to solve the above problem, the assumption was made 
that under normal conditions the growth energy is transformed 
into the work with least loss of energy. It was shown that in 
order that this assumption should be true we must have 8A—0 
in the following integral 
A (action) = f mvds. 
Applying this principle it was proved that the formula for the 
growth of brain in weight (and any other data which satisfy the 
same conditions) must be a function which renders the following 
integral minimum 
The integral is minimized when the function y has the following 
relations : 
