GROWTH OF THE FETAL CENTRAL NERVOUS SYSTEM 415 
The empirical formulae expressing the curves obtained from the 
material are of several types. As certain of the lineal dimensions 
of the brain are straight lines when plotted against crown-heel 
length, they may be expressed by the formula: 
Dei AL) 
where Y is the value in question expressed in em., X is the crown- 
heel length in cm., and a and 6 are empirically determined con- 
stants. 
The growth of other lineal dimensions of the central nervous 
system is not so simply related to the lineal growth of the body 
as a whole and the expression of this relation is more complex. 
But all may be represented by formulae having the general form: 
Vo (aXe ae 
where Y is the value in question (in em.), X is the crown-heel 
length of the body (in cm.), and a, b, and c are empirically de- 
termined constants, b being a fractional exponent. Curves cor- 
responding to formulae of this type may also be expressed fairly 
satisfactorily in the logarithmic form: 
Y =aX +blogX +c 
which will be recognized as the formula which Hatai employed 
with great success in the study of the growth of the various organs 
of the albino rat and which is regarded by him as of fundamental 
importance as exemplifying the application of the law of Mau- 
pertuis to the process of growth. However, the exponential form 
has been found the more convenient for application in the pres- 
ent work. 
The formulae for the expression of the inspected curves of 
volumes of the various parts of the central nervous system have 
as their simplest form: 
ake 
which is modified in certain instances to: 
GX) Pear 
and in others to: 
Y =d[(aX)® +¢| 
In these formulae Y is the value in question in ec., X is the crown- 
heel length in cm., and a, b, c, and d are constants, b being always 
an exponent with a value greater than 1. 
