486 HALBERT L. DUNN 
cephalon weight require a third constant in their expression, while 
the volume of the cerebral hemispheres can be expressed mathe- 
matically with two constants. The general empirical formula 
of compound growth can be expressed: 
y 2 axe 
in which Y is the volume of the encephalon or entire central 
nervous system in cc., X is the crown-heel length in cm., and a, 
b, and ¢ are constants separately determined for the entire brain 
volume and the central nervous system volume. 
The significance of the relation between lineal and volumetric 
dimensions in the growth of the parts of the brain. The classifica- 
tion of the types of growth of the central nervous system is shown 
by both the volume and linear curves. For instance, both the 
volume curve of the cerebellum and the linear measurements of the 
vermis cerebelli length and the vermis cerebelli height indicate 
the characteristic cerebellum type of growth. It is logical that 
there should be a definite relation between the linear and the 
volume measurements of a brain part. It is also evident that 
the length of a brain part when it is cubed should form a curve 
identical in type and constant in relationship to the correspond- 
ing volume curve, provided that no additional factor, other than 
that which influences the growth in the linear dimensions, influ- 
ences the growth in volume. Such a relationship actually exists 
between the formulae of the linear cerebellum curves and the 
formula of the cerebellum curve of volume. The formula for the 
cerebellum length when cubed is practically identical to the 
formula of the cerebellum volume. This relationship is seen 
somewhat better when those values are based on the cube of the 
body length as modified by three constants rather than by a 
formula based on the body length raised to a fractional exponent. 
The first formula is expressed below: 
Cerebellum volume (cc.) = [0.01 (0.073 Vermis cerebelli 
length (em.) + 2.85)3]§ 
Likewise, the formula of the cerebellum height when cubed and 
multiplied by the constant 2.13 is practically identical with the 
formula of the cerebellum volume: 
