Vol.. 8, 1922 
STATISTICS: PEARL AND REED 
365 
Finally, with the new experimental data we are now in a position to 
calculate for the first time the changes in the specific heat of a metal at 
high pressures. It appears that the specific heat at constant volume de- 
creases under pressure by an amount of the same order of magnitude as 
the change of volume under the same pressure, but in most cases by a factor 
several fold greater. 
1 Bridgman, P. W., Proc. Amer. Acad., Boston, 44, 1909 (255-279), and 47, 1911 
(362-368). 
2 Kraus, C. A., J. Amer. Chem. Soc, Easton, Pa., 44, 1922 (1216-1238). 
3 Born, M., Verh. Deut. Phys. Ges., Brauschweig, 21, 1919 (533-538). 
4 Schottky, W., Phys. Zs., Leipzig, 21, 1920 (232-141). 
A FURTHER NOTE ON THE MATHEMATICAL THEORY OF 
POPULATION GROWTm 
By Raymond Peari^ and l^ownhh J. Rekd 
In an earlier paper in these Proceejdings we^ showed that the expression 
y = (l) 
1 + ce'''' 
gives an excellent fit to the known population growth of the United States 
since 1790. Since the first paper was published, we have extended and 
generalized our ideas on population growth with the results herein presented 
in skeleton outline. A more extended paper, giving a full discussion of our 
new results and of the pertinent literature is in press in Metron. 
Considered generally, the curve 
y = 
may be written 
where 
1 + m/'^'"' 
(ii> 
k = b/c, m = l/c, and ka'= — a. 
Now the rate of change of y with respect to x is given by 
? = -a'y ik-y) 
dx 
