546 
proportional to the surface. Thus we may say that the factors 
dependent on the 4*t power of the length are preponderatingly 
favourable to growth, whereas those factors, which are connected 
with the surface, are chiefly disadvantageous. 
Physics. — “Note on P. Scunrerur’s: calculation of the entropy- 
constant.” *) By J. M. Burerrs. Supplement N°. 410 to the 
Communieations from the Physical Laboratory at Leiden. 
(Communicated by Prof. H. KaMeERLINGH ONNms). 
(Communicated in the meeting of Sept. 30, 1916). 
The object of this note, which is suggested by a remark made 
by Dr. W. H. Krusom, is to point out that: 
(1). If a model of a monatomic gas constructed according to the 
theory of quanta on cooling at constant volume ceases to conform 
to the classical theory at temperatures which are too low (i.e. lower 
than is indicated by experiment), it will also give values for the 
entropy-constant which are too high, unless the entropy is not taken 
as zero at the absolute zero of temperatures for ideal gases. 
(2). The model suggested by Scuurrer remains ideal to tempera- 
tures far below the allowable limit. 
§ 1. If for 77=0 the entropy S is taken as 0, the absolute value 
of the entropy of one grammolecule of a gas for a given temperature 
T' and a given volume V may be found by the following integration 
from 0 to 7, the volume being kept constant at V, 
r 
a] Ge 
S= ar EE pe « . . . . . . it 
fer (1) 
0 
This integral may be divided into two parts as follows 
To ji REE 
S ar Co ar ve 1* 
aS lr d fom Mr 
far + fare (1) 
0 To 
and the temperature 7, may be chosen such, that above 7, the 
deviativas from the ideal gaseous state are to be neglected. (In 
general 7, will depend on the value of the volume; to begin with 
we will take as a special case V —1ce.. For Ke 1 ce. see below). 
The first part of equation (1*) is certainly positive; we shall call 
DP; Scuearer: Gott: Nachr. 1916. 
