547 
it e. In the second part, according to the supposition made, we 
have C’,= const. = */, R and therefore 
S= 3/2. R.lgT— 3/2.RigT, + = 3/2.RigT+8,.... (2) 
For mercury-vapour the chemical constant is from i7 to 19 R; 
from this fact it can be easily deduced that fora volume V = 1 cc, 
we must have S, = about 3A. 
A lower limit of 7, is found by taking C,=0O below 7%, so 
that ¢ = 0, which gives 
lgT, = about — 2 
Li = about OPT 
In the gas-model given by Scuerrer 7’, is very much lower, it 
may be estimated at about 10—° of a degree, as shown below. 
This would give for S, the value: 41.5 R He 
and for the chemical constant: 57.2 R + «. 
§ 2. Let us consider by what circumstances the said temperature 
is determined in Scnerrer’s model. The equation of state correspoud- 
ing to the model can be obtained by the wellknown method from 
the formula for the entropy, which ScuurrEr derives from the value 
of the thermodynamic probability of the system. Except for a con- 
stant factor *) this thermodynamic probability is completely determined 
by the number of elementary cells in the phase-space of the system, 
which lie inside the hyper-surface of constant energy. For large 
values of the energy, i.e. for high temperatures, this number may 
be calculated approximately by dividing the volume of an elementary 
cell into the volume enclosed by the energy-surface, the method 
also followed by ScHerRER; in this manner the equation of state of 
the ideal gas is obtained. It is therefore necessary to make an esti- 
mate of the possible error in this calculation for small values of 
the energy. 
Both volumes, that enclosed by the energy-surface as well as 
that of an elementary cell, may be considered as a product of a 
volume in the space of coordinates and a volume in the space of 
momenta. The former is equal for both; the latter is a hyper-sphere 
for the energy-surface and a hyper-cube for the elementary cell. 
Taking N= 65x10" and 4— 6.415 10-2" it. appears, that 
for one grammolecule of mercury vapour of volume 1 ce. by 
assuming the energy to be £ == 1.055 & 10 # erg the radius of the 
hyper-sphere becomes six times the diagonal of an elementary cell, 
the ratio of the volumes in question being 
Z = about 1025610, 
1) A constant factor in W, i.e. an additive term in the entropy S, has natur- 
ally no influence on the equation of state. 
35* 
