104 THE ROYAL SOCIETY OF CANADA 
for the molecular kinetic energies and n, and n, for the relative number 
of molecules. That is, we must have, if x —n,/n, 
ny 
E 
ang == then also 
2 Ny E, Ny 
Dyed asi Pr 

The value of H — 243 calories, may be taken as representing 2 (E,—E,). 
Hence an assumption as to the relative number of molecules enables us 
at once to calculate E, in calories, and such calculated value must, at 
least, not be inconsistent with experimental facts. If we assume that 
the molecule of water has the formula 4 (H, O) as indicated by Ramsay 
and Shields in their determination, then n, — 4 n,, so that 

Mona es) We, SR eae en 
Ny 2 E, 2E, 
or the total molecular energy remaining is 81 calories. Now we know 
that water in freezing gives out about 80 calories per gram while the 
specific heat drops to about one-half its former value. Thereforeno 
assumption making the residual molecular energy of the water at 0°C 
less than 160 calories could be entertained as agreeing with the experi- 
mental facts. The total energy may be more but probably not less 
than 160 calories. If we suppose the specific heat of ice to be the same 
at low temperatures as at 0°C the total residual molecular energy might 
1; 

reach 216 calories. The value of x (= 3) when we write 2E, — 160, 
Ny 
2-0 and for 2h, — 216. %— Del. 
In case no other limit as to the residual molecular energy is avail- 
able an upper limit may be obtained by assuming that the total residual 
molecular energy of a liquid cannot exceed the product of the specific 
heat and the absolute temperature. In this case the value of x may 
possibly be too small but is probably not too large. If we apply this 
243 
— 271 7 a — 19) (nearly)2 Ofte 
€ 
ake 
> ws 
. . ° 
criterion to water at 0 C we get 

_ 
three values for x the second seems the most probable and is also almost 
exactly the mean between the other two. 
It should not be overlooked in this connection that the value of x as 
above determined shows only the change in the number of molecules. 
ee . L à 
In the case of acetic acid, for instance, we shall find that = ris only 
1-3 at the normal boiling point. From Ramsay and Young’s value’ 
for the vapour density it may be seen that the molecular weight is already 


? Winkelmann’s Handb. Warme, p. 1050. 
