PROCEEDINGS OF SECTION A. 369 
and that for the pairs being 7/2, so that when the volume 2 is 
reached all the molecules are paired, and then through the whole 
range of liquid volume the pairs behave as single molecules in 
the matter of molecular force. These equations apply down to 
the critical volume ; in the case of the elements and methane the 
critical volume pressure and temperature are given by the con 
3k 
ditions df/dv=od'p/dv’ = o, whence 2, Sh VE OO eae 
p. = 47/27. At the critical volume 2 i 1+  Iw-5) | 
Dui , ¥ : 
becomes sea and the form established below the critical volume is 
— us 
pu= if z. (1 pba ) —- Im the case of compounds the 
Zi = U. 
condition @’f/dv° =o is not a possible one, and the critical 
Tk 
values are given by @f/dv=o and v, = = whence 7, = 120// 
409 Rk, p. =367/409 &. By means of Ramsay and Young’s data 
aon ¥Tv,- 4 
for ethyl oxide, the general form fp 7= ra 
hate , Ga 
eis established for compounds below the volume 4, while 
25 R ae Cee 
between & and 7 £/6 the form is J v = ares ile Ser . - e 
4 
v+ hk. 
of the present experimental range of fluidity, one can proceed 
to applications too numerous to detail in an abstract ; thus it 
is possible to amend to a more accurate statement Van der 
Waals’ generalisation that, if volume pressure and temperature 
for any substance be expressed in terms of its critical values, 
as units, then one and the same law applies to all fluids. 
The more accurate statement is that above the critical volume 
the elements and methane follow the same law, while compounds 
with the previously mentioned exceptions follow another law, the 
same for all compounds, but different from that for elements. 
Below the critical volume these statements are not strictly but 
only approximately true. With these equations there are five 
main methods of finding values of the virial constant / from 
available data. The first is from extended enough observations 
on the compression and expansion of bodies as gases ; the second 
from one measurement of the co-efficient of expansion a and of the 
compressibility ». at temperature Z of the body as a liquid 
x 
Thus equipped with equations covering the whole 
