368 PROCEEDINGS OF SECTION A. 
the centre, whence it diminishes uniformly to each end, when it 
need be no greater than is necessary to accommodate the optical 
apparatus. 
The axis may remain a double cone as at present, but preferably 
enlarged in diameter at its centre, whereby flexure will be 
reduced. 
6.—FURTHER INVESTIGATIONS ON THE LAWS OF 
MOLECULAR FORCE. 
By WituiamM SUTHERLAND, M.A., B.Sc. 
[ Adstract. | 
In this paper the author gave a brief sketch of the methods and 
results of his researches during the past year on the subject of 
molecular force. The most important point in the theory of 
molecular force is the establishment of the characteristic equation 
for fluids on the model of Clausius’s equation of the Virial— 
8pv = SimV -—- 4433/7. where F is the force between two 
molecules at distance ~ apart. According to a law of force 
3.A m’ |r between two molecules of mass m, + > 3/7 the internal 
virial must vary inversely as the volume. In agreement with 
this, the equation for the elementary gases and methane is 
from Amagat’s experiments proved down to the critical volume 
to be pu=K r{ 1 +5/(o-5 ; “5 where //v is 2:43 3 Fr for 
unit mass of gas. But in the case of compound gases a different 
form is, from Ramsay and Young’s experiments on ethyl oxide 
and Amagat’s on carbonic dioxide, proved to hold down to the 
9 
critical volume pv= Rk T (1 +24) wife which is indirectly 
v+k/i utk 
proved to apply to the great majority of compounds, the most 
prominent exceptions being the alcohols and water, ethylene and 
bodies such as acetic acid and nitric peroxide, which have been 
shown to contain double molecules. The most notable point 
about this equation for compounds is that the form //(v+) for 
the internal virial holds down to yolume v=4, at which it 
becomes 7/2, and below which it becomes 7/2v. Hence, below 
a certain volume, 4, the internal virial for compounds varies 
inversely as the volume, as the law of the inverse fourth power 
requires, but above the volume & the form //(v+) would seem 
to be in contradiction to that law, only that the author is able to 
show that this form is due to the pairing of molecules in com- 
pound gases, the virial constant for the free molecules being J, 
a ee 
an 
