326 
PHYSICS: F. G. KEYES 
The original mode of guessing the form of function is accordingly 
given. 
The value sought, denoted by 8, would be a function of the volume 
alone and such a function that at infinite volumes it becomes constant, 
since when large distances separate the di-atoms the effect of the field 
due to the surrounding molecules would be negligible. The value of 8 
for V = oo let it be assumed then is j8, a constant. The rate of chang'j 
of 8 for changes in volume would presumably be a function of the field 
due to the assemblage of particles and the value of 5, since the effect is 
due to the mutual action of the forces holding the di-atoms together and 
the external field due to the diatoms conjointly. This may be expressed 
by writing d8/dv = f{8F), where F is the force. Now the simplest as- 
sumption under the circumstances is to assume that d8/dv = k8F where 
^ is a constant. The value of F taken per unit of area is approximately 
a/v^ and the primitive of the equation becomes then, log 8 = log ^ —a/v 
where ka = a another constant, and ^ is of course the limiting value 
which 8 assumes when v is infinite. The equation for a diatomic assem- 
blage of particles becomes then equation (1). 
The equation (1) arrived at by such crude methods has been found 
to accord with the facts in a surprisingly exact manner, but in the present 
paper I will exhibit the evidence which has to do with the gist of the 
whole argument underlying the deduction of equations one and two. 
A later paper will present a discussion of the equation from a more 
general point of view including a comparison with all the available experi- 
ment data for various substances. It accordingly suffices for the present 
purpose to point out that the whole thought is tested uniquely by com- 
paring a diatomic system with a monatomic system. The value of 8 for 
the monatomic substance reduces to the constant jS independent of the 
volume while 8 becomes a volume function when the system consists of 
diatomic particles alone. 
Recently sufficient data have appeared for argon which enables the 
test to be applied, while the diatomic system nitrogen will serve to test 
the functional form of 8. The triatomic molecule carbon dioxide ap- 
pears to follow the same functional form for both gas and Hquid phases. 
It should be emphasized that only those regions are available as legiti- 
mate for comparison purposes in which one order of molecule is present. 
That is to say, there must be no doubhng of the argon atoms to form 
diatoms or association of the nitrogen molecules within the region of 
experimental data where comparisons are made. Such regions are for- 
tunately a part of the experimental data contained in the hterature. 
It is noted that when the volume is held constant equations one and 
two state that the pressure will increase linearly with the temperature. 
