324 
PHYSICS: F. G. KEYES 
which electrons are revolving. The negative electrons are assumed to 
possess a charge in the aggregate equal and opposite to the positive 
central charge. This model atom is essentially the atom discussed by 
Nicholson and Bohr. 
Imagine an assemblage of such model atoms contained within an 
envelope and subject to their mutual attractive forces. The revolving 
electrons of a given atom generate a magnetic field and for convenience, 
therefore, the revolving electrons may be conceived as circles of current 
about the positive central portion of the atom. The positive central 
portion of one such atom repels the positive charge of another atom in a 
manner varying inversely as the square of the distance, and similarly the 
negative charges repel as The negative charges attract the positive 
also according to r"^; but since, if all of the atoms were suddenly fixed 
in position their average distances apart would be equal, it may be as- 
sumed that the attractions and repulsions of the positive and negative 
charges mutually cancel. The potential due to the fields of the re- 
volving electrons however do not cancel and therefore on the whole 
the resultant attraction in the assemblage of particles varies ap- 
proximately as r~^. 
The attempt to calculate the complete expression for the force be- 
tween two such model atoms is difiicult and will require a more detailed 
knowledge of the atom. Sufficient is known, however, to make it certain 
that the attraction increases sHghtly more rapidly than r~^. 
An envelope of volume v and containing n particles would provide a 
space for the habitation of each particle on the average equal tov/n, so 
that the distance apart of the molecules, if a is the radius of the spherical 
envelope, would be equal to o- = a(47r/3w)3. Therefore the potential 
energy would be proportional to }/2 SSo— ^ or equal to h/v where h is 
a suitable constant. The attraction then directed toward the center, 
would be per unit of surface identical in form to van der Waals' cohesive 
pressure a/v"^. Now if the attractive force really increases slightly 
more rapidly than as appears to be really the case^ it is easily per- 
ceived that a/v'^ would only be vaHd at very large volumes. A simple 
device to correct the expression is to assume that <l>, the cohesive pres- 
sure, may be represented by a/{v —ly, where / is a small constant which 
will of course make ^ increase more rapidly with diminution of volume 
than a/v^ in the ratio of v'^/(v—iy. 
The truth of the cohesive pressure expression ^> = a/(v—iy can be 
determined only by experiment since a rigorously complete solution 
for the attraction of an assemblage of the model atoms appears to be 
impracticable. If then the volume function for # given, is in agreement 
