576 MR W. J. M. RANKINE ON THE 
the fraction cos @ only strikes the plane; while the force of the blow also is less 
than that of a normal blow in the ratio cos@:1. Hence the mean force of col- 
lision is 
r 
J? cos? Osin da =4 
0 3 
of the force of a perpendicular collision; so that the expansive pressure is repre- 
sented by 
1 4 LRA Oat Pp 
Bug 2 Vil OMe 
Hence, according to this hypothesis, we should have for a perfect gas 
2 
PV=59 
or the product of the pressure and volume of a mass of a perfect gas equal to two- 
thirds of the mechanical equivalent of its total heat. 
It is known, however, that the product of the pressure and volume of a mass 
of sensibly perfect gas is only about four-tenths of the equivalent of its total heat. 
The hypothesis, therefore, requires modification. 
By supposing the particles to attract each other, or to be of appreciable bulk 
compared with the distances between them, the ratio in question is diminished ; 
but either of these suppositions is inconsistent with the perfectly gaseous con- 
dition. 
It appears to me, that, besides this difficulty connected with the gaseous con- 
dition, there exists also great difficulty in conceiving how the hypothesis can be 
applied to the solid condition, in which the particles preserve definite arrange- 
ments. The limited amount of time and attention, however, which I have 
hitherto bestowed on this hypothesis, is not sufficient to entitle me to pronounce 
whether these difficulties admit of a solution. 
(58.) The idea of ascribing expansive elasticity to the centrifugal force of 
vortices or eddies in elastic atmospheres surrounding nuclei of atoms, originated 
with Sir Humppry Davy. The peculiarity of the view of the hypothesis taken 
in this paper consists in the function ascribed to the nuclei or central physical 
points of the atoms, which, besides retaining the atmospheres round them by 
their attraction, are supposed, by their actions on each other, to constitute the 
medium which transmits radiant heat and light; so that heat is radiant or ther- 
mometric, according as it affects the nuclei or their atmospheres. 
In this form the hypothesis of Molecular Vortices is not a mere special suppo- 
sition, to elucidate the theory of expansive heat, but becomes connected with the 
theory of the elasticity of matter in all conditions, from solid to gaseous, and 
with that of the transmission of radiations. 
I have already investigated mathematically the consequences of this hypo- 
thesis by two different processes, which are necessarily somewhat complicated. 

