166 ~~ Prof. Maxwell on the Theory of Molecular Vortices 
traversing similar parts of the systems will be m; so that /®mn 
is the ratio of the momenta acquired by similar portions in 
traversing similar parts of their paths. 
The ratio of the surfaces is /?, that of the forces acting on 
them is /*p, and that of the times during which they act is 
l : me 
3 80 that the ratio of the impulse of the forces is —, and we-. 
have now eck ot 
m 
or 
mn=p ; 
that is, the ratio of the pressures due to the motion (p) is com- 
pounded of the ratio of the densities (n) and the duplicate ratio 
of the velocities (m*), and does not depend on the linear dimen- 
sions of the moving systems. 
In a circular vortex, revolving with uniform angular velocity, 
if the pressure at the axis is po, that at the circumference will be 
Pi=Po+4pv’, where p is the density and v the velocity at the 
circumference. The mean pressure parallel to the axis will be 
Pot gp" =Po- 
If a number of such vortices were placed together side by side 
with their axes parallel, they would form a medium in which 
there would be a pressure p, parallel to the axes, and a pressure 
p; in any perpendicular direction. If the vortices are circular, 
and have uniform angular velocity and density throughout, then 
Pi —Po= apr" 
If the vortices are not circular, and if the angular velocity and 
the density are not uniform, but vary according to the same law 
for all the vortices, 
P1—Po= Cpr’, 
where p is the mean density, and C is a numerical quantity de- 
pending on the distribution of angular velocity and density in 
the vortex. In future we shall write = instead of Cp, so that 
1 
Pi—Pa= Gp, RE) 
where w is a quantity bearing a constant ratio to the density, and 
v is the linear velocity at the circumference of each vortex. 
A medium of this kind, filled with molecular vortices having 
their axes parallel, differs from an ordinary fluid in having dif- 
ferent pressures in different directions. If not prevented by 
properly arranged pressures, it would tend to expand laterally. 
In so doing, it would allow the diameter of each vortex to expand 
