40 Proceedings of Royal Society of Edinburgh. [sess. 
same time under the action of gravity. For instance, the earth’s 
speed in her orbit is about equal to 18 J miles per second, while 
the distance she falls towards the sun, under gravity, in the same 
time, is about the -Jth of an inch. Of course the disproportion 
would not be nearly so great as this, but something of this order. 
The centrifugal force increases inversely as the radius, and the 
radii of these orbits are excessively small, but, as shall presently 
appear, the force of gravity is a mere differential force, and is not 
likely in any case to be equal to the total pressure in the 
medium, whereas the pressure on these particles is equal to the 
total pressure in the medium for their mass. But this merely by 
the way, the meaning of which will be more apparent further on. 
The larger the bubble, or atom, then, in proportion to its weight, 
the greater the speed of its constituent particles. For instance, 
two atoms of the same size, but weighing one twice as much as the 
other; the speed of the particles of the lighter of the two would be 
twice as great, for they would have twice the area to protect from 
penetration. Of course, with twice the speed there would be 
four times the centrifugal tendency, but also there would be four 
times the centripetal, for, with twice the speed, each particle of 
the bubble, or atom, would come into contact with twice the 
number of in-pressing particles of the medium, and their pressure 
would be continued through twice the distance. Or, the pressure 
would be twice the quantity through twice the distance, equal to 
four times; and so on in proportion for other speeds.* Now, it 
would appear from a superficial view of the foregoing that the 
pressure on any atom would be proportional to the surface area, 
and not to the number of particles in it ; but this is an erroneous 
view of it. The pressure would be at any instant directly 
proportional to the number of particles in the atom, and which, 
as they (the particles) are of equal size and mass, is the same 
as saying that the pressure on any atom would be directly propor- 
tional to its mass. 
* Or, to put it in another way, as in twice the distance of a circular orbit 
there is four times the curvature, twice the pressure for the same time pro- 
duces twice the velocity = four times the kinetic energy, which would produce 
four times the curvature in the paths of the particles. 
