338 Mr. lExley*s JVev) Demonstration 



the parts of the increment of a; are equal. Again, because 

 the pressure at T is given, and there is a perfectly free 

 communication of the ethereal atoms between the two 

 vessels, and the tenacious atoms in the inner vessel are 

 separated by intervening ethereal matter, the initial resist- 

 ance to any increment of density, that is, the re-action of 

 the ethereal atoms between those of the tenacious class is 

 always the same, being in equilibrium with the given 

 pressure at T, therefore d u is constant ; hence, it follows, 



d u 

 that T— = a, where a is a constant ; therefore, u = a x, 

 dx 



which needs no correction, because when the compressing 



force is nothing, the density at the surface V P W is 



nothing, as shown above : therefore, u is proportional to x, 



or the compressing force to the density is a constant ratio, 



which was to be shown. 



Cor. 1. (prop. 2 of the paper.) The resistance between 

 two tenacious atoms, which opposes an additional com- 

 pressing force on the inner vessel, is inversely as the distance 

 between the two atoms. 



By this proposition the compressing force varies as the 

 density, and the density varies inversely as the cube of the 

 distance between adjacent atoms ; therefore, the com- 

 pressing force varies as the same cube ; but it also varies 

 as the number of atoms on a given surface and the force 

 of each ; now, the number of atoms on a given surface is 

 inversely as the square of the distance ; therefore, the force 

 of each is inversely as the distance. 



Scholium 1. It might, perhaps, at first seem strange to. 

 some, that the limit of the ratio of the compressing force 

 and the density should always be the same, and yet, that the 

 actual resistance to a definite additional compressing force 

 should vary : but the difficulty will vanish by a little atten- 

 tion to the 1st prop., which shows that the tenacious atoms 

 are invested with atmospherules of ethereal matter in- 

 creasing in density to the surface of repulsion ; hence, as 

 these approach nearer together up to a certain term, there 

 will be a denser and greater portion of ethereal matter to 

 be acted on, and pressed against the spheres of repulsion, 

 and forced out from between the tenacious atoms, than 

 when these tenacious atoms are at a greater distance; hence, 



