400 Cambridge Philosophical Society : — 



repulsive force varies inversely as the cube, and not, as usually stated, 

 the simple power of the distance ; that it is not true, without some 

 limitation, that the force varies as the inverse first power, was urged 

 from the fact that such a force would decrease more slowly than one 

 varying as the inverse square, and consequently would be the force 

 observed in astronomical phaenomena ; and even the oxygen of the 

 ocean would repel that of the air instead of attracting it. That the 

 force varies as the inverse cube was deduced from the law of elas- 

 ticity, that the density varies as the pressure ; for if a particle repels 

 other particles with a force varying as the inverse cube, it repels a 

 fixed plane of them with a force varying as the inverse first power. 

 That this is the case may be seen, by considering that though the 

 particle repels particles similarly situated with a force varying as the 

 inverse cube, yet the number of such particles varies directly as the 

 square of the distance, and therefore the whole effect upon the plane 

 varies inversely as the first power. And if this is true for a plane, 

 it is also true for the solid side of the containing vessel ; for any 

 solid may be considered as made up of a succession of planes. 



The law being the inverse cube, it follows that in any position the 

 sum of the forces exerted by any particle on two particles, one on 

 each side of it, is least when that particle is half-way between them, 

 and increases the further the particle is removed from the middle 



point. This is seen directly, for the value of - ^ , -l - — t^ — is 



least when .r=0, and increases until a:=a. And therefore, in order 

 to produce the same force, it would be necessary that the mean 

 distance should be increased ; and hence if the particles of any aeri- 

 form body be in motion, the force exerted by them would be greater 

 than when at rest ; that is, if the pressure to be supported be con- 

 stant, the average distance of the particles must increase, and the 

 body must expand. 



III. That every aeriform body not in contact with a liquid expands 

 in the same proportion. This was accounted for by the circumstance, 

 that the increase of pressure depends only upon the ratio of the dis- 

 turbance to the original distance, and not at all upon the absolute 

 distance. 



IV. That air and elastic fluids give out heat on compression. By 

 compression the absolute distance of the particles from one another 

 is diminished ; but the absolute motion remaining the same, the rela- 

 tive motion is increased. 



V. That the same amount of heat is generated in two gases sub- 

 jected to the same pressure ; for the absolute distance of the particle 

 in both being diminished in the same proportion, and the absolute 

 motion remaining unaltered, the relative motion is increased in the 

 same proportion in both. 



VI. The specific heats are inversely as the atomic weights. Here 

 it was necessary to show that mass is not necessarily proportional to 

 the quantity of matter, as usually stated ; or rather, that a body may 

 have a different mass when considered with regard to the molecular 

 force from what it has with respect to the force of gravity. With 



