62 Mr. Herapath on M. Laplace's Jhcori) 



it may be said that explanations by analogy are in most physical 

 cases illusive and deceitful, and in all unsatisfactory. M. La- 

 place therefore, discarding the limitation of Newton, proceeds 

 to determine the laws of elastic fluids on the suj)position of the 

 corpuscular rejiulsion being sensible at insensible, and insen- 

 sible at sensible distances. Each particle of a fluid which is 

 at a sensible distance from the envelope, is on this hypothesis 

 kept in cquilibrio by the balance of iej)ulsion in the surround- 

 ing particles. This repulsion he first assumes exclusively due 

 to the caloric of the particles; theirmutualdistances being such, 

 though insensibly small, that their reciprocal attraction has no 

 sensible effect. In the general equation therefore of a fluid 

 sphere, dp-=pi^(h\ 



in which ^ is the repulsion of the whole sphere of the density 

 p on a point at the distance r from its centre, andy? the pressure 

 in an opposite direction to the repulsion, M. Laplace conceives 

 (f) = o; which gives J9 = constant. 



So far I apprehend no great objection would be made to 

 M. Laplace's assumptions; though some of them are certainly 

 not unexceptionable. His statement however, that " en nom- 

 mant r la distance mutuelle de deux molecules de gaz, nous 

 exprimerons la loi de repulsion par H c^ <^ [i-)" <f> (r) being 

 insensible with a sensible value to r, and H being a constant, 

 we cannot I think so easily admit. For since the particles of 

 caloric are supposed to have a mutually repulsive force, and 

 each particle of the gas to retain by its attraction its caloric, 

 the caloric must assume about a particle of the gas, the form 

 of a sphere or spherical shell. Nor would the repulsion of the 

 surrounding particles have any effect on the figure, unless to 

 promote or preserve it. Supposmg therefore the distance r 

 between the particles to remain the same, the function f (r) 

 must involve the dimensions of the spheres or shells ; conse- 

 quently, as these dimensions would vary with the quantity of 

 caloric, the repulsion would not be as c^, as M. Laplace con- 

 ceives ; unless wheji the particles of caloric mutually repel one 

 another by a force reciprocally proportional to the square of 

 the distance, which would give the gas a very different law to 

 that which experiment requires. 



Conceding to M. Laplace the above law, which I think it is 

 plain cannot be correct, he finds by some ingenious considera- 

 tions, P being the pressure on any point, and 2 tt H K an in- 

 variable factor, thai, 



V=2itllKq'-c'; (I) 

 a theorem which of itself exjiresses nothing that I know of in 

 the laws of gases. 



This 



