22 O'l the Hypothesis of Gaseous Repulsion. 



of Continuity 1k)1c1.s good. Nor could the attraction be reci- 

 procally proportional to the square of the distance, unless 

 the calorific at'.nosphcrc was entirely taken away; that is, 

 unless the body was absolutely cold; which we do not admit. 

 We may therefore infer, that if the law of gaseous repulsion 

 be inversely proportional to the distance, no diminution of 

 the calorific atmosphere can change the repulsion into an at- 

 traction inversely proportional to the square of the distance ; 

 and, conversely, if the attraction be reciprocally proportional 

 to the square of the distance, no increase of caloric can pro- 

 duce a repulsion varying as tlie distance inversely. 



By the same method of reasoning it may be shown, that no 

 law of repulsion diflering from the reciprocal duplicate of the 

 distance, can, by a diminution of caloric, produce an attraction 

 following this law, that is the law of gravitation. But if the 

 particles repel each other by forces inversely proportional to 

 the square of the distance, the cubes of the elasticity will be 

 as the biquadrates of the density; that is, the elasticity will in- 

 crease faster than the density; which does not accord with ex- 

 periment. 



This will be the case on the supposition that the repulsion 

 of the particles extends and confines itself to those particles 

 tliat are nearest them ; a supposition which by no means adds 

 to the probabilit}' of the hypothesis. Should the repulsion be 

 diffused to an indefinite distance every way about; or should 

 it reach to a certain extent, so that a gi'eater number of forces 

 act upon a given particle in a greater density than in a less, 

 the elasticity will increase or diminish in a still greater ratio 

 than the density. Experience however tells us that, the tem- 

 perature remaining the same, the elasticity of any air is di- 

 rectly proportional to its density. Therefore the hj^jothesis 

 of a repulsion in the inverse duplicate ratio of the distance does 

 not agree with phaenomena. 



The only chance of probability, which it appears to me is 

 left for the hypothesis of caloric, is to give to the calorific par- 

 ticles a repulsion reciprocally proportional to the sfjnare of the 

 distance. Any body placed within a spherical homogeneous 

 atmosphere of this kind, would be repelled by a force varying 

 as the distance inversely from the centre ; and placed without 

 that sphere, it would be repelled by a force reciprocally j)roj)or- 

 lional to the square of the distance. Two particles with this 

 hj-pothesis may be so placed that they shall mutually repel with 

 forces recijirocally proj)ortional to their distance ; and, if the 

 atmos])here be diminished, shall at length have their repulsion 

 converted into an attraction reciprocally proportional to the 

 square of the distance. But even here conditions arc neces- 

 sary 



