Historical survey 371 



imaginary plane, and therefore the product of the repulsion between two given 

 molecules into the distance between them must be constant, in other words the 

 repulsion varies inversely as the distance. 



In this demonstration the repulsion considered is that between two given 

 molecules, and it is shown that this must vary inversely as the distance between 

 them in order to account for Boyle's law of the elasticity of air. 



If, however, we suppose the same law of repulsion to hold for every pair of 

 molecules, Newton shows in his Scholium that it would require a greater pressure 

 to produce the same density in a larger mass of air. 



We must therefore suppose that the repulsion exists, not between every 

 pair of molecules, but only between each molecule and a certain definite number 

 of other molecules, which we may suppose to be denned as those nearest to the 

 given molecules. Newton gives as an example of such a kind of action the 

 attraction of a magnet, the field of which is contracted when a plate of iron is 

 interposed, so that the attractive power appears to be bounded by the nearest 

 body attracted. 



If the repulsion were confined to those molecules which are within a certain 

 distance of each other, then, as Cavendish points out, the pressure arising from 

 this repulsion would vary nearly as the square of the density, provided a large 

 number of molecules are within this distance. Hence this hypothesis will not 

 explain the fact that the pressure varies as the density. 



On the other hand, if the repulsion were limited to particular pairs of 

 particles, then since the particles are free to move, these pairs of particles 

 would move away from each other till only those particles were near each other 

 between which the repulsive force is supposed not to exist. 



It would appear therefore that the hypothesis stated by Newton and adopted 

 by Cavendish is the only admissible one, namely, that the repulsive force is 

 inversely as the distance, but is exerted only between the nearest molecules. 



Newton's own conclusion to his investigation of the properties of air on the 

 statical molecular hypothesis is as follows: "An vero Fluida Elastica ex 

 particulis se mutuo fugantibus constent, Quastio Physica est. Nos proprie- 

 tatem Fluidorum ex ejusmodi particulis constantium mathematice demon- 

 stravimus, ut Philosophis ansam prabeamus Quaestionem illam tractandi." 



The theory that the molecules of elastic fluids are in motion satisfies the 

 conditions of the question as pointed out by Newton in a much more natural 

 manner than any modification of the statical hypothesis. 



According to the kinetic theory of gases, each molecule is in motion, and 

 this motion is during the greater part of its course undisturbed by the action 

 of other molecules, and is therefore uniform and in a straight line. When however 

 it comes very near another molecule, the two molecules act on each other for 

 a very short time, the courses of both are changed and they go on in the new 

 courses till they encounter other molecules. 



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