490 Mr. J. J. Waterston on the Theory of Sound. 



Now suppose these balls reduced excessively in their dimen- 

 sions, and to be perfectly elastic as well as the cushion, and we 

 shall have obtained an idea of how pulses may be conveyed in a 

 manner quite different from that depending upon a statical re- 

 pulsive force between adjacent particles. Instead of such stu- 

 pendous force, we have to substitute molecules simply moving 

 with the velocity of a cannon-ball, and assume the atmosphere 

 to maintain its elasticity by its particles striking against each 

 other with such velocity, which, viewed cosmically, by no means 

 exceeds what is moderate, and even highly pi'obable if heat is 

 molecular motion. 



Such a theory of elastic fluids was started by Mr. Herapath 

 so far back as 1821 in the pages of the Annals of Philosophy, 

 and has more recently suggested itself to M. Kronig, as we find 

 noticed by M. Clausius iu his memoir " On the Nature of the 

 Motion we call Heat" (Phil. Mag. vol. xiv. p. 108). 



The following is an extract from Mr. Hcrapath's memoir, 



p. 278, vol. i. Annals of Philosophy, April 1821 :— " if 



gases, instead of having their particles endued with repulsive 

 forces, subject to so curious a limitation as Newton proposed, 

 were made up of particles or atoms mutually impinging on one 

 another, and the sides of the vessel containing them, such a con- 

 stitution of aeriform bodies would not only be more simple than 

 repulsive powers, but, as far as I could perceive, would be con- 

 sistent with phsenomena in other respects, and would admit of 

 an easy application of the theory of heat by intestine motion. 

 Such bodies, I easily sav/, possessed several of the properties of 

 gases : for instance, they would expand, and if the particles be 

 vastly small, contract almost indefinitely ; their elastic force 

 would increase by an increase of motion or temperature, and 

 diminish by a diminution; they would conceive heat rapidly 

 and conduct it slowly ; would generate heat by sudden compres- 

 sion, and destroy it by sudden rarefaction ; and any two having 

 ever so small a communication, would quickly and equally 

 intermix." 



At p. 341, in paragraph beginning "These impulses," &c., 

 and in those which succeed, ending " have from one another," 

 we have a very clear announcement of the mode by which a 

 static force of pressure is counterbalanced by a dynamic force of 

 elastic impact. 



At p. 345, Prop. 8. " The same things remaining, the elas- 

 ticity of a gas under a variable temperature and compression is 

 proportional to its numeratom (number of atoms in constant 

 volume) and the square of its temperature conjointly ; or the 

 elasticity varies as the square of the temperature directly, and the 

 simple of the space inversely. 



