in his paper on the Problem of the Velocity of Sound. 103 



represented by the quantity of absolute molecular force. The 

 mathematician who has to deal with forces, takes account of the 

 quantity of heat existing among the particles when he assigns a 

 magnitude to his absolute molecular forces ; and if these forces 

 continue unchanged through his investigations, this unchange- 

 ableness is the mathematical expression of the physical fact that 

 no heat escapes during the compression, and that none is gained 

 during the dilatation that takes place in the passage of a wave. 

 Now in my investigations the absolute molecular forces remain 

 constant throughout ; and consequently the physical hypothesis 

 is perfectly taken into account that no change in the quantity of 

 heat in a given molecule or element of the atmosphere takes 

 place ; which otherwise expressed, in the language of the physi- 

 cist, is this : the heat developed during condensation, and the 

 cold of rarefaction, are fully taken account of. Dr. Le Conte 

 seems to have forgotten that, in speaking of gases, heat and mole- 

 cular force are equivalent terms, the one belonging to the lan- 

 guage of the physicist, and the other to that of the mathematician. 

 Mathematicians, by adopting the hypothesis of the continuity of 

 the aerial medium, had nothing to do with molecular force in 

 their investigations, any further than as it might be contained in 

 the further assumption of a relation between pressure and density. 

 If they assumed Boyle's law, then in so doing they assumed that 

 heat escaped by radiation as fast as it was developed by compres- 

 sion ; but if they assumed Laplace's relation between pressure and 

 density, then they in so doing assumed also that no heat was 

 lost by radiation. But in the supposition of finite intervals 

 between the molecules of the aerial medium, the mathematician, 

 as a matter of course, supposes the absolute molecular forces 

 constant throughout his whole investigation, and therefore in 

 doing so takes perfect cognizance of Laplace's suggestion with- 

 out having even so much as to mention it. The assumption of 

 a medium constituted of separate particles includes Laplace's 

 suggestion, and takes account of it without the necessity of 

 knowing anything about it. And on this account it is that I 

 said that, had mathematicians adopted the finite-interval theory, 

 instead of the continuity theory, and worked out the integrals 

 (as I have done) without introducing changes in the forms of 

 their differential equations for the purpose of effecting approxi- 

 mate integrals, there never would have been any occasion for 

 Laplace's suggestion. Theory would have furnished a velocity 

 large enough without any additional suggestions. 



Before concluding, I must say one word more. I am one of 

 those who think that some heat does escape during the passage 

 of a wave of condensation through a given element of the atmo- 

 spheric medium. I find it difficult to believe that a given 



