in his paper on the Problem of the Velocity of Sound. 99 



tion is," &c. To this I answer that Dr. Le Conte has quite mis- 

 understood my investigations. No such assumption as this which 

 he here calls in question is made in them. There is no difficulty, 

 however, in seeing what is the origin of his mistake. He has 

 mistaken the differential coefficient of the law of molecular action 

 for the law itself. The law assumed was that of the inverse 

 third power of the distance; and for such an assumption there is 

 very good authority, besides that which is alleged in the investi- 

 gation where the assumption is made. For if Dr. Le Conte will 

 turn to the Cambridge Philosophical Transactions, vol. vii. part 1, 

 he will there find a paper, entitled " On the Nature of the Mole- 

 cular Forces which regulate the constitution of the Luminiferous 

 iEther," and in that he will find it proved by strict mathematical 

 reasoning, that if the particles of an elastic medium act on each 

 other according to an inverse power of their distances, that power 

 must be greater than 2; and as it is hardly accordant with the 

 simplicity of nature to suppose the power fractional, the simplest 

 and therefore the most likely power is 3. My investigation in 

 your Magazine led me to the same result, though by a process 

 quite distinct from that employed in the Cambridge Transactions. 

 I hope, therefore, that after reading this statement Dr. Le Conte 

 will not think the assumption I have made (not that which he 

 erroneously ascribes to me) so extremely improbable as to justify 

 him in condemning my theory on its account. 



He asks another question also in disparagement of my theory, 

 a question which no person acquainted with the integral calculus 

 would think of putting forward as any objection to my results : 

 "Does not the fact that the analytical processes lead to two 

 entirely distinct types of waves indicate that there must be some 

 error in the assumptions of the mathematician?" To this I 

 answer that the equations of motion lead to exponential inte- 

 grals, which it is well known take the form of circular integrals 

 under certain relations of the parameters. Thus there are of 

 necessity two possible forms of the integrals, the exponential and 

 the circular, and each of these has its own physical interpretation.. 

 Thus, then, it appears that there are two possible types of waves, 

 which for distinction's sake I denominated the violent and the 

 gentle. The objection which Dr. Le Conte raises to the duality 

 of possible wave-types can only be owing to his want of acquaint- 

 ance with mathematical processes, and the physical interpreta- 

 tion of mathematical formulae. This explanation involves also 

 a sufficient answer to another disparaging query which Dr. Le 

 Conte asks : " Is it not almost a physical impossibility that the 

 same elastic medium" &c. The obvious reply to this is, that the 

 mathematical investigations show that it is not " almost a physical 

 impossibility" that an elastic medium should transmit waves of 



H2 



