406 Prof. Challis on the Tlieory of the Velocity of Sound. 



distinctly pointed ont svicli contradictions. In the prosecution 

 of my hydrodynamical researches, I disco\ ered, that in addition 

 to the recognized principles of hydrodynamics, another not previ- 

 ously noticed is equally necessary, viz. that the directions of motiop 

 in each element in successive instants must be normals to conti- 

 nuous surfaces. The introduction of this principle gives the means 

 of treating hydrodynamical questions in an entirely new manner, 

 and gets rid of the above-mentioned contradictions. By making- 

 use of it, I have ascertained, ^jrior to the consideration of any case 

 of disturbance of the fluid, that the general hydrodynamical equa- 

 tions admit of a particidar and unique solution which involves 

 no arbitrary functions, and that fi'om such solution all the cir- 

 cumstances of the motion which are not under our control, and 

 therefore not expressed by arbitrary functions, are to be deduced. 

 It may readily be conceived that this particular solution satisfies 

 the hydrodynamical equations at the same time that they may 

 be satisfied in an infinite variety of ways by solutions involving 

 arbitrary functions, just as a common differential equation is 

 simultaneously satisfied by a particular solution and the general 

 integral, the former not containing, and the latter containing, 

 arbitrary quantities. 



The above principles applied to a compressible fluid conducted 



me to the expression a A/ 1 + — i for the velocity of sound, 



which agrees nearly with observation, a being the Newtonian 

 value. I recognized also that this result differed from that 

 hitherto obtained on hydrodynamical principles, solely on account 

 of its being deduced prior to the consideration of any case of 

 motion, the determination of the velocity of propagation in the 

 usual method being made to depend on an assumed case of 

 motion. The particulars of the reasoning by which the above 

 result was obtained are scattered over different Numbers of the 

 Philosophical Magazine, and on this account it may be difficult 

 to trace them. I propose in the continuation of the resume of 

 my hydrodynamical researches which I have connnenced in this 

 Journal, to present in detail the course of reasoning which I have 

 here indicated only in general terms. 



From the above statement it will appear, that the method 

 which I advocate determines the velocity of sound exclusively on 

 hydrodynamical principles. The received method of accounting 

 for the difFerenoe between the Newtonian and the observed value 

 rests on hypotheses. Now as it is contrary to sound philosophy 

 to explain by an hypothesis what may be explained without an 

 hypothesis, I am compelled by my reasoning to conclude that 

 those hypotheses arc inadmissible. To reconcile this conclusion 

 with what is observed respecting the effect of heat developed by 



