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XL. On the Theoretical Falne of the Velocity of Smmd^ in 

 reply to Mr. Stokes. By the Rev. J. Cuallis, M.A., F.R.S., 

 F.R.A.S., Pliimia?i Professor qfAstro?iomt/ and Experimental 

 Philosophy in the University of Cambridge^. 



nnHE velocity of propagation of waves in an elastic medium 

 •*■ so constituted that the pressure varies in the same pro- 

 portion as the density, is usually deduced from the hydrody- 

 namical equations by assuming, either that the motion of the 

 vibrating particles is a function of the distance from a fixed 

 plane, or that it is a function of the distance from a fixed 

 centre. On the former assumption, an exact integral, appli- 

 cable to propagation in a single direction, may be obtained, 

 which conducts to the inference that a point of maximum ve- 

 locity of a given wave travels at a rate different from that of 

 a point of no velocity, so that, however large the maximum 

 velocity may be, one of these points may overtake the other, 

 without any indication on the part of the analysis of the phy- 

 sical impossibility of such an occurrence. The inevitable con- 

 clusion from this result is, that the integral admits of no inter- 

 pretation compatible with fluid motion, and that the assumption 

 of plane- waves is inadmissible. 



The assumption of spherical waves is shown to be inad- 

 missible by conducting to an incompatibility of another kind, 

 as I have proved by an argument contained in the Number 

 of the Philosophical Magazine for last February. The argu- 

 ment is divided into five heads ; the four first of which include 

 the proof of incompatibilit}', and the fifth is merely an appeal 

 to an admitted principle in physics, viz. that of constancy of 

 mass, to which the result of the previous reasoning is opposed. 

 Mr. Stokes, in the March Number, after assenting to the four 

 first heads, meets the fifth by a simple denial for which he 

 gives no reason. But surely the weight of this denial falls 

 very harmlessly on a part of the argument which admits of 

 no dispute ; for I presume that Mr. Stokes does not intend to 

 maintain that in physics there is such a thing as generation or 

 annihilation of matter. 



My argument put in syllogistic form is as follows : — 



Let the waves be supposed to be spherical. 



Then, as the analysis shows, the same portion of matter has 

 a different value (expressed, for instance, in cubic feet of the 

 matter in a given state of density) at onetime from that which 

 it has at another time. 



But by the principle of constancy of mass the same portion 

 of matter has the same value at all times. 



* Communicated by the Author. 



