160 . Prof. Challis on Objections recent ly made to 



that "it holds without reference to any hypothesis as to the law 

 of pressure." I should rather say that it involves no specifica- 

 tion of a particular fluid, and is therefore applicable to all per- 

 fect fluids. 



I see nothing to object to in the argument which follows (in 

 p. 11 7) , from which Mr. Moon comes to the general conclusion 

 that the pressure (p) is a function of the density (p) and velo- 

 city (v). This theorem, which, as far as I know, Mr. Moon has 

 the merit of first demonstrating, is in the same sense general as 

 the equation (1); that is, it contains no specification of the fluid. 

 It shows in fact that, in defining the particular fluid, we are 

 limited to the hypothesis that the pressure is some function of 

 the density and the velocity. Now evidently this general theorem 

 includes the more particular case in which the pressure is a 

 function of the density only. Therefore, by Mr. Moon's own 

 showing, it is legitimate to make the hypothesis that the pressure 

 of the fluid is always in exact proportion to its density, and by 

 this supposition to define the fluid. This argument proves, since 

 it wholly depends on the fluid being in a state of motion, that 

 the equation p=a 2 p may be assumed relatively to fluid in motion , 

 and that it is not necessary, if it were possible, to establish its 

 truth for that case by direct experiment. 



Mr. Moon is evidently not aware that such an inference is 

 deducible from his argument, inasmuch as he proceeds to employ 

 the equation (1) and the theorem p = funct. (p and v) in all 

 their generality, as if no other course of reasoning were legiti- 

 mate; and in this manner he obtains expressions for the pressure, 

 density, and velocity which satisfy the general equation (1) (see 

 Phil. Mag. vol. xxxvi. p. 124). According to the view I have 

 indicated, these expressions embrace the values of the pressure, 

 density, and velocity for every particular fluid comprehended 

 under the general definition p — funct. (p, v). I have found, 

 in fact, that they are inclusive of the values obtained for air cf 

 given temperature in the ordinary way from the equation p = a <2 p. 



But after proving analytically that it is allowable to assume 

 that/>=fl 2 /> for fluid in motion, the question as to whether this 

 equation is true for a particular fluid (as the air) is, as Lord 

 Kayleigh rightly urges, a physical one, and can only be settled 

 by the aid of experiment. The proper process for this purpose 

 is to introduce into the general differential equations applicable 

 to the motion of a fluid the relation p — a^p (already shown to 

 be, pro hac vice, legitimate), and then, after applying the inte- 

 grals of the equations in solving various hydrodynamical pro- 

 blems, to compare numerically the results of the solutions with 

 experiment. Such evidence of the exactness of the equation 

 P~a?p is accumulative, increasing with the number and variety 



