On Objections to the received Principles of Hydrodynamics. 247 



form of the nodal Hues is not (as I had supposed) entirely in- 

 dependent of the relation between the two elastic constants. 



I may, however, be permitted to remark that my calculation, 

 though not strictly applicable to a glass or metal plate, belongs 

 to an extreme case of the true solution ; for it would be correct 

 if the nature of the material composing the plate were such that 

 the extension produced by a longitudinal force acting along a 

 bar of it were unaccompanied^ by lateral contraction. This 

 condition of things, though probably not realized in nature, is 

 approximated to in the case of substances such as cork (Thomson 

 and Tait's ' Natural Philosophy/ § 685) . 



I remain, Gentlemen, your obedient Servant, 



Rayleigh. 



XXVIII. Reply to some Remarks by Professor Challis*, "On Ob- 

 jections recently made to the received principles of Hydrody- 

 namics. 33 By Robert Moon, M.A., Honorary Fellow of 

 Queen's College, Cambridge-]-. 



I AM glad to find that my argument in proof of the equation 

 p= funct. (p, v), applicable to fluid motion in one direction, 

 has received the sanction of Professor Challis. When personal 

 friends have concurred with opponents in regarding such a rela- 

 tion between the pressure, velocity, and density as a wild sug- 

 gestion, unworthy of a moment's consideration, it will be readily 

 understood that I am not insensible to the value of support. 



Professor Challis labours under a misapprehension, however, 

 when he asserts that the " general theorem includes the more 

 particular case in which the pressure is a function of the density 

 only/' and that, therefore, by my "own showing, it is legiti- 

 mate to make the hypothesis that the pressure is always in exact 

 proportion to the density." 



For motion in one direction it is axiomatic that we must have 

 in every fluid, in every case of motion, 



P =/i (v*)> P =/g (**) > v =M Xt ) 7 



whence it follows that, for every value of x and t for which each 

 of the foregoing equations represents a substantive relation be- 

 tween the variables, we shall have 



p = funct. (p, v) . 



It is not axiomatic, however, though it happens to be true, 

 that in every fluid for particular cases of motion we may assume 



p=f{xt), p = a*f(zt); 

 where a? is a constant whose value or values depend on the 

 nature of the particular fluid dealt with. 



And it is neither axiomatic nor true, that in any particular 

 * See Phil. Mag. for August. f Communicated by the Author. 



