The Hon. J. W. Striitt on the Law of Gaseous Pressure. 321 



soiling (1) that the weight W will fall^ and (2) that it will not 

 fall. The same may be said of the other arguments. Now, 

 whether air obey Boyie^s law or not, surely an ideal fluid may 

 be imagined which shall do so without any inherent contradic- 

 tion. However interesting Mr. Moon's problems may be as 

 logical paradoxes, they convey no information on the physical 

 question which is under discussion. 



In his restatement of the analytical arguments by which it is 

 proved that |} is a function of Vj Mr. Moon has made some 

 alterations the effect of which is to obviate the objection that I 

 urged in the July Number. 



^' If we have three relations, 



p=fM)y p=f2i^'i)> '^=fM), 



where the forms of /j, f, /g are utterly unknown to us, the pre- 

 sumption is that jo = funct. (p,v). This is the rule, to which 

 there may possibly be exceptions ; but those who rely on the ex- 

 ceptions must prove them to exist.''' 



On this I have two remarks to make. In the first place, I 

 had understood (as it now appears mistakenly) that the argu- 

 ment was put forward to prove that p was necessarily a function 

 of V. Understanding may instead of must, the reasoning is be- 

 yond cavil. But the objection is only transferred to the pre- 

 mises ; for, of course, I entirely deny that the forms of/1,/2,/3 

 are utterly unknown to us. On the contrary, I assert that 

 /j a/2 ; and even Mr. Moon admits that we have this a priori 

 knowledge of the forms of the functions in the case of relative 

 equilibrium. I quite agree with Mr. Moon that the attempt to 

 extract Boyle's law from the sole conditions that jo, p, v are func- 

 tions of X and t subject to 



dv 1 dp , , . , 



must necessarily fail ; but this is only because some of the re- 

 quisite conditions have been omitted. The reason why I reject 

 his expressions for the pressure, velocity, and density is simply 

 that, though they satisfy the conditions he prescribes, they do 

 not satisfy the conditions that I prescribe. 



If Mr. Moon has really obtained the most general values con- 

 sistent with (A) (a point on which 1 am scarcely competent to 

 judge), they necessarily include all the results of the received 

 theory. Only so far would they have any application to gaseous 

 dynamics, though i'rom a purely analytical point of view their 

 value may be very great. 



* Another equation should properly be added, 



I (^\_ dv 



dt \pj- dx 



