102 Mr. It. Moon on the Law of Gaseous Pressure. 



enables us to determine the law of pressure in the fluid at that 

 time, that the law of pressure at the time in question may be 

 any whatever. In fact, if when /=0 we have p=f 3 (%), where f 3 

 denotes any continuous function, we shall have 



an equation which can be satisfied by means of <£, and of which 

 indeed it is the special and exclusive office to determine cf>. This 

 can be done as follows : — 



Putting ( a 



and solving with respect to x, we get 



x= funct. 0) = /" (rw) suppose. 

 Hence (4) becomes 



which determines the form of (f>. 



It thus appears that the office performed by (1) is of this kind ; 

 viz. the law of pressure prevailing at a certain time, and also the 

 laws of velocity and density prevailing at the same time being 

 given, (1) enables us from those data to determine the law of 

 pressure prevailing in the same case of motion at any other time. 

 Obviously, therefore, it is as unreasonable for Mr. Strutt to ask 

 me to state " the real physical law of pressure true at all times 

 and places," as it would be for me to require him to determine 

 in any particular case of motion the velocity and density at any 

 instant by means of Euler's equations, without affording him 

 any information as to the circumstances of the initial motion. 



Of the particular cases of failure which I have adduced against 

 the received law of gaseous pressure, the first which Mr. Strutt 

 considers is that of a closed cylinder filled with air, which at the 

 time t is destitute of velocity, but in which the density to the 

 right of a certain plane is uniformly equal to 2D, while that to 

 the left of the plane is D. I contend that if the received law 

 of pressure held under these circumstances, it would contradict 

 the principle that action and reaction are equal and opposite. 



Mr. Strutt meets this by suggesting that u an infinitely small 

 «... layer of air situated at the boundary is subject to an infi- 

 nite acceleration," and that the fact " that the pressures which 

 act on its two faces are unequal is therefore not in contradiction 

 to any true principle." 



Now by "infinitely small" Mr. Strutt must mean here "in- 

 definitely small," whereas all the circumstances which I have 



