the received principles of Hydrodynamics, 1G3 



expression for the square of the velocity of the piston becomes 



This expression is still applicable if m be a negative quantity — i 

 that is, if the mass M of the piston be supposed to be suddenly 

 diminished by the quantity m. In that case z l is greater than 

 a, and the velocity becomes zero for the value of z x which satis- 

 fies the equation 



UK l ; M— m °a 



If we suppose that m = — M, which is to suppose that the sur- 

 face of the fluid is exposed to vacuum by a sudden abstraction 

 of the piston, the above expression for the square of the velo- 

 city fails to give any definite result, because the factor .., - 



becomes infinite. This case is referred to by Mr. Moon at the 

 end of his article in the Philosophical Magazine for February 

 1873; and a similar one is adduced in p. 27, vol. xxxvi., where 

 a finite density D is assumed to be immediately contiguous to a 

 density 2D. Such instances of changes of the density, and 

 consequently of the pressure, per saltum, are not embraced by 

 the ordinary principles of analytical hydrodynamics ; if suscep- 

 tible of treatment, they would require the application of new 

 principles. I do not profess to be able to indicate what would 

 be the appropriate process ; but I regard it as certain that no 

 argument against the validity in general of the equation p = a 2 p 

 can be drawn from exceptional cases in which the density and 

 pressure vary per saltum. 



The general expression for the acceleration of the piston 

 downwards being 



_ May 

 9 (M+mjir/ 



at the first instant, when z^ — a. this becomes a— .., " , oy 



* M-fm 



~--^- — . The piston begins to descend by the action of this force. 

 M + m . 



for the same reason that a free body begins to descend by the 

 action of gravity; and, as Lord Kayleigh justly maintains, any 

 argument adduced to prove that the descent cannot commence 

 in the former case must equally apply in the other. I think I 

 have sufficiently shown that Mr. Moon's dissent from this view 

 is attributable to his misunderstanding the character of the 

 equation p = funct. (p and v). 



I propose to conclude this communication by making some 



