20 . Mr. Holmes on 



Then if P^.j Is the uniform pressure between A^.i A^ the 

 force required per unit area on the plane A^ is P^— P, i. 



We may notice that P^.i is the actual pressure in the 

 original state of the gas at some point between A^.^ A^. 



Let ^x be taken normal to the planes . . . A^^iA^ . . . and 

 suppose that in some one of the compartment plane waves 

 of sound of a given period are set up, the direction of pro- 

 pagation being 0,t'. 



Let Xs be the equilibrium distance of a normal plane in 

 the compartment A^A^+i from the equilibrium position of 

 the plane A^, 



x^ + ^; 3 the disturbed position due to the wave motion^ 



P^, D5 the pressure and density in equilibrium, 



/^, p^ the pressure and density at the disturbed position 



of the plane x^ when there is wave motion. Then for the 



compartment A^A^+i we arrive at the ordinary equations of 



wave motion, viz. : — 



ae • at' 



D, 



dx. 



If ^^ be the distance of the plane A^ from the origin, and 



/, be the distance between the planes A^ A^+i, then a 



solution of (i.) which holds for all values oi x^ between and 



/, may be written 



js = (CsCos;^/ + B,.sin«/)sin;;/(^, + x)i 



+ (C/cos/^/+ B/sin/z/)cosw(s5 + x^ 



where c^^ &c., are constant between Xs = o and x^ = l^. By 



changing the suffixes we may write the solution for any 



other compartment. 



At the surface of separation of any two compartments, 



say A^+i, we have the condition of equal velocities, viz. : — 



A<+i\ (d\\ 



\ dt )x,j^x = \dt)x, = l, 



which must hold for all values of the time. 



