92 PROPAGATION OF LONGITUDINAL WAVES 
MACGREGOR. 
at A during any time may be supposed to be identical with the 
mass issuing at B; and during its motion it may be supposed to 
be acted upon by a resultant force equal to p,—j, in the direc- 
tion of the propagation of the wave. The mass Q, which enters 
in unit of time has initially, on entering, the momentum Qu, in 
the same direction, and finally, on issuing, the momentum 
(Ju, also in the same direction. Hence the rate of increase of 
the inomentum in the direction of the resultant force p,—p, is Q 
(u,—u,), and therefore, by the Second Law of Motion, 
P2—P, = Q (Uu—m). 
When, now, we substitute in this equation the values of wu: and 
u, given by equations (5), we obtain 
D—p~pi = Q? (v.—v.). 
Consequently 
(po (Oe eonsts 
for planes indefinitely near, and therefore also for planes at a 
finite distance from one another. Waves of the kind under con- 
sideration are thus seen to be possible of transmission through 
actual substances, provided the changes of pressure and volume 
are small, and the result, 
Ua shi 
may therefore be deduced. 
