Radiation and Vibrations in Conical Pipes. 71 
Then the mas> o£ air entering the parallelepiped at the 
face dy dz in the time dt is pu (dy dz) dt, and that leaving by 
the opposite face in the same time is 
Hence, the mass lost by this pair of faces is 
d{pu) 
dx 
dxdy dz dt, 
Therefore, considering the other four faces in like manner, 
we have as the total mass lost by the parallelepiped in time 
dt the quantity 
jd(pu) d(pv) d{pw) ) 
1 — j 1 -j 1 — ~ — \ dx d'l dz dt. 
i dx dy dz ) J 
But this quantity can also be expressed in terms of the 
decrease of density, viz. : 
— : dx dy dz dt. 
dt 
Whence, equating the two forms, we have 
dg + d^u) d^v) d(^) =0 
dt dx dy dz v J 
Xow, since p = p fl-f 5), the first term of (1) becomes p ds/dt* 
Again, 
d(pu) „ . du dp du . 
the product of the two small quantities u and dpjdx being 
negligible. Thus for our case (1) becomes 
2+Z'+$+t-* ■ • • • « 
and this is the form of the equation of continuity for small 
oscillations of a light elastic fluid. 
Equation? of Motion. — AVe have now to express, for the 
fluid in our parallelepiped, the condition that the product, 
mass into acceleration, equals the moving force to which it is 
subjected. The mass into acceleration is (p dx dy dz) du/dt. 
The moving force is the excess of that due to pressure, p y 
