396 Mr. Challis oti the general Equations 



in contact with the disc, will, according to the theory, be less 

 than that of the atmosphere. This will not be the case just 

 about the centre, for there, from the manner of flowing:, the 

 fluid must be in some degree stationary. 



The preceding problems suflice to exemplify the nature of the 

 integral we set out with, and to shew the manner of making use 

 of it : I proceed to the consideration of elastic fluids. 



II. Compressible Fluids. 



4. The general equations relating to the motion of compres- 

 sible fluids, in which the pressure varies as the density, are, 



«^hyp.io,.,= .-^-i(g.g;.g:) (.), 



" ~ \dx^^ dy- ■*" dz'/ df 



d/Vdf dV df dF d^ 

 dx ' dx dy' dy dz dz' 



_2^ J^. _2^ -^-2^.-^ (n) 

 dx'dxdt dy'dydt dz'dzdt 



d(p- drtf) d<}>' d'fj) d(pr d^(p 

 da^ ' dx'' dy^ ' dy- dz" ' dz" ' 



d<p d(p d''<f) d<p d<j) d^<}> d^ d<^ cf^ 

 dx dy\dxdy dx dz dxdz dy dz dydz 



(Lagrange, Mec. Anal. Part II. Sect. 12.) 



