OF THE MOTION'S OF FLUIDS. 30? 



effect must depend on the ultimate elasticity of the par- 

 ticles themselves, and not on the rigidity of the aggregate ; 

 although Mr. Poisson seems disposed to consider the 

 primary transmission of the pressure as dependii\g on the 

 same conditions as the propagation of a small wave of 

 finite magnitude. With regard to the want of vertica- 

 lity of the pressure, depending perhaps on a want of per- 

 fect fluidity, it seems to be dillicult to make any allowance 

 for it in a correct computation : but fortunately, in the great 

 problem of the tides, the depth being inconsiderable in 

 comparison with the extent of a similar and synchronous 

 state of the surface, neither of these sources of inaccuracy 

 can have any material effect.] 



It may in general be observed, that having regard to 

 the variations of 9 and -or only, [and neglecting the slight 

 vertical motion] the equation (L) becomes equivalent to 

 (M) for all the interior parts of the fluid. The values of 

 u and V, relative to all the particles of the sea, situated in 

 the same radius of the earth, are therefore determined by 

 the same differential equations : consequently, if we sup- 

 pose, as it will be convenient to do in the theory of the 

 tides, that at the origin of the motion, the values of tt, 



-r-, V, and — were the same for all the particles situated 

 dt dt ^ 



in the same radius, these particles will still remain in the 

 radius, during the oscillations of the fluid : the values of r, 

 u, and V may therefore be supposed very nearly the same 

 throughout the small portion of the radius intervening be- 

 tween the bottom and the surface of the sea: we may 



d (7'T'Si 



therefore consider r^s as the fluent of — ^ dr, and call- 



dr 



iug the value of r^s at the bottom of the sea {r"s) we shall 



X 2 



