S18 CELESTIAL MECHANICS. I. vii. 37. 



tion of the oscillations of the sea, and of the atmosphere, to 

 investigate the forces which act on their respective fluids, 

 and to find the fluents of the preceding fluxional equations 

 with regard to those forces ; which will be done in a subse- 

 quent part of this work. 



[Scholium 3. Instead of attempting to shorten and 

 simplify the steps of this refined investigation, which will 

 hereafter appear to be unnecessarily general, it will be 

 sufficient to insert some collateral considerations on the 

 simplest cases of the transmission of motion through 

 fluids, adapted to a notation resembling that which is em- 

 ployed by the author. 



378. Theorem. "395." When the sur- 

 face of an incompressible fluid, contained in a 

 narrow prismatic canal, is elevated or de- 

 pressed a little at any part above the general 

 level ; if we suppose a point to move in the 

 surface each way, with a velocity equal to that 

 of a heavy body falling through half m the 

 depth of the fluid, the surface of the fluid, at 

 the part first affected, will always be in a right 

 line between the two moveable points. 



The particles constituting any column of the fluid, ex- 

 tending across the canal, are actuated by two forces, 

 derived from the hydrostatic pressures of the columns on 

 each side, these pressures being supposed to extend to the 

 bottom of the canal, with an intensity regulated only by the 

 height of the columns themselves ; and this supposition 

 would be either perfectly or very nearly true, if the particles 

 of the fluid were infinitely elastic, that is, absolutely incom- 



