OF THE MOTION OF FLUIDS. 195 



stern of the vessel. The theory, in fact, determines these pressures to 

 be in every respect alike, so that if we proceeded to investigate the 

 total pressure in the horizontal direction, we should find it to be 

 nothing, when the motion is uniform. This may serve to shew that, 

 if friction be left out of consideration, a front ill-adapted to cleave the 

 water, is not unfavorable to speedy motion, if the stern be of the same 

 shape; and that the resistance to the motion of vessels in the open 

 sea is principally owing to the friction of the water against their 

 surface. This cause operates to produce unequal actions on the front 

 and stern, making the directions of the motions of the particles in 

 contact with the surface of the former, less inclined to the horizon 

 than they would be in the case of no friction, and of those in contact 

 with the surface of the latter more inclined. To counteract this inequality 

 probably the stern should be less curved than the front. 



SECTION IV. 



General Propositions respecting the Motion of Compressible Fluids. 



14. The considerations applied at the beginning of Section II. to 

 incompressible fluids, are equally applicable to compressible. I shall 

 therefore assume that in a mass of fluid in which the density varies 

 as the pressure, the directions of the motion at all the points of any 

 element pass at a given instant through two focal lines. Let p be 

 the density at a point distant by r and r -vl from the focal lines, and 

 V the velocity : p and V the same for a point indefinitely near the 

 former. Also let the transverse section of a cuneiform element aclk 

 (Fig. 5.) which is bounded by four pli.nes passing through the focal 

 lines kl, mn, be at the first point efgh, and at the other, abed. The 

 pressure and consequently the density will be the same at all points 

 of the section eg; as also the velocity; at least our reasoning does not 

 apply to cases in which this condition is not fulfilled. The same may 

 be said of the section ac and of all sections intermediate to ac and eg. 



