TRANSACTIONS OF THE SECTIONS. 231 



Although, in order to get past the body, these streams follow some courses 

 or other, various both iu direction and velocity, into which courses they settle 

 themselves in virtue of tlie various reactions which they exert upon one another 

 and upon the surface of the body, yet ultimately, and through the operation of 

 the same causes, they settle themselves into their original direction and original 

 velocity. Now the sole cause of the original departure of each and all of these 

 streams from, and their ultimate return to, their original direction and velocity, is tlio 

 submerged stationary body ; consequently the body must receive the sum total of the 

 forces necessary to thus affect them. Conversely this sum total of force is the only 

 force which the passage of the fluid is capable of administering to the body. But 

 we know that to cause a single stream, and therefore also to cause any combination 

 or system of streams, to follow any courses changing at various points both in direc- 

 tion and velocity, requires the application of forces the sum total of which in a lon- 

 gitudinal direction is zero, provided that the end of each stream has the same direc- 

 tion and velocity as its beginning. Therefore the sum total of forces (in other words 

 the only force) brought to bear upon the body by the motion of the fluid in the 

 direction of its flow is zero*. 



I have now shown how it is that an infinite ocean of perfect fluid flowing past 

 a stationary body cannot administer to it any endways force, whatever be the nature 

 of the consequent deviations of the streams of fluid. The question, what will be 

 in any given case the precise configuration of those deviations, is irrelevant to the 

 proof I have given of this proposition. Nevertheless it is interesting to know some- 

 thing, at least, of the general character which these deviations, or " stream-lines," 

 assume in simple cases ; therefore I have exhibited some in Plate XI. figs. 26, 27, 

 which are drawn according to the method explained by the late Professor Rankine. 

 The longitudinal lines represent paths along which particles flow; they may 

 therefore be regarded as boundaries of the .streams into which wo imagined the 

 ocean to be divided. 



We see that, as the streams approach the body, their fii-st act is to broaden, and 

 consequently to lose velocity, and therefore, as we know, to increase in quasi- 

 hydrostatic pressm-e. Presently they again begin to narrow, and therefore quicken, 

 and diminish in pressure, until they pass the middle of the body, by which time 

 they have become narrower than in their original undistmbed condition, and con- 

 sequently have a greater velocity and less pressure than the undisturbed fluid. 

 After passing the middle they broaden again until they become broader than in 

 their original condition, and therefore have less velocity and greater pressure than 

 the undistiu-bed fluid. Finally, as they recede from the body they narrow again, 

 until they ultimately resimie their original dimension, velocity, and pressm-e. 



Thus, taking the pressm'e of the surrounding undisturbed fluid as a standard, 

 we have an excess of pressure at both the head and stern ends of the body, and a 

 defect of pressure along the middle. 



We proved just now that, taken as a whole, the fluid pressures could exert no 

 endways push upon the stationary body. We now see something of the way in 

 which the separate pressures act, and that they do not, as seems at fii'st sight 

 natural to expect, tend all in the du'ection in which the fliud is flowing ; on the 

 contrary, pressure is opposed to pressure, and suction to suction, and the forces 

 neutralize one another and come to nothing ; and thus it is that an ocean of per- 

 fect fluid flowing at steady speed past a stationaiy submerged body does not tend to 

 push it in the direction of the flow. This being so, a submerged body travelling 

 at steady speed through a stationary ocean of perfect fluid will experience no 

 resistance. 



We wiU now consider what wiU be the result of substituting an ocean of water 

 for the ocean of perfect fluid. 



The difl'erence between the behaviour of water and that of the theoretically 

 perfect iiuid is twofold, as follows : — 



First. The particles of water, unlike those of a perfect fluid, exert a drag or 

 frictiouul resistance upon the surface of tlie body as they glide along it. This 

 action is commonly termed surface-friction, or slriu-friction ; and it is so well 

 known a cause of resistance that I need not say any thing fmlher on this point, 



* See Appendix, Note C, 



