Dec, i6, 1 875 J 



NATURE 



131 



changing at various points both in direction and velocity, requires 

 the application of forces the sum total of which in a longitudinal 

 direction is zero, as long as the end of each stream has the same 

 direction and velocity as the beginning. Therefore the sum total 

 of forces (in other words the only force) brought to bear upon the 

 bo ^y by the motion of the fluid in the direction of its flow, is 

 zrro* 



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 devia- 

 tions of the streams of fluid. The question, what will be in any 

 given case the precise configuration of those deviations, is irrele- 



vant to the proof I have given of this proposition. Nevertheless 

 it is interesting to know something, at least, of the general 

 character which these deviations, or "stream-lines," assume in 

 simple cases ; therefore I have exhibited some in Fig?. 26, 27, 

 which are drawn according to the method explained by the late 

 Prof. Rankine. 



The longitudinal lines represent paths along which particle? 



flow ; they may therefore be regarded as boundaries of the 



streams into which we imagined the ocean to be divided. 



j We see that, as the streams approach the body, their first act 



j is to broaden, and consequently to lose velocity, and therefore, 



I as we know, to increase in quasi-hydrostatic pressore. Presently 



Fig. 26. 



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 undis- 

 turbed condition, and consequently 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 undisturbed fluid. Finally, as they 

 recede from the body they narrow again until they ultimately 

 resume their original dimension, velocity, and pressure. 



Thus, taking the pressure of the surrounding undisturbed fluid 

 as a standard, we have an e.^ccess 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 bod/. We 

 now see something of the way in which the separate pressures 

 act, and that they do not, as seems at first sight natural to 

 expect, tend all in the direction in which the fluid is flowin;j ; on 

 the contrary, pressure is opposed to pressure, and sactioa to 



suction, and the forces neutralise one another and come to 

 nothing, and thus it is that an ocean of perfect fluid flowing at 

 steady speed past a stationary 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 will now consider what will be the result of substituting 

 an ocean of water for the ocean of perfect fluid. 



The difference between the behaviour of water, and that of the 

 theoretically perfect fluid is twofold, as follows : — 



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

 exert a drag or frictional resistance upon the surface of the body 

 as they glide along it. This action is commonly termed surface- 

 friction, or skin-friction ; and it is so well-known a cause ot 

 resistance that I need not say anything furttier on this point, 

 except this, that it constitutes almost the whole of the resistance 

 experienced by bodies of tolerably easy shape travelling under 

 water at any reasonable speed. 



Secondly. Tne mutual frictional resistance experienced by the 

 particles of water in moving past one another, combined with 



Fig. 28. 



the almost imperceptible degree of viscosity which water pos- 

 sesses, somewhat hinders the necessary stream-line motions, 

 alters their nice adjustment of pressures and velocities, and thus 

 defeats the balance of stream-line forces and induces resistance. 

 This action, however, is imperceptible in forms of fairly easy 

 shape. On the other hand, angular or very blunt features 

 entail considerable resistance from this cause, because the stream- 

 line distortions are in such cases abrupt, and degenerate into 

 eddies, thus causing great differences of velocity between adjacent 

 particles of water, and great consequent friction between them. 

 * See Supplementary Note C. 



I " Dead water," in the wake of a ship with a full run, is an in- 

 I stance of this detrimental action. 



I So far we have dealt with submerged bodies only ; we will 

 j now take the case of a ship travelling at the surface of the water. 

 i But first, let us suppose the surface of the water to be covered 

 \ with a sheet of rigid ice, and the ship cut off level with her 

 } water-line, so as to travel beneath the ice, floating, however, 

 I exactly in the same position as before (see Fig. 28). As the ship 

 I travek along, the stream-line motions will be the same as for a 

 I submerged body, of which the ship may be regarded as the lower 

 half; and the ship will move without resistance, except that due 



