108 LECTURES TO SCIENCE TEACHERS. 



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 show some in Figs. 15 and 16, which are drawn 

 according to the method explained by the late Professor 

 Rankine. 



The longitudinal lines represent paths along which par- 

 ticles flow ; they may therefore be regarded as boundaries 

 of the streams into which we imagined the ocean to be 

 divided. 



We see that, as the streams approach the body, their 

 first act is to broaden, and consequently to lose velocity, 

 and therefore, as we know, to increase in pressure. Pie- 

 sently they 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 undisturbed 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 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 pres- 

 sures due to the inertia of the fluid 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 first sight natural to expect, tend all in 

 the direction in which the fluid is flowing ; on the contrary, 

 pressure is opposed to pressure, and suction to suction, and 

 the forces neutralise one another and come to nothing ; and 

 thus it is that an ocean of frictionless 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 a steady speed through a 

 stationary ocean of frictionless fluid will experience no 

 resistance. 



