3o6 SECTION MECHANICS. 



this supposition. If the body were out of the way, v/e could imagine 

 the whole ocean to be cut up into filaments or minute streams of fluid, 

 each following a straight course ad infiniium. Cut when the fixed 

 body intervenes those streams must behave differently in two separa'.e 

 respects. Each stream as it approaches the body, in the first place, 

 is deflected from its course in order to get past the body, and back 

 into its former course ; again when it has passed the body in the next 

 place it has to undergo changes of velocity, chiefly a temporary increase 

 of speed in passing the local con'.raction of the waterway, which the 

 presence of the body has created, so that the same ocean of water 

 may pass the body as would have passed through the whole of the 

 unoccupied space. These streams as they pass the body have an, 

 increased velocity and pass on and lose their increased velocity. 

 Now what the theory of stream lines shows indisputably is, in the 

 first place, that the dafiection of a stream from its course if it returns 

 to its former course, causes no total force in the line of motion. That 

 is easy enough to see if you imagine a pipe of parallel diameter all 

 throng'.}, bent into an easy curve, like the watcrline of a ship, and 

 terminating in the same direction which it had at its entrance. The 

 stream while being first deflected no doubt exercises centrifugal force 

 which tends to push the pipe forward, but when the deflection is 

 reversed the centrifugal force tends to push the pipe in the opposite 

 direction. If that operation is traced through exactly, it is easy to see 

 that the total result is that there is no aggregate pressure in the line of 

 motion. It is the ordinary problem of a marble running round a friction- 

 less curve ; the marble loses no total velocity, the curve it passes round 

 does not obstruct its run, nor does it push the curve in the aggregate in. 

 any direction, if it leaves the curve in the same direction, and with the 

 same velocity it had on entering the curve. By the time it has 

 traversed the whole curve it has pushed it just as much backward 

 as forward. The next proposition is, that a stream flowing through 

 a pipe of which one portion is contracted or enlarged, behaves 

 in a very different manner from what one would expect. If we 

 imagine a level parallel pipe of any length, and a stream of water 

 flowing through it with a steady speed, if the flow be frictionless the 

 pressure will be uniform throughout the length of the pipe. Now let 

 a portion of the pipe be tapered to a smaller diameter, and again 



