106 LECTURES TO SCIENCE TEACHERS. 



If we trace the streams to a sufficient distance ahead of 

 the body, we shall there find the ocean flowing steadily 

 on, completely undisturbed by, and, so to speak, ignorant 

 of the existence of the body which it will ultimately have 

 to pass. There, all the streams must have the same 

 direction, the same velocity of flow, and the same pressure. 

 Again, if we pursue their course backwards to a sufficient 

 distance behind the body, we shall find them all again 

 flowing in their original direction ; they will also have 

 all resumed their original velocity ; for otherwise, since the 

 velocity of the ocean as a whole cannot have changed, we 

 should have a number of straight and parallel streams 

 having different velocities side by side with one another. 

 This, in a frictionless fluid, would be clearly an impossible 

 state of things, for we have seen that in a frictionless fluid 

 the velocities exactly correspond with the pressures, so that 

 if the velocities of these streams were different the pres- 

 sures would be different, and if the pressures were different 

 the fluid would begin to flow from the greater pressures 

 towards the less, and the streams would thus become curved 

 instead of straight. 



Thus, although in order to get past the body these 

 streams follow some courses or other, various both in 

 direction and velocity, settling themselves into these 

 courses in virtue of the various reactions which they exert 

 upon one another and upon the surface of the body, yet 

 ultimately, and through the reverse operation of corre- 

 sponding forces, 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 of their ultimate return to, their original direction and 

 velocity, is the submerged stationary body ; consequently 

 the body must receive the sum total of the forces necessary 

 to thus affect the streams. 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 direction and velocity, 

 requires the application of forces the sum total of which 

 in a longitudinal direction is nil, provided that the end 

 of each stream has the same direction and velocity as 



