ON NA VAL ARCHITECTURE. 305 



were not unaware of the defects of that mode of viewing the question, 

 although in text books on mathematics and hydraulics, it was always 

 entered as a provisional way of looking at things ; but in recent years 

 the higher mathematicians have worked out, in a very correct and 

 conclusive form, what is called the theory of stream lines, a theory 

 which represents correctly all the motions that the particles of the 

 water would undergo in encountering any body which is passing 

 through them, and the force which they would exert on each other and 

 in the body if water were a frictionless fluid ; and in order to explain 

 that theory tolerably clearly I must first ask you to go with me 

 beneath the water. We will consider first what happens to a fish. 

 The theory of stream lines tells us that were water a frictionless fluid, 

 the fish would swim absolutely without resistance when once put in 

 motion. The proposition sounds extremely paradoxical, but I do not 

 mind stating it in the most paradoxical form. The theory of stream 

 lines has demonstrated most conclusively that if water were a perfectly 

 frictionless fluid, even a plane moving at right angles to itself would 

 not experience any resistance when once put in motion. It would 

 experience resistance while being put in motion, because of the dyna- 

 mical conditions of the surrounding fluid ; all the particles around it 

 must have some motion duly related to the motion of the plane or 

 other body, and that companion motion has to be established at 

 starting, and the force experienced by the plane or other body while 

 the motion is being established will be felt initially as a resistance ; 

 but when once the motion had become steady, no farther resistance 

 would be experienced. The converging stream lines behind the plane 

 or body would exercise just as great pressure on its back surface, as 

 would be experienced by its front surface, while forcing the particles 

 from their natural position into the divergent stream lines in front. 

 This seems paradoxical, but we can arrive at the conclusion by rational 

 steps by changing our mode of approaching the question. 



If we imagine that the fish is a fixed body, and the ocean is moving 

 past it, we shall get a conception which will render it more easy to 

 follow the law that I am endeavouring to explain. If we imagine 

 the body, say this egg-shaped body, moving straight through the fluid, 

 in one direction, it is obviously the same thing to imagine the body at 

 rest and the water moving in straight lines past it. Let us trace out 



