330 REPORT — 1875. 



cumstances here involve an instability which does not exist there, so that the small 

 initial disturbance presently magnifies itself into one of considerably greater range. 

 This curious corollary phenomenon of the alternated retardation of discharge, 

 thouo-h not strictly relevant to the main object of the experiment, is nevertheless 

 highfy interesting in itself, and tends to enlarge our apprehension of some of the 

 characteristic features of fluid dynamics. 



In this treatment of the propositions concerning the flow of fluid through pipes, 

 I have at length laid the necessary foundation for the treatment of the case of the 

 flow of an iuflnite ocean past a submerged body. I have shown these propositions 

 to be based on principles which are imdeniable, and the conclusions from which, 

 when they seemed in any way startling or paradoxical, you have seen confirmed 

 by actual experiment. 



I have dealt with the case of a single stream of uniform sectional area (and there- 

 fore of uniform velocity of flow) enclosed in a pipe of any path whatever ; I have 

 dealt with the case of a single stream of very gradually varying sectional area and 

 velocity of flow; and I have dealt with the case of a combination (or fiiggot, as it 

 were) of such streams, each to some extent curved and to some extent varying in 

 sectional area, together composing the whole content of a pipe or passage having 

 enlargements or contractions in its course ; and in all these cases I showed that, 

 provided the streams or pipe-contents finally retm'n to their original path and their 

 original velocity of flow, they administer no total endways force to the pipe or 

 channel which causes their deviations. 



I am now going to deal with a similar combination of such streams, which, 

 when taken together, similarly constitute an infinitely extended ocean, flowing 

 steadily past a stationarv submerged body ; and here also I shall show that the 

 combination of curved streams surrounding the body, which together constitute the 

 ocean flowing past it, retm-n finally to their original direction and velocity, and 

 cannot adniinister to the body any endways force. 



The argument in this case is, in reality, precisely the same as that in the case of 

 the contractions and enlargements in pipes which I have already dealt with ; for, 

 in fact, the flow of the ocean past the stationary submerged body is only a more 

 general case of the flow of fluid through a contracted pipe ; but, though the cases 

 are really the same, there is considerable difference in their appearance ; and there- 

 fore I will proceed to point out how the arguments I have abeady used apply 

 equally to this case. 



Everv particle of the fluid composing the ocean that passes the body must 

 undoubtedly follow some path or o\her, though we may not be able to find out 

 what path ; and every particle so passing is preceded and followed by a continuous 

 stream of particles all following the same path, whatever that may be. We 

 may, then, in imagination, divide the ocean mto streams of any size and of any 

 cross-section we please, provided they fit into one another, so as to occupy the 

 whole space, and provided the boimdaries which separate the streams exactly 

 follow the natural courses of the particles. 



I before sugo-ested a similar conception of the constitution of the ocean flowing 

 past the stationary body, and there pointed out that the streams forming this 

 system must not only be ciu-Ved in order to get out of the way of the body, but 

 might each require to have to some extent a diflerent sectional area, and therefore a 

 ditferent velocity of flow at diflerent points of their course. If we trace the streams 

 to a sufficient distance ahead of the body, we shall there find the ocean flowing 

 steadily on, completelv undisturbed by, and as we may say ignorant of, the exist- 

 ence 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 pm-sue 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 parallel streams 

 having different velocities and therefore different pressures side by side with one 

 another, which is an impossible slate of things*. 



* In an imperfect fluid it is possible to have p.irallel streams having different velocities 

 side by side with one another, because, in an imperfect fliud, change of velocity may have 

 been communicated by friction, and therefore does not imply difference of pressure. 



