644 



SCIENCE. 



[N. S. Vol. Vlll. No. 202. 



a large tank whicli is full, by means of a 

 projecting tube in the side of the tank, the 

 fluid, instead of spreading in all directions 

 (by the theory), actually moves like a fluid 

 cylinder for a short distance. In fact, the 

 fluid, instead of moving back along the out- 

 side of the projecting tube, actually moves 

 the other vray. The difference is, of course, 

 caused by the viscosity of the fluid, which, 

 even when small, produces vortex or eddy 

 motion of a complicated kind. The difii- 

 culties have been stated with some detail 

 and with several illustrations by Lord Kel- 

 vin in Nature, 1894. 



Just lately Professor Hele-Shaw has suc- 

 ceeded in photographing the movements of 

 an actual fluid under similar circumstances. 

 It is striking to observe that when the 

 motion of the water takes place between 

 two parallel plates not far apart, and when 

 its velocity is not very great, the stream- 

 lines follow almost exactly the theoretical 

 positions which they would have under the 

 assumptions made above. In the case of a 

 rectangular plate held at an angle of 45° 

 to a steady stream the stream-lines agree 

 almost exactly with the hyperbolas given 

 by theory. When the parallel plates are 

 not close, however, or the motion takes 

 place in a tube of not too small section, any 

 variation in the diameter of the tube soon 

 produces turbulent motion. 



When the motion takes place in three 

 dimensions I divide it again into continuous 

 and discontinuous motion. On neither is 

 there much to say. When the motion is 

 continuous, and there are no forces acting 

 on the solid which is moving through the 

 fluid, the system of differential equations 

 admits of three integrals, and the integra- 

 tion is practically finished if we can find a 

 fourth. Several Continental writers have 

 been considering, during the past two or 

 three years, under what circumstances a 

 fourth integral of specified form may exist. 

 Miss Fawcett has examined the case of the 



motion of a solid of the form known as an 

 isotropic helicoid when gravity is the only 

 force acting. The most interesting case is 

 that where the solid starts from rest. The 

 path followed by the center of gravity is 

 traced. The motion of an anchor ring 

 when there is circulation through the aper- 

 ture has been discussed by Greenhill, Bas- 

 set and Dyson. The first-named has ap- 

 plied the (T-functions to the solution of the 

 problem. Basset has also discussed the 

 motion of a spherical bowl. No problem 

 of discontinuous motion in three dimen- 

 sions has been yet solved, notwithstanding 

 many unpublished attempts. I shall re- 

 turn to this subject later on. 



Coming next to the general theory of 

 wave-motion, including the problem of the 

 tides, two main classes may be distin- 

 guished. Waves of expansion belong pri- 

 marily to the theory of sound and they 

 will not be touched upon here. The second 

 class concerns the different kinds of waves 

 which our every- day experience of water in 

 motion brings before us. It includes wave- 

 motion on the large scale as exhibited by 

 the tides, and on a smaller scale in the long 

 waves which are known under the name of 

 a ' ground-swell ' in the Atlantic ; next 

 the waves whose eflects have the greatest 

 destructive power — the short waves whose 

 height is not very small compared with 

 their length — the waves raised by the wind 

 in a river, those which follow in the wake' 

 of a ship, the solitary wave travelling up a 

 canal or in some rivers, known in England 

 as a 'bore;' finally, the waves which are 

 very small and which are mainly propagated 

 by the surface tension of the fluid. These 

 last are known as capillary waves and will 

 only be mentioned incidentally. A general 

 distinction of all these waves on the surface 

 of water is made by mathematicians — the 

 long waves, where it appears permissible to 

 neglect the vertical acceleration of the par- 

 ticles of the fluid without materially affect- 



