142 REPORT— 1898. 



revolution round the edge of the wedge of the body interrupting the 

 flow in the wedge of fluid, the equation is 



dx^ dy^ y dy 



which is not the same as the other, and therefore the stream lines are not 

 the same in the two cases. ^ 



If we compare together the case in three dimensions given by Pro- 

 fessor Lamb of the flow of a perfect fluid round a sphere and the case 

 actually obtained by this method with glycerine, it will be noticed, as 

 might have been expected, that the lines round the section of the sphere 

 are crowded much more closer together for physical reasons which are 

 easily explained ; for it is obvious that, as the whole of these efiects depend 

 upon viscosity, the efiect of viscosity diminishes in the thicker portion of 

 the wedge in such a way as to make the general velocity of flow greater, 

 and hence the stream lines round the obstacle are not deflected from their 

 path to the same extent as they would be if they were of uniform flow in 

 a parallel portion of the stream. 



One result, however, of great interest was obtained, and that was that 

 with less viscous fluids, such as water, the exact point at which the colour 

 bands broke up could be traced by this method, and the flow studied side 

 by side with stream-line motion. 



This leads the author, in conclusion, to bring forward an experiment 

 upon continuity with thick sheets, which it may be interesting to show, 

 as indicating clearly the great difference between the flow according as 

 the motion is sinuous or otherwise, and particularly as throwing some 

 insight into the birth of eddies, at the sharp edges of the body. The 

 obstacle itself is of wedge -shape cross section, the edges of the wedge 

 being ground as sharply as possible. Coloured liquid is now allowed to 

 flow behind the plate by means of a small orifice, and the effect can be 

 immediately seen. As long as the water is flowing steadily, the shape of 

 the curves formed by the clearly marked border between the dead water 

 and the water flowing over the edges of the plate agrees more or less 

 with that given by calculation. When, however, the flow, instead of 

 being steady, takes place in a series of impulses, the exact character of 

 the succession of eddies formed at the sharp edges of the plate is 

 clearly seen. 



' Since this paper was read Professor Sir G. G. Stokes has further investigated 

 the matter, and has been able to obtain the equation of the stream lines for the case 

 of a slender wedge of a viscous fluid interrupted by a wedge forming a section of a 

 sphere, which he finds in terms of polar co-ordinates to be as follows : — 



c;-) 



sin* d = constant. 



The two following equations, therefore, may, for convenience, be expressed thus 

 Case of flow of perfect fluid round a sphere : 



■* sin' 9 = constant. 



Case of slender wedge with spherical sector : 



(1 — ^ ) r* sin* 8 = constant ; 



and Professor Stokes remarks that the equation shows, even without plotting, the 

 general character of the difference between the wedge lines and spherical lines. 



