1884.] on the Two Manners of Motion of Water. 49 



the screen ; it is surrounded with clear still water. The mouth of 

 the tube at which the water enters is the largest part, and it contracts 

 uniformly for some way down the channel, then the tube expands 

 again gradually until it is nearly as large as at the mouth, and then 

 again contracts to the tube necessary to discharge the water. I draw 

 water through the tube, but you see nothing as to what is going on. 

 I now colour one of the elementary streams outside the mouth ; 

 this colour-band is drawn in with the surrounding water, and will 

 show us what is going on. It enters quite steadily, preserving its 

 clear streak-like character until it has reached the neck where con- 

 vergence ceases ; now the moment it enters the expanding tube it is 

 altogether broken up into eddies. Thus the motion is direct in the 

 contracting tube, sinuous in the expanding. 



The hydrodynamical theory affords no clue to the cause why ; and 

 even by the method of colour-bands the reason for the sinuosity is 

 not at once obvious. If we start the current suddenly, the motion 

 is at first the same in both tubes, its change in the expanding pipe 

 seemed to imply that here the motion was unstable. If so, this ought 

 to appear from the equations of motion. With this view this case 

 was studied, I am ashamed to say how long, without any light. I 

 then had recourse to the colour-bands again, to try and see how the 

 phenomena came on. It all then became clear: there is an inter- 

 mediate stage. When the tap is opened, the immediately ensuing 

 motion is nearly the same in both parts ; but while that in the con- 

 tracting portion maintains its character, that in the expanding portion 

 changes its character. A vortex ring is formed which, moving for- 

 ward, leaves the motion behind that of a parallel stream through the 

 surrounding water. 



If the motion be sufficiently slow, as it is now, this stream is 

 stable, as already explained. We thus have steady or direct motion 

 in both the contracting and expanding parts of the tube, but the two 

 motions are not similar : the first being one of a fagot of similar 

 elementary contracting streams, the latter being that of one parallel 

 stream through the surrounding fluid. The first of these is a stable 

 form ; the second an unstable form, and, on increasing the velocity, 

 the first remains, while the second breaks down ; and we have, as 

 before, the exj)anding part filled with eddies. 



This experiment is typical of a large class of motions. Wherever 

 fluid flows through a narrow, as it approaches the neck it is steady, 

 after passing, it is sinuous. The same effect is produced by an 

 obstacle in the middle of a stream ; and very nearly the same thing 

 by the motion of a solid object through the water. 



You see projected on the screen an object not unlike a ship. Here 

 the ship is fixed, and the water flowing past it ; but the effect would 

 be the same if we had the ship moving through the water. In the 

 front of the ship the stream is steady, and so till it has passed the 

 middle, then you see the eddies formed behind the ship. It is these 

 eddies which account for the discrepancy between the actual and 



Vol. XI. (No. 78.) e 



