136 Professor Osborne Reynolds [June 2, 



has never been seen before by any one but Mr. Foster and myself, 

 namely, the complete process of the formation of a cylindrical vortex 

 sheet resulting from the motion of a solid surface. To make it 

 visible to all I am obliged to limit the colour band to one section 

 of the sheet, otherwise only those immediately in front would be 

 able to see between the convolutions of the spiral. But you will, 

 understand that w r hat is seen is a section, a similar state of motion 

 extending right across the tank. From the surface you see the plane 

 vane extending half-way down right across the tank ; this is attached 

 to a float. 



I now institute a colour band on the right of the vane out of the 

 tube. There is no. motion in the water, and the colour descends slowly 

 from the tube. I now give a small impulse to the float to move it 

 to the right, and at once the spiral form is seen from the tube. Similar 

 spirals would be formed all across the tank if there were colours. 

 The float has moved out of the way, leaving the revolving spiral with 

 its centre stationary, showing the horizontal axis of the spiral is 

 half-way between the bottom and surface of the tank, in which the 

 water is now simply revolving round this axis. 



This is the vortex in its simplest and rarest form (for a vortex 

 cannot exist with its ends exposed). Like an army it must have its 

 flanks protected ; hence a straight vortex can only exist where it has 

 two surfaces to cover i:s flanks, and parallel vertical surfaces are 

 not common in nature. The vortex can bend, and, as with a horse- 

 shoe axis, can rest both its flanks on the same surface, as this piece 

 of clay, or with a ring axis, which is its commonest form, as in the 

 smoke ring. In both these cases the vortex will be in motion 

 through the fluid, and less easy to observe. 



These vortices have no motion beyond the rotation because they 

 are half-way down the tank. If the vane were shorter they would 

 follow the vane ; if it were longer they would leave it. 



In the same way, if instead of one vortex there were two vortices, 

 with their axes parallel, extending right across, the one above another, 

 they would move together along the tank. 



I replace the float by another which has a vane suspended from 

 it, so that the water can pass both above and below the vane extending 

 right across the middle portion of the tank. In this case I institute 

 two colour bands, one to pass over the top, the other underneath, the 

 vane, which colour bands will render visible a section of each vortex 

 just as in the last case. I now set the float in motion and the two 

 vortices turn towards each other in opposite directions. They are 

 formed by the water moving over the surface of the vane, downwards 

 to get under it, upwards to get over it, so that the rotation in the 

 upper vortex is opposite to that in the lower. All this is just the same 

 as before, but that instead of these vortices standing still as before they 

 follow at a definite distance from the vane, which continues its motion 

 along the tank without resistance. 



Now this experiment show r s, in the simplest form, the modus 



