SSK WILLIAM SIEMENS, F.R.S. Ill 



the other hand, it appears to depend for its correct action upon 

 the perfect condition of many mechanical details. 



Some months since an idea suggested itself to me which, while 

 it furnishes the elements of a very general and complete solution 

 of the problem under consideration, appears to possess also a 

 separate scientific interest, which chiefly induces me to bring the 

 subject before the Royal Society. 



LIQUID IN ROTATION. If an open cylindrical glass vessel or 

 tumbler containing some liquid be made to rotate upon its vertical 

 axis, the liquid will be observed to rise from the centre towards the 

 sides to a height depending on the angular velocity and the 

 diameter of the vessel. As soon as the velocity has reached a 

 certain limit the liquid will commence to overflow the upper edge 

 of the vessel, being thrown from it in the form of a fluid sheet in 

 a tangential direction. If the velocity remain constant from this 

 moment, the overflow of the liquid will be observed to cease, 

 although the liquid remaining in the vessel will continue to touch 

 the extreme edge or brim. Supposing that the velocity of the 

 vessel be now diminished, the liquid will be observed to sink, but 

 will rise again immediately to its former position when the rotation 

 returns to its previous limit of angular velocity. This velocity is 

 the result of the balance of two forces acting on the liquid 

 particles, namely, gravity and centrifugal force. 



It is a well-known fact that the curvilinear surface produced by 

 a liquid in rotation is that of a paraboloid, the parameter of 



which is expressed by -^, and the curve itself therefore by the 

 formula 



x signifying vertical distance from the apex, y the corresponding 

 horizontal distance from the axis of rotation, w the angular 

 velocity of rotation, and g acceleration by gravity in one second. 



In this formula there is no factor denoting the density of the 

 liquid, which proves that the point to which the liquid is raised by 

 a given angular velocity is independent of the specific gravity of 

 the liquid employed. 



By substituting for y the radius r of the rotating cup at the 

 brim, and for x the height h of the brim above the lowest level 



