ME. C. W. SIEMENS ON UNIFOEM EOTATION, 



665 



Fig. 3. 



duced by the rotation of a vertical parabola, as represented in the accompanying diagram. 

 In order to maintain the hydrostatic equilibrium 

 between the rotating column and the external liquid, 

 it is necessary that its mean height of column should 

 remain the same, or that the plane of external liquid 

 level should divide the solid figure comprised between 

 the cylinder and the curve of rotation into equal 

 parts. In order to realize these conditions experi- 

 mentally, it would be necessary to provide the lower 

 portion of the rotating cylinder with an easy fitting 

 and balanced piston, without which circular currents 

 would be produced within the rotating liquid (de- 

 scending by force of gravity at the sides, and rising 

 again in the centre) and mar the result. 



The body comprised between a paraboloid of the 

 height /t' and a cylinder is, however, divided equally 

 by a horizontal plane cutting it at the distance of 

 U 



—r^ from the edge, or at 



A'-^=-293A' 



from the apex. The form of the curve depends upon the angular velocity alone, and 

 would remain the same if the upper diameter of the tube were to be increased, only 

 the curve would in that case have to be continued until it met the sides (as shown by 

 dotted lines), and to the extent of these prolongations the liquid would be raised higher 

 above the external level without producing a corresponding depression in the centre of 

 rotation. 



It follows that the aperture at the bottom of the rotating cup causes a vortex or 

 depression of the apex of the curve of rotation below the external liquid to the extent 

 of '293 part of the height due to its own diameter, and to the correct number of rotations 

 n' per second. 



Now 



y,'_ '^2ff(^ + -293A') 

 2nr ' 



and also 



2gir 



if g is the radius of lower aperture of cup ; therefore 



or 



^'2g{h+-2mh') _ '/2gh' 

 2nr ~ 2j» ' 



h!=h 



r*--293g«' 



4y2 



