.s/A' WILLIAM SIEMENS, F.K.S. Ii; 



per second, or *G revolution per second more than was indicated by 

 t lift ry, a result which seemed to stamp the action of the instru- 

 ment with uncertainty, when it was recollected that no allowance 

 had been made for the aperture at the bottom of the cup, leaving 

 a portion of the rotating liquid without an external support. 



CORRECTION FOR LOWER ORIFICE OF Cur. If we assume, for 

 instance, that the sides of the cup were cylindrical and merely 

 descended below the surface of the liquid without closing in at the 

 bottom, we should find that by rotation of this cylinder, supposing 

 the inner surface to be rough or armed with radial projections, the 

 liquid would rise on the circumference above the external level of 

 surface, but would also form a depression or vortex in the centre of 

 rotation. The surface of the rotating liquid would be that pro- 

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

 diagram (Plate 19, Fig. 3). In order to maintain the hydrostatic 

 equilibrium between the rotating column with the external liquid, 

 it is necessary that its mean height of column must remain the 

 same, or that the plane of external liquid level must divide the 

 solid figure comprised between the cylinder and the curve of 

 rotation into equal parts. In order to realise these conditions 

 experimentally, 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 (descending 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 ti and 

 a cylinder is, however, divided equally by a horizontal plane cutting 



it at the distance of - - from the edge, or at ti -j- = - 293# from 



\[' J i 



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 



