72 



Mr. C. W. Siemens on Uniform Rotation. 



[Apr. 12, 



bottom and mounted upon a vertical axis, which cup dips with its smaller 

 opening into a liquid contained within a casing completely enclosing the 

 cup. It is shown that a certain angular velocity of the cup will raise the 

 liquid (entering from below) in a parabolic curve to its upper edge or brim, 

 and that a very slight increase of the velocity will cause actual overflow, in 

 the form of a sheet of liquid, which, being raised and projected against the 

 sides of the outer chamber, descends to the bath below, whence fresh 

 liquid continually enters the cup. Without the overflow scarcely any 

 power is required to maintain the cup, with the liquid it contains, in motion ; 

 but the moment an overflow ensues, a considerable amount of power is 

 absorbed in raising and projecting a continuous stream of the liquid, 

 whereby further acceleration is prevented, and nearly uniform velocity is 

 the result. When absolute uniformity is required, the cup is not fixed 

 upon the rotating axis, but is suspended from it by a spiral spring, which 

 not only supports its weight, but also transmits the driving-power by its 

 torsional moment. The cup is guided in the centre upon a helical surface, 

 which arrangement has for its result that an increase of resistance or of 

 driving-power produces an increased torsional action of the spring, and 

 with it an automatic descent of the cup, suflicient to make up for the 

 thickness of overflow required to effect the readjustment between power 

 and resistance, without permanent increase of angular velocity. 



It is shown that the density of the liquid exercises no influence upon the 

 velocity of the cup, which velocity is expressed by the following formula, 



2rir 



in which 



n signifies the number of revolutions per second, 



h the height of liquid from the surface to the brim of cup, 



r the radius of the brim, and 



p the radius of lower orifice of cup ; 



only the rigidity of the spring must be greater when a comparatively dense 

 liquid is employed. 



In order to test the principle of action here involved, Mr. Siemens has 

 constructed a clock consisting of a galvanic battery, an electro-magnet, and 

 his gyrometric cup, besides the necessary reducing- wheels and hands upon 

 a dial face, which proceeds at a uniform rate, although the driving-power 

 may be varied between wide limits, by the introduction of artificial resis- 

 tances into the electrical circuit. The instrument appears, therefore, well 

 calculated for regulating the speed of all kinds of philosophical apparatus, 

 and also for obtaining synchronous rotations at different places for tele- 

 graphic purposes. One of its most interesting apphcations is embodied in 

 the "Gyrometric Governor" for steam-engines, of which an illustration is 

 given. This consists of a cup of 200 millimetres diameter and the same 



