Mr. C. W. Siemens on Uniform Rotation. 77 



date itself to the rotations imposed by the independent pendulum. 

 The differential-motion wheels are taken advantage of for imparting 

 independent driving- or sustaining-power to the pendulum ; and a 

 constancy of the angle of rotation, notwithstanding unavoidable 

 fluctuations in the sustaining-power, is secured (within certain limits) 

 by calling into play a break, or fluid resistance, at the moment when 

 the angle of rotation reaches a maximum, which maximum position is 

 perpetuated by increasing the sustaining-power beyond what is strictly 

 necessary to overcome the ordinary resistance of the pendulum. 



The chronometric governor is used by the Astronomer Royal to 

 regulate the motion of the large equatorial telescope and recording 

 apparatus at Greenwich, in which application a very high degree 

 of regularity is attained ; but the instrument proved to be too deli- 

 cate in its adjustments for ordinary steam-engine use. 



After a short allusion to M. Foucault's governor, the paper enters 

 upon the description of a new apparatus which the writer has ima- 

 gined for obtaining uniform rotation, notwithstanding great variations 

 in the drivmg-power, and which consists, in the main, of a parabolic 

 cup, open at top and 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 pro- 

 duces an increased torsional action of the spring, and with it an 

 automatic descent of the cup, sufficient to make up for the thick- 

 ness 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, § r, : 



\M i+ ft=W) 



n—- — — — — > 



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 ; 



