ME. C. "W. SIEMENS ON UNIFOEM ROTATION. 661 



h of the brim above the lowest level of the liquid, we may write the foregoing general 

 formulae as follows, 



*=^'. • • • (11) 



and 



w=^^; (III.) 



r 



two convenient formulae for determining the height to which liquid will rise when the 

 diameter of the rotating vessel and its angular velocity are given, or for determining the 

 angular velocity due to a given height and diameter, it being understood that the values 

 of g, r and h must be expressed in the same unit of length. 



If it is desired to determine the number of revolutions per second «, instead of the 

 angular velocity w, we may put 



and in putting this value for w (=2^«) into the last formula, we have 



n^^^ (IV.) 



These formulae are applicable to vessels of every possible external form rotating upon 

 their vertical axis, and to every possible liquid, but they are based upon the supposition 

 that the liquid is raised by rotation to the upper edge or brim of the vessel, a con- 

 dition which it may appear at first sight difficult to realize for practical purposes. 



If the production of uniform rotation be the object in view, it is necessary that the 

 liquid in the rotating vessel should always be at the point of overflow, although the 

 driving-power might vary considerably, and that all surplus driving-power should be 

 absorbed by other work than that of accelerating the rotating vessel, also that the stock 

 of liquid within the vessel should never diminish. I hope to prove by the following 

 demonstration that these various conditions can be fulfilled by suitable mechanical 

 arrangements resulting in the construction of a simple and efficient instrument, which is 

 is represented on Plate XXIX., and which has survived the ordeal of experimental 

 proof. 



Liquid Gyrometer. — The rotating vessel consists, in this case, of a cup C (Plate XXIX. 

 fig. 1) open both at the top and bottom, but widest at the top, the sides being made 

 to close in towards the bottom in a parabolic curve analogous to that formed by the 

 liquid in rotation. This cup contains upon its inner surface three or four radial ribs 

 which unite in a central boss, by which the cup is supported upon the spindle S. This 

 support is not an absolute one, but the spindle is armed with a screw-thread of rapidly 

 ascending path, into which the screw-threads upon the inner surface of the boss ai"e made 

 to fit ; a fixed connexion between the driving-spindle and the cup C is established by 

 means of a spiral spring E, one end of which is fastened to the projecting end of the 

 spindle S, and the other to the cup. Before this spring is fixed, it is drawn out longi. 



