112 THE SCIENTIFIC PAPERS OF 



of the liquid, we may write the foregoing general formula as 

 follows : 



r z w~ 

 A-^-, ....... (II.) 



and 



(III.) 



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 



w 

 second n, instead of the angular velocity w, we may put n = ^- , and 



Z7T 



in putting this value for w ( = 2nri) into the last formula, we 



have w = lSr ...... (IV 



These formulas are applicable to vessels of every possible exter- 

 nal 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 

 condition 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 represented by Plate 20, Fig. 1, and which has sur- 

 vived the ordeal of experimental proof. 



LIQUID PYROMETER. The rotating vessel consists, in this case, 

 of a cup C 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. 



