114 THE SCIENTIFIC PAPERS OF 



below the brim of the rotating cup, an excess of driving-power 

 must be applied, and that excess must be disposed of otherwise 

 than in producing further acceleration of the cup. This is accom- 

 plished by means of a continual overflow of a thin sheet of liquid, 

 which is projected against the sides of the outer vessel and falls 

 back into the lake at the bottom, whence a similar quantity of 

 liquid penetrates into the cup, to be also raised by its rotation and 

 projected over its edge. 



The power absorbed in raising and projecting the liquid must 

 be strictly proportionate to the quantity of liquid so acted on in a 

 given time, or to the thickness of overflow, provided the condi- 

 tion of uniform velocity be realized ; but the velocity of the cup 

 depends upon the height to which the liquid has to be raised, and 

 must therefore be increased in order to raise the liquid column 

 above the brim of the cup. The. necessary increase of velocity to 

 produce such an overflow is not great, considering that the height 

 of the liquid column increases in the square ratio of the velocity, 

 and may be neglected in all cases where only approximate results 

 are required, or where variations in the driving-power are com- 

 paratively small ; but no high degree of accuracy could have been 

 claimed for this instrument unless the following compensation 

 action had suggested itself : 



AUTOMATIC DIP OF CUP. We have assumed hitherto a rigid 

 connexion between the cup and its driving-spindle, and unless the 

 cup does overflow, we are, indeed, justified in this assumption, the 

 spring E being too rigid to yield to the resistance of the cup in 

 motion when no work is performed. With an increase of power 

 the resistance of the cup also increases, and an overflow of liquid 

 proportionate to the power is produced ; the connecting spring E 

 must yield, at the same time, proportionately to the torsional 

 resistance thus created, and in the same ratio the cup will descend 

 upon the helical surface which serves for its guide. While, there- 

 fore, on the one hand, the h of our formula increases with the 

 overflow, it is diminished, in the same ratio, by the descent of the 

 cup, both depending directly upon the driving-power. In so ad- 

 justing the stiffness and length of the spring that the one action 

 equals the other for any given increase of power, it must 

 equal it also for other amounts of increase within reasonable 

 limits, and strictly uniform rotation must le the result. The 



