Manchester Memoirs, Vol. xlii, ( 1 898), No. 6. 9 



when moment of momentum is introduced into a fixed 

 space without altering the moment of momentum within 

 that space, the rate at which moment of momentum leaves 

 the space must equal that at which it enters. The brake 

 wheel imparts moment of momentum to the water within 

 the case, and the friction of the shaft imparts moment of 

 momentum to the case. If, therefore, the moment of 

 momentum of the water in the case is steady, the water 

 must impart moment of momentum to the case as fast as 

 it receives it from the wheel, and the time-mean of the 

 moment of the load must be equal to the time-mean of the 

 moment of effort of the shaft, and this is not affected by- 

 water entering or leaving the case as long as it enters and 

 leaves it radially. The condition of steadiness is, however, 

 essential in order that the moment of effort may at each 

 instant be equal to the moment of resistance, since any 

 change in the moment of momentum of the water is the 

 result of the difference of the moments of effort and 

 of resistance. 



Fluctuations in the speed of running may thus cause 

 two classes of error, even when the load has been constant 

 all the time, (i) A terminal error resultmg from a difference 

 in the moments of momentum of the water at starting and 

 ending the measurements. The relative magnitude of this 

 error is the difference of the terminal moments divided 

 by the product of the mean moment of the load and 

 the interval of time in seconds; so that as the length 

 of the time increases this will become indefinitely smaller. 

 (2) The difference between the time-mean of the moment 

 as measured by the load, and the angular mean of the 

 actual moment which measures the work. This error can 

 only occur where both the moment of effort on the wheel 

 and the velocity fluctuate. With the automatic adjust- 

 ment of the resistance, such fluctuations are limited to 

 those of so short a period that they do not give the water 



