282 HENRY A. EOWLAND 



However, it is hardly probable that this last condition would be often 

 satisfied, in which case this formula would give too great a value. 

 When the harmonics are small this last formula can be written nearly 



As an example, suppose a 3 =-3 and a 5 -2 and a 7 = 1, these two 

 formula give an increase of 10 and 24 per cent in the loss due to 

 hysteresis. 



The current heating is only 



l + a\ + a\ + etc. 4 

 Or, in the example, 



1 + -09 + -04 + -01 == 1-14. 



It would seem, then, that the losses due to hysteresis and current 

 heating may be much increased by the harmonics. 



I believe the statement has been made that the form of the curve 

 does not influence the hysteresis. This is evidently incorrect, unless 

 we take the top of the curve to reckon from, in which case the statement 

 agrees with the second hypothesis given above if the harmonics are of 

 the proper phase. 



To estimate the influence on the efficiency of a plant, assume the 

 efficiency of the dynamo and synchronous motor with primary currents 

 as each equal to 90 per cent, and of the two transformers equal to 93 

 per cent, and assume that all the currents have the same harmonics as 

 given above. The total efficiency will be 70 per cent. If the harmonics 

 are now added, the 30 per cent loss will become about 35 per cent, the 

 efficiency will be decreased to 65 per cent nearly, a loss of 5 per cent. 

 There is too much assumption about this calculation to warrant full 

 belief, and the figures are given more as a challenge to further investi- 

 gation than as facts. That there is a decrease of efficiency is certain, 

 but the amount must be determined by further experiment and mathe- 

 matical investigation. But, however small the loss, provided it occurs 

 in the transformers or the dynamos and motors, it may be of great 

 consequence on account of its heating effect, because the output of 

 these is limited by the amount of the heat generated. 



The practical conclusion seems to be that transformers and the arma- 

 tures of dynamos to be used in the transmission of power must be 

 designed for low magnetizations. By experiment with transformers, 



4 This formula assumes that the resistance is the same for the harmonics, whereas 

 it is greater on account of the ' skin ' effect. 



