﻿462 Prof. Lyle and Mr. Baldwin on Propagation of 



which the phase retardation and the leakage coefficient of 

 the first harmonic attain their maxima ; (b) that the retar- 

 dations in phase # 3 , /3 5 of these harmonics behind the primary 

 first diminish, become minima, and then increase, and that the 

 point of minimum values of /3 3 and /3 5 is the same apparently 

 as that of maxima / 3 //i and /5//1 as well as that of maxima 

 S x —6 and Xj. The above may be differently stated as 

 follows : — As the flux-wave moves away from the origin its 

 form gradually changes, becoming flatter and flatter until it 

 reaches the point of maximum lag and maximum leakage 

 coefficient. After this as it continues to move on its flatness 

 steadily diminishes. This change of form is exhibited in 

 fig. 9, in which are plotted the two wave forms for #=0 and 

 .i< = 60 in the series given in Table XVIII. They are placed 

 inaccurately as regards relative phase, but the ordinates of 

 the one for #=60 are increased so that the amplitudes of the 

 first harmonics of the two curves are the same. 



Further interesting information as to the behaviour of the 

 upper harmonics of the flux may be obtained by considering 

 their actual amplitudes. Taking the third harmonics for any 

 of the series in this paper, we find that the leakage coeffi- 

 cients are different from what we estimated they would be for 

 a primary or first harmonic of the same amplitude and 

 frequency at the same section of the rod. In some cases, 

 indeed, as will be seen from the tables given, the amplitude 

 of the third harmonic actually increases as the distance from 

 the magnetizing coil increases. 



Hence we cannot consider the upper harmonics as being- 

 independent of the first harmonic or of each other. Each 

 seems to get continually reinforced by the first harmonic as 

 well as by other harmonics lower in order than itself as it 

 travels along. Such a transference of energy from the first 

 harmonic to the higher ones must be accompanied either by 

 a reduction of the amplitude of the first harmonic, which in 

 these experiments would manifest itself as leakage in \ l9 or 

 by a retardation of its phase helping to increase X —O O , or by 

 both ; so it is probable that this reinforcement of the higher 

 harmonics by the first has an important bearing on the theory 

 of the experiments described in this paper. 



14. In order to investigate the effect of change of diameter 

 we made two smaller bundles with wires taken from speci- 

 men D. One of these called d x contained 46, and the other 

 called d 2 12 wires, and as D originally consisted of 185 wires 

 the sectional areas of D, d h and d 2 were very " nearly in the 

 proportions of 16 to 4 to 1 or their diameters as 4 to 2 to 1. 



