﻿Waves of Magnetic Ilux along Iron Wires. 467 



critical distance,, and from their observations concluded (1) 

 that the leakage coefficients were practically constant at all 

 distances x, thus arriving at a logarithmic decrease o£ flux 

 amplitude ; (2) that the fairly regular space-rate of phase 

 retardation dQ/dx observed would be completely accounted 

 for by a velocity of magnetization r, deduced by the formula 



- 27r 

 v ~ Td0/dx 



We find that neither of these conclusions is correct, as 

 (a) \, for the same rod and conditions of experiment, varies 

 within wide limits along the rod, and (7>) the retardation, after 

 increasing as they observed within the critical distance, 

 becomes stationary at the critical point, beyond which the 

 phase of the flux advances : so that if their conclusion (2) 

 were correct, we should have to admit an infinite velocity at 

 the critical point and a negative velocity beyond it. 



(5) As the flux passes along the specimens made of wires, 

 the amplitudes /' 3 , / 5 of its upper harmonics get continually 

 reinforced by a transference of energv from the first harmonic 

 (see § 13, Tables XVIII.-XXL). The ratios /,$//i, fjf t first 

 increase with #, attain maxima, and then diminish ; at the 

 some time the differences /3 3 , j3 :) between the phases of these 

 harmonics and the phase of the first diminish first with x, attain 

 minima, and then increase ; and the positions of maxima of 



fz/fi, f»l f\ and minima of /3 3 , /3 5 are at (or near) the critical 

 point. From this it results that as the flux-wave moves away 

 from the origin its form changes, becoming flatter as x in- 

 creases (see fig. 9) until the critical point is reached, when 

 its flatness is a maximum ; beyond this as x increases its 

 flatness diminishes. 



(6) The effects of an end on a flux-wave approaching it are 

 to increase the leakage coefficient and to cause an advance 

 in the phase. (See fig. 6.) 



(7) When a rod whose behaviour has been determined is 

 shortened and subjected to the same magnetization as before, 

 no difference is observed in the flux-waves until (for a ^in. 

 rod) within 30 cms. from the new end. (See § 8 and fig. 6.) 



(8) For the same frequency, initial flux, and cross-section, 

 increase of permeability increases the critical distance, in, 

 creases the critical value of the retardation (see fig. 7), and 

 diminishes the critical value of the leakage coefficient. (See 

 § 9 and fig. 8). 



(9) Eddy currents diminish the critical distance, increase 

 the critical value of the retardation, and increase the leakage 

 coefficients. (See § 12.) 



2 E2 



