MAGNETIC REACTIONS 33 



The total original flux <fj across the disk will thus be diminished by a 

 certain amount which we will call <f>', the "counter flux" due to the eddy- 

 currents. This diminution in flux may be assumed for moderate speeds to 

 be proportional to the intensity i of the eddy currents and to the angle 6, or 



<$>' = k,6i (2) 



Thirdly, in accordance with the fundamental principle of electro- 

 magnetic induction, we have 



i = h-^ (3) 



where the actual resultant magnetic induction through the disk is 



From these assumptions (1), (2), and (3), the following equations 

 may be derived, in which the product kJc 2 Jc 3 is replaced by a single con- 

 stant k : 



a 



(f> a 



<f>' k 

 i 2 a k 2 :i (0(f) 2 



O) 



(4) 

 (5) 



As will be seen, these assumptions do not take into account all of the 

 variables; nevertheless, it will be shown on p. 37 that equation (4) 

 is roughly verified. The significance of equation (5), which represents 

 the heat per revolution of the disk, will be discussed in a later paragraph. 



MEASUREMENT OF MAGNETIC FIELD BY MEANS OF A 



BISMUTH SPIRAL. 



It seemed desirable to measure not simply the total magnetic flux 

 at different speeds, but the induction at a number of points in and near 

 the air-gap as well. Among the various practicable methods, that of 

 the bismuth spiral seemed best adapted for our purpose. Most of the 

 observations described below were made with a Hartmann and Braun 

 spiral, kindly loaned us by the Worcester Polytechnic Institute. The 

 fine bismuth wire of this spiral, coiled into a flat disk about 17 mm. in 

 diameter, had a resistance under normal conditions of about 20 ohms. A 

 small portion of the work was done with a second spiral, similar to the 

 first, and the results obtained with the two instruments agreed very well. 

 Unfortunately we did not have at our disposal a spiral of smaller diameter. 



In order to make it possible to introduce the bismuth spiral into the 

 narrow gap between pole-face and disk, it was necessary to shift the electro- 

 magnet slightly, bringing one of its faces almost into contact with the disk, 

 while the gap on the other side was correspondingly widened. The effect 

 of this change on the heat per revolution was considered in Part II. Even 

 with this increased air-space on one side of the disk, it was not easy to 

 bring the spiral into the center of the field without its being chafed by the 



