MAGNETIC REACTIONS 



37 



'trailing" side the induction was about doubled when the disk was run- 

 ning at 364 revolutions per minute. 



COMPARISON OF RESULTS WITH THEORY. 



Although, for the reasons given, the curves in fig. 15 do not represent 

 the facts quite accurately, still it is worth while to inquire how well they 

 satisfy the conditions expressed in equations (4) and (5). In these equa- 

 tions it is necessary to know the value of cf>, the resultant flux at angular 

 velocity co, and <', the " counter flux " at the same angular velocity. 

 From the areas of the distorted curves in heavy lines 9 is obtained, and 

 4>' from the areas of the curves in fine lines (algebraic sum of negative 

 and positive lobes). The areas were taken arbitrarily between 40 and 

 H-45 mm., since outside of these limits the ordinates are small. From 

 the areas and the measured dimensions of the pole-faces, the values 

 shown in columns 2 and 3 of table 7 were obtained. 



Table 7. Magnetic fluxes at different speeds. 



Since only relative values are required, co is here given as the num- 

 ber of revolutions per minute of the disk. 



9 

 The quantity co 2 ~j-, in column 4 should, by equation (4), be equal 



a 

 to j, a constant. This condition is satisfied as well as could be ex- 

 pected, considering that the increase in co from the first to the third ob- 

 servation is ten-fold and the increase in cf>' is nearly fifty-fold. It must 

 also be remembered that as the speed increases, the distribution of the 

 current paths and hence also the resistance of the paths may change to 

 a marked degree. In other words, our assumptions considered only the 

 total flux, although theoretically the distribution of magnetic induction 

 and of the current loops in space ought to be considered. Moreover, 

 since the magnetic lines pass between pole-pieces of limited extent, it is 

 possible that our first assumption, equation (1), does not hold at the 

 higher speeds. Changes of a with temperature can hardly have affected 

 the result materially; but, on the other hand, the lack of reliable obser- 

 vations in the central portions of the field lends an element of uncertainty. 



In equation (5) we expressed the relation 



i 2 a 



CO 



2 3 cod> 2 



