362 



Prof. E. Wilson. 



[May 28, 



cuts the axis of time, has been halved, and the sum of the values thus 

 obtained is taken to be the effective electromotive force in volts acting 

 around the assumed path of the induced electric current. Similarly 

 for coils 2' 4 at angles $i 6 2 respectively in fig. 3. The rate of dissipa- 

 tion of energy in watts is taken to be the square of this electromotive 

 force in volts, divided by the resistance of the path in ohms. These 

 watts have been plotted on squared paper, and the total watts in the 

 plane a have been obtained by integration with respect to the vertical 

 •distance from the horizontal axis. Finally, by integrating with respect 

 to the horizontal axis ox, the total watts dissipated in the half cylinder 

 have been found. The figures thus obtained at periodic times, 45, 90, 

 and 360 seconds, for different values of the total flux of induction 

 between the pole pieces, are set forth in Table I. Strictly this method 

 is only applicable when the electromotive forces of coils 1, 2', and 4 

 .are in phase. With a periodic time of 360 seconds the curves are 

 nearly in phase for all values of the external magnetising force, but 

 this is not the case for the other periodic times, except at the high 

 forces. The electromotive force curves are assumed to be in phase in 

 each experiment when applying the above process of integration. 



Influence of Wave-form. 



If reference be made to fig. 3 it will be seen that No. 4 coil gives an 

 electromotive force whose wave-form lies between a sine curve and a 

 rectangle. Suppose that the electromotive-force curve of No. 4 coil 

 were a rectangle having the same area as a sine curve about the same 

 base line. Since the maximum ordinate of the sine curve is 7r/2 of the 

 ordinate of the rectangle, it follows that the minimum induction density 

 in the case of the rectangle will be 2/tt of the average induction 

 •density. Since also with the rectangle the electromotive force is 

 constant for the No. 4 coil, the induction density will increase 

 inversely as sin 2 (fig. 2). The value of the intensity of magnetic 

 induction in each of the planes a, /?, y . . . has been calculated, and 

 the graphical treatment described in connection with the experiments 



has been applied. It gives as a result 2-08 for the watts per 



cubic centimetre dissipated by induced currents, the symbols having the 

 definition given in the next section of this paper. The graphical 

 treatment has also been applied when the intensity of magnetic induc- 



B 2 / 2 ? 2 



tion is constant, and gives 3*93 for the watts per cubic centi- 



metre. This formula is in close agreement with the result of theory. 

 We should expect, therefore, that the experimental results would give 

 .a less rate of dissipation of energy than dictated by the considera- 

 tion of constant intensity of induction, and this is found to be the case. 



