Electromagnetic Induction. 333 



on the other side. In all cases these two balancing positions 

 were found ; and the half-difference of the readings on the 

 scale M N, which was numbered from one end, was taken as 

 the result of the experiment. In this way the measurements 

 obtained were independent of any uncertainty in the deter- 

 mination of the point P. In using the numbers thus obtained 

 for plotting a curve of constant induction, the distances read 

 off along P were taken as abscissas, and the half-differences 

 of the pairs of readings along M N were taken as ordinates. 

 Thus in all the figures which accompany this paper, the axis 

 of x is taken as coinciding with the axis of the primary coil 

 with its centre fixed at the origin of coordinates, and the 

 curves of constant induction are to be taken as representing 

 the paths traced out by the centre of the secondary coil in a 

 ■ plane containing the axes of x and y. The induced electro- 

 motive force changes sign when the centre of the secondary 

 coil passes from one side to the other of the curve of no in- 

 duction. In what follows, the induction is reckoned positive 

 when the axes of the primary and secondary coils coincide. 

 Hence, in the figures, all the curves lying between the axis 

 of abscissae and the zero-curve are to be taken as curves of 

 positive induction; while those which lie further from the axis 

 of abscissse than the zero-curve are to be taken as curves of 

 negative induction. The negative curves were traced experi- 

 mentally in the same way as the positive curves, except that 

 the two leading wires of one of the four coils were inter- 

 changed. Thus the inversion of electromotive force, due to 

 the relative positions of the coils C and D, was counteracted 

 by the inversion of the connections ; and the inductive action 

 between A and B could be balanced by that between C and D, 

 just as in the measurements which gave the curves of positive 

 induction. 



The positive and negative divisions of the set of curves 

 already alluded to, which, in what follows, are spoken of as 

 the first set of curves, were each traced out with the apparatus 

 arranged as in the diagram. But in order to trace out another 

 set of curves, which are afterwards spoken of as the second 

 set of curves, the axis of the coil D was set at right angles to 

 that of C, but otherwise every thing remained unaltered. The 

 zero-curve of the second set coincides with the axes of x and 

 y ; and therefore it did not require to be traced ; each of the 

 other curves is complete in one quadrant. The induced elec- 

 tromotive force changes sign when the centre of the coil D 

 passes from one side to the other of the axes of x or of y : 

 hence in the figures the second set of curves are to be taken 

 as positive in one quadrant and negative in another alternately. 



