348 On the Curves of Electromagnetic Induction. 



curves. If the curves figs. 2 and 5 are superposed as in 

 fig. 7, PI. X. ; we may resolve by the parallelogram of forces 

 at a number of points where the curves intersect. For this 

 purpose components are taken whose values are proportional 

 to the values of M for the curves, and, from the point where 

 any two curves intersect, lines are drawn proportional to these 

 values for the two intersecting curves. The component which 

 is proportional to the value of M for the curve of the first 

 set is drawn parallel to the axis of x ; and that for the curve 

 of the second set is drawn at right angles to it. Compounding, 

 we then obtain as resultant a straight line proportional to the 

 magnitude, and in the direction, of the resultant inductive 

 effect on the secondary coil in two positions at right angles to 

 each other. The arrows at the points of intersection of the 

 curves in fig. 7 shoAV the directions of these resultants. If 

 the curves had been obtained by means of an indefinitely 

 small secondary coil, the resultants would have been tangents 

 to the lines of force, and the straight lines drawn through the 

 same points at right angles to the resultants would have been 

 tangents to the equipotential curves ; but with the coils em* 

 ployed this is not strictly the case. 



The two sets of curves in the figures are so related 

 to one another that the one set may be viewed as a 

 modified form of the other. If we begin with the axes of the 

 primary and secondary coils parallel, and gradually increase 

 the angle between them, the curves of maximum induction, as 

 it were, carry the curves of constant induction round with 

 them, while the curves of zero induction, in moving round, 

 always form lines of demarcation which separate the positive 

 from the negative regions. The positive curves of constant 

 induction at the same time become distorted and gradually 

 contract, the linear dimension of each curve becoming less 

 until the angle between the axes is about 90°. When this 

 angle has become exactly 90°, the positive curves of constant 

 induction have become separated into two distinct divisions 

 by the intervening zero-curve (which coincides with the axes 

 of x and ?/), so that they then occupy two opposite quadrants. 

 Now, both the positive and the negative curves move round 

 together ; but as the negative curves are carried round they 

 become distorted and gradually expand, the linear dimension 

 of each curve becoming greater until the angle between the 

 axes of the coils is 90°. When this, which is the extreme or 

 limiting case, has been reached, the form and linear dimension 

 of any negative curve are the same as those of either of the 

 two corresponding positive curves for which the value of M 

 is the same, and the two sets of negative curves, which 



