346 



Mr. W. Grant on the Curves of 



Table VI. {continued). 



Curve 5, M=2. 



Curve 6, M = 4. 



X. 



y- 



y'- 



X. 



y- 



y'- 



08 



10 

 1-6 

 20 

 30 

 4-0 

 5-0 

 5-2 

 6-0 

 7-0 

 8-0 

 9-0 



6*69 

 0-92 

 1-37 

 2-23 

 4-13 



5 54 

 617 



7-27 

 7-76 

 8-54 

 8-91 

 9 



8-85 



8-41 

 7-58 

 5-56 



1-6 



1-8 

 2-0 

 2-5 

 30 

 4-0 

 50 

 5-5 

 60 

 6-5 

 7-0 



1-55 

 1-9 



245 

 3-62 



5-5 



576 



6-0 



6-45 



6-72 



6-96 



6-82 



666 



6-31 



5-78 



4-61 



The positive and negative curves of the second set have the 

 same form, and are positive in one quadrant and negative in 

 another alternately. They have been treated as an indepen- 

 dent set of curves ; but, as will afterwards appear, they are 

 not so, but are merely a special case in which the positive 

 curves of the first set have become separated by the interve- 

 ning zero -curve which coincides with the axes of x and y. In 

 this case any corresponding pair of positive and negative 

 curves, besides having the same form, have also the same 

 linear dimensions. In every other case the form and linear 

 dimensions of any corresponding pair of positive and negative 

 curves are different, the linear dimension of the negative 

 curve being always less than that of the positive. Hence 

 this is the case in which the linear dimension of any negative 

 curve is greatest, and in which that of the corresponding posi- 

 tive curve is least. The second set of curves, for the whole of 

 the magnetic field, are given in fig. 6, PL IX., which shows the 

 relative positions occupied by them in the various quadrants. 



When a system of curves of constant induction have been 

 obtained for a given pair of coils, they may be used to give 

 the total inductive effect produced on one of the coils by a 

 given change of relative position while the other coil is 

 traversed by a current of known strength. To simplify the 

 statement, suppose the primary coil in which there is a current 

 of uniform strength C to remain at rest while the secondary 

 coil is moved from a position such that the coefficient of mutual 

 induction is M l5 to a position in which this coefficient becomes 

 M 2 . Then, if t is the time occupied by the movement, the 



