412 Mr. G. Chrystal on Bi- and Unilateral 



the varying residual magnetism of the iron core in the induc- 

 tion-coil. 



I next made some experiments to determine whether, other 

 things being equal, C varies as I 2 , which by the above theory 

 it ought to do. With this object in view different resistances 

 were interpolated in the secondary, every thing else being- 

 kept the same. The resistance of the secondary, including the 

 galvanometer, was about 2768 ohms. Resistances of 1000 

 and upwards were put in, a and 6 observed, and the resulting 

 values of C calculated. 



If we suppose the time which elapses between two successive 

 interruptions . of the primary to be so long that the current in 

 the primary arrives at the steady state in the interval, and the 

 induced currents in the secondary due to make and break do 

 not interfere, then it is very easy to calculate the value of I 2 

 for the induction-currents. The result is 



i -2NQl i+ LQ + NP/' • • • {A) 



where L, N are the coefficients of self-induction for the pri- 

 mary and secondary, M the coefficient of mutual induction, 

 and P and Q the respective resistances, j the steady current in 

 primary, and n the number of interruptions per second as 

 before. Of the two terms within the bracket the first is con- 

 tributed by the current due to the break, the second by that 

 due to make. 



Now with an induction-coil such as I used — where L = '013, 

 M = -79, N = 52, and P = 2 (say) and Q =2768 (these num- 

 bers are very rough estimates deduced from experiments per- 

 formed for practice) — the time-constants of the coil are such 

 that with tuning-forks such as I used for producing the break 

 (which gave n = 50, 100, or 200) the above formula is very 

 far from being applicable. 



In fact the result is much nearer what we should get by 

 assuming that the primary current followed the sine law, in 

 which case we should get, A being the maximum electromotive 

 force in primary, and v = 27T7i, 



i V 2 M 2 A 2 

 F= (LN-M 2 )V + (N 2 P 2 2 + 2M 2 PQ + L 2 Q 2 > 2 + P 2 Q 2 ' ' ^ 



in which case it is easy to see that if v be big enough, the 

 effect on I 2 of doubling and trebling the resistance Q will be 

 comparatively small. This is confirmed by experiment, as the 

 following Table will show : — 



