Induction^ Coil Potentials. 571 



diminution of the intensity of magnetization of the core with 

 increasing frequency is not sufficient to account for the large 

 falling off in the value of k 2 shown in Table II.; and we may 

 conclude that the drop in k 2 is due to the change in the dis- 

 tribution of the current in the secondary coil, i. e. that as the 

 current changes from the uniform to the cosine distribution, 

 the coefficient L 12 diminishes more rapidly than L 2 . It would 

 be interesting to make similar measurements of k 2 for coils 

 of different dimensions and forms, especially coils with non- 

 magnetic cores. 



In the above method for measuring k 2 the oscillations 

 were all started by sparking to the terminals of the secondary 

 coil. There is, however, another way of setting up the 

 oscillations with the primary coil closed, which may be 

 referred to here. If the interruptor of an induction-coil is 

 connected in a shunt across the primary coil, instead of being 

 in the main circuit as usual, when contact is made the 

 primary coil becomes short-circuited and its current begins 

 to decay exponentially. At the same moment oscillations 

 of small amplitude are set up in the secondary, and these are 

 the natural oscillations of the secondary with the primary 

 closed. The potential at the terminals of the secondary coil 

 may be represented by the expression ae~ kt -f b sin nt, and the 

 electrometer (being connected idiostatically) shows a de- 

 flexion which is proportional to the square of this quantity. 

 This includes a term proportional to sin nt, and another 

 proportional to cos 2nt. The curve should therefore show 

 an oscillation of frequency nl2ir and another of twice this 

 frequency. As a rule the slower oscillation is much the 

 more prominent, though traces of the octave appeared in 

 some of the photographs. 



The most prominent feature of the curves obtained was, 

 therefore, an oscillation of frequency n/27r, i. e. the frequencv 

 of the oscillations of the secondary with primary closed, and 

 not twice this frequency as is the case in the sparking 

 method. 



This " short-circuiting" method was tried with various 

 capacities in the secondary circuit. Owing to the smallness 

 of the amplitude of the oscillations, the most sensitive form 

 of electrometer had to be used. The potential at the 

 secondary terminals was in fact not sufficient to produce a 

 1 mm. spark between the ball electrodes. 



The frequencies obtained by both methods are given for 

 comparison in Table III., and one of the curves obtained by 

 the short-circuiting method (no condenser) is shown in 

 Plate VIII. fig. 6. 



