Induction- Coil Potentials. 585 



principal maximum spark-length at about d = '05 mfd., and 

 for the second (smaller) maximum at about C 1 = *3 m£d. 



Other cases may be obtained by varying the self-inductance 

 of the primary circuit. If, for example, the four sections of 

 the primary coil are connected in parallel Lj is reduced to 

 approximately one sixteenth, L 21 and L 12 to one quarter, 

 of their former values, and k 2 is unaltered. Calculating as 

 above, we find that the maximum value of U is given by 

 m=4*31, i. e. C x = 2*304 mfd. The nearest coincidence 

 (?? 2 =7n 1 ) occurs at m = 9*798, or C 1 = 1'013 mfd., and the 

 longest spark should be given by a capacity of about this 

 value. By experiment the longest sparks were found to 

 occur at 0, = 1*025 mfd., the variation being however very 

 slight over the range 1*0 to 1*05 mfd. 



A case of special interest is obtained by diminishing the 

 coefficient of coupling so as to bring in the ratio n <2 /n 1 ^=3. 

 The least possible value of ■n 2 /n l is *S(l + k)(l — k')> con- 

 sequently in order that ra 2 should be equal to 3%, k must not 

 be greater than '8. In this case it is also possible to make 

 the maximum value of U, and the ratio n^n^ — 3, occur at 

 the same value of the primary capacity. The necessary 

 value of k 2 is found by eliminating m between 



1 



m == 



1-k 2 



m + 1 + \/(m — 1 ) 2 + 4:k 2 m 



and '- — ,\ . _ = 9. 



m - l—\/(m — 1 ) 2 + 4Pra 



This leads to the equation 



91#— 164P + 64 = 



for P, giving P = *571, the other root being greater than 

 unity. 



Consequently with P=«571 (£ = -756), and LAs-429 

 L 2 C 2 , an exceptionally high secondary potential should be 

 given by an induction-coil. 



The most effective way of diminishing P is to introduce 

 external self-inductance into the primary circuit, since this 

 does not involve any diminution of L 21 . In the present case 

 (primary sections in series) the value of L x required to 

 give Zr = *571 is *241 henry, and the primary capacity 

 (C 1 = '429 LoCs/Lj) is *198 mfd. On trying the experiment 

 it was found that by introducing the necessary external 

 self-inductance the maximum spark-length for a given 

 primary current was considerably increased. Thus at 



