Induction- Coil Potentials. 581 



Calling this m, and writing a for l/87r 2 L 2 C 2 (l — k 2 ), we have 

 n 1 2 = a(m + l — \/(m — l) 2 + 4P>?i), 

 n 2 2 = a(m+ 1 + \/(m~l) 2 + 4Fm). 

 Thus 



nj 2 + n 2 2 = 2a(m + l), 



mW = a 2 {(m + l) 2 -(m-l) 2 -4Pm}, 

 = 4ma 2 (l-F), 

 O'2-^i) 2 = 2a{m + l)-±a\/m{i-k 2 ), 



n x W 2mg(l — P) 



K-^i) 2 ~ m + l-2-\/wi(l — P)' 



and the upper limit to Y 2 is, for given L 21 , L 2 C 2 , and z , 

 proportional to the square root of this quantity. 



If we wish to consider the effect of varying the primary 

 capacity only, then the upper limit to V 2 is proportional to 

 the square root of 



m 

 m + l-2\/m(l-k 2 y 

 or if 



1 LA 



m Li 2 U 2 

 to the square root of 



1 + u— 2Vw(l — A 8 )" 



This expression has a maximum value of ljk 2 at w=l — P, 

 and is equal to unity when w=0, ?'. 0. when Ci = 0. Con- 

 sequently, if the resistances of the coils were negligible, the 

 secondary potential might be expected to be greatest when 

 the primary capacity Ci has a value of about L 2 C 2 (1— A ,2 )/L l5 

 and this maximum value would be about 1/k times the value 

 the potential would have if the primary condenser were 

 removed altogether. 



It is well known that for a given primary current there is 

 a certain value of the primary capacity that gives a maximum 

 secondary sparking distance with an ordinary interruptor *, 

 but it has been usual to attribute the inferiority of smaller 

 capacities to their failure to prevent sparking at the inter- 

 ruptor, and the view appears to be generally accepted that 

 with a sufficiently rapid interruption of the primary current 



* Cf. Walter, Wied. Ann. lxii. 1897; Miziuio, Phil. Mag*, xlv. 1S9S. 



