154 



Prof. E. Taylor Jones on the Potential 



The two conditions (34) and (38), determining the most 

 effective adjustments o£ the system from the point of view 

 of spark-length, are the same as those which hold in the 

 case of an ordinary induction-coil, for which it has been 

 shown * that they are also the conditions that the energy 

 should exist, at the time £ = 1/4^, entirely in the electrostatic 

 form in the secondary circuit. The value of U, however,, 

 in the magneto differs from that in the induction-coil problem 

 in that in the latter s is replaced by unity. 



When the value of s is known we can, by combining 

 equations (17) and (38), find the value of k 2 corresponding 

 with any of the values of ?? 2 /rii given by (34) . For example, 

 if 5=1*04 we find for ^2/^ = 3, & 2 = 0*554; for n 2 /n 1 = 7 y 

 & 2 = 0-832; for nJn^ll, P = 0'897. If the coupling has 

 one of these values, and if the capacity of the condenser is 

 such that L 1 C 1 /L 2 C 2 = 1 — k 2 , Y 2m is then given by the 

 equation 



Y *» = i °\/k\/ 



L1 + L21 

 Li + L 12 



(39} 



The expression on the right of (39), with (g+l)E added 

 to it, represents the greatest secondary potential attainable 

 by any magneto in which the circuit connexions are 

 arranged as in fig. 1. 



If k 2 has not one of the above special values Y 2m is not 

 given by equation (39), but it can always be expressed 

 in the form f 



(Lj + L 21 )z'q 



U sin <j), 



(40). 



where U is given by (37), and 



</> = 

 </> = 



2irn l .„ n 2 . , , 



it — is between 1 and 



n^ + n 2 n x 



kirn-i 



ni+n 2 



n! + n 2 



, 5 „ 9, Y 

 1 9 ,, lo, 



(41) 



and so on. 



* Phil. Mag. Jan. 1915, p. 2. 

 t Phil. Mag. Aug. 1915, p. 226. 



