584 Prof. E. Taylor Jones on 



As far as these experiments go they do not support the 

 view that the longest spark can be obtained without any 

 primary condenser, but rather indicate a most effective 

 capacity at about *05 mfd. 



The theory also points to this result. For, returning to 

 the expression for the upper limit to V 2 , which may be 

 written L 21 z U/\/L 2 O 2 , where 



U* = m 



m+l-2x/m(l-P)' 



and m = L^CyLjCx, we find that in the present case U has a 

 maximum at m = 4'31, i. e. Ci = '144 mfd., but that it does 

 not vary by more than 3 per cent, over the range (\ = *3 to 

 •05 mfd. 



Now the expression for U is arrived at on the supposition 

 that the maxima of the two waves occur simultaneously, and 

 these coincidences will take place (the resistances being 



neglected) when w 2 / w i = 3, 7, 11, The values of n 2 /n 1 



for various values of m can be calculated from the equation 



n 2 m 



+ l-f\/(m-l) 2 + 4Pm 



The least value of n 2 \n x occurs at m = l (i. e. L 1 Ci = L 2 C 2 ), 

 and is 3*896 at C 1 = , 62 mfd. The ratio ^2 = 3^, therefore, 

 doe* not occur. 



The next coincidence (« 2 = 7>i 1 ) occurs at m = 9*798, giving 

 C^'063 mfd., and this is the coincidence which comes 

 nearest to the maximum value of U. It is also within the 

 range over which U is practically constant and equal to its 

 greatest value. The longest spark should therefore be given 

 by a primary capacity of about *06 mfd. As described 

 above the value actually found was *05 mfd. 



At w 2 = 5%, (C 1 =*154 mfd.) the maximum of the long- 

 wave occurs simultaneously with a minimum of the other, 

 and a shorter spark is to be expected. At C^'3 mfd. 

 (72 2 /';i 1 = 4*194) the maximum potential will be rather greater 

 than at *154 mfd. in consequence of the closer proximity of 

 the maxima. These two cases were worked out by the 

 expression (1), the damping factors k Xi k 2 , and the phase 

 angles S l7 8 2 being neglected, with the result that '3 mfd. 

 gives a maximum potential about 5 per cent, higher than 

 that given by *154 mfd. A similar calculation shows that 

 the maximum potential in the case L 1 C 1 = L 2 C 2 , L e. 

 G 1 — '62 mfd., is about 10 per cent, less than that given 

 by *3 mfd. The theory thus accounts for the observed 



