330 Prof. E. Taylor Jones on the Secondary 



in the ratio 4/1. But if the total primary resistance Ri m 

 maintained at its original value, the ratio R1/L1 is increased 

 in the ratio 16/1, and consequently the damping factors k% 

 and 8 are greatly increased, and this tends to reduce V 2m . 

 On the whole, however, there is usually a very marked increase 

 in the spark-length at make when the primary connexion is 

 changed from series to parallel. Thus, with the four 

 primary layers of the 18-inch coil in series (E = 98 volts,. 

 R x = 10 ohms) the spark-length at make between the ball 

 electrodes was 4' 5 mm.; with the layers in parallel and the 

 same values of E and Rj the spark-length was 13*1 mm. 

 If, instead of keeping Rj constant, the resistance were re- 

 duced in the same ratio as L 1? the difference between the series 

 and parallel connexions would be still greater, owing to the 

 fact that &! and 8 are then unaltered by the change of connexion. 



The nature and to some extent the magnitude of the above 

 effects may be illustrated by the following numerical results, 

 in which the values of n, k u and 8 are calculated from the 

 cubic equation (6). It should be borne in mind that the 

 coefficients of equations (4) and (5), i. e. the inductances 

 and resistances, are not strictly constant, but are mean 

 values for the time-interval t x immediately after u make/' 

 and that during this short time the primary current does not 

 rise to more than a small fraction of its maximum value, sa 

 that the core is not strongly magnetized and its permeability 

 is small. The values here assumed are typical of a fairly 

 large (18- or 20-inch) coil. j 



The expression in the brackets of (15), with sign changed, 

 that is, — £~**'cos (2irnt — 6) -{-e~ st , is denoted by <£, its 

 maximum value by <£ m . 



The following values are common to all the cases : — 

 Lsi/L^lOO, /c 2 = 0'75, L 2 C 2 = 7-66.10- 8 c.g.s., 

 C 2 = 0-000053 mfd., R 2 = 40000 ohms, 



E- 100 volts. 



(I.) 1^=13 ohms, L 1 = 0-145 henry, R 1 /L 1 = 89'6. 

 By (6) 2t™ = 7220, ^ = 191*5, S=88'5, 

 </> m = l-883, V 2?n =18830 volts. 



(II.) 1^ = 8 ohms, L x = 0-145 henry, R 1 /L 1 = 55'2, 

 2t™ = 7223, ^ = 139-5, 8 = 52*5, 

 <£ m = 1-918, Y 2m = 19180 volts. 



These two examples illustrate the effect of reducing the 

 primary resistance. The difference of 5 ohms causes a con- 

 siderable reduction in k 1 and 8; but since these quantities 

 are already rather small, the effect on <f> m , and therefore on 



