236 Prof. E. Taylor Jones on most Effective Primary 



developed. Again, L 21 and L 2 are inversely proportional to 

 the magnetic reluctance of the core, and the factor L 21 / \/L 2 

 is therefore increased by closing, or nearly closing, the 

 magnetic circuit of the core*. 



On the other hand, the conditions do not seem so 

 favourable from the point of view of the other factor of (9), 

 viz. U sin <£. The values of the inductances and of the 

 coupling coefficient are not stated, but from the description 

 it would seem that the primary and secondary coils are very 

 closely coupled. If this is the case U sin cj) cannot be large 

 (see Table I. or fig. 3), and according to the present theory 

 the instrument should give a longer spark for a given 

 primary current, or the same spark-length at a smaller 

 -current, if suitable self-inductance were connected in series 

 with the primary coil. If, for example, the instrument is so 

 adjusted that lc* = 0'835 and u — 0*165 (n 2 ln x = l), and if L^ 

 and Qj are increased, the former by 46 per cent, and the 

 latter by 78 per cent., we should then have h 2 — 0*571, 

 w = 0*429, and the maximum secondary potential for a given 

 primary current should — apart from any effect due to change 

 in the logarithmic decrements of the oscillations — be increased 

 by over 20 per cent, without loss of efficiency. 



The Tesla Coil, 



In the case of the Tesla coil the difference of potential Y 2 

 of the terminals of the secondary coil, at time t after the 

 beginning of the discharge in the primary circuit, is (neglect- 

 ing resistances) 



v * = vAla-w+Wala (oos 2 ™ lt ~ cos 2 ™^> 



• ■ • (12) 



where V is the initial (discharge) potential of the primary 

 condenser. The primary potential difference is given by 



, r ^ T ni 2 n 2 2 l~l — 47r 2 7i 2 2 L 1 Ci 



Y '= V °;^?L #^ cos 2 ™'* 



1-WLA...W]. • • (13) 



ii 2 



cos 



These results may be deduced from the solutions given in 

 Fleming's ' Principles of Electric Wave Telegraphy and 

 Telephony/ 2nd ed. p. 264. The full expression for V 2 , in 



* See du Bois, ' The Magnetic Circuit/ p. 276, 1896. 



