32 1) Prof. E. Taylor Jones on the Secondary 



We may neglect (&i — 8) 2 in comparison with 47r 2 » 2 so that 



_, , Ge-W 27rn-(k 1 -8)i, „ . . . 



i5 .g-i r =- • ; — s— s (cos Z7r^^ -f i sin lirnt). 



4zirn ±Tr z n" 



The real part of this is 



— , ; — 5— 9 {27r?i cos lirnt -j- (/n — 8) sin 27rtt£} 



1 Gg-M 



.2 



2 47r 2„2 cos \2irnt-e\ (14) 



7 ^ 



where tan = ~ . 



Similarly we find that the real part of B 2 e z ^ is also equal 

 to the expression (14), while B 3 is real and equal to G/47rVi 2 . 

 Thus the complete solution for V 2 is 



Y 2 =-^- 2 \e-^GO S (2irnt-e)-e- st }. 



Now the approximate value of 47r 2 >i 2 , obtained by neglecting 



the en°ect;of the resistances on the frequency, is j n , j^r; 



that is, the frequency is that of the secondary circuit with 

 the, primary closed. Thus G/47r 2 « 3 = — EL 21 /L l5 and finally 



V 2 =^{e-*'cos(2irt-0)--«r*} . . (15) 



The wave of potential in the secondary circuit at make thus 

 consists of a damped oscillation superposed upon an expo- 

 nentially decaying part, the initial values of the two parts 

 being ±EL 21 /L 1 . The greatest numerical value of the 

 expression (15) for V 2 occurs at a time t x somewhat less 

 than l/2/i, and will in all cases be less than 2EL 2 i/Li, the 

 value of the maximum when ~k x and 8 are zero. The ex- 

 pression 2EL 21 /L! may be regarded as giving the limiting- 

 value of the maximum potential at make, to which the actual 

 value would approximate if k x and 8 were indefinitely re- 

 duced. In actual cases, however, k A and 8 are probably never 

 so small as to allow the above limit to be very closely 

 approached. 



According to (15) the secondary potential at make is pro- 

 portional to the battery E.M.F. in the primary circuit, but it 

 depends to a much smaller extent (only through k Y and 8) on 

 the resistance in this circuit. These results agree with the indi- 

 cations of the secondary spark at make. For example, a certain 

 18 -inch coil, excited by a slow interrupter worked by hand, 

 gave at E = 20 volts, Ji x = 10 ohms, a make-spark about 0*7 mm. 



