148 Prof. E. Taylor Jones on the Potential 



of the armature. The effective resistances include variable 

 factors depending upon eddy currents and hysteresis in the 

 core and pole-pieces. It is to be understood that the above 

 symbols represent mean values of the various quantities during 

 the short interval of time between break and the moment of 

 maximum secondary potential. 



2. Calculation of the Secondary Potential. 



Calling the current in the primary coil t ls the current 

 entering the secondary coil at J i z , the current entering 

 the condenser i 3 (the directions being as shown in fig. 1), 

 the potential difference of the plates of Cj V/, that at the 

 sparking-plug V 2 ', we have the following equations : — 



i*£.+i»a?+BA+Vi' = b, a) 



I*^+La^+BA+V,'-V 1 '=j ? B, ... (2) 



where E and #E are the induced E.M.F.'s in the primary and 



secondary coils due to the roiation. q is approximately equal 



to the ratio of the secondary and primary turns. 



Further, n . 



*!— H— h = 0? (3) 



H-P.^> (*> 



** = C ^> ( 5 > 



Thus ^=^+0^. . . . (6) 



Substituting for i x and t 3 in (1) and (2) we have 



LlGl SF + (Ll + Ll2) ° 2 IF + Kl V 1 ~dT + Lr Wj 



+ V/ = E, (7) 



,T ^T ^P^' + T O^'+EO^' 

 (L s +L sl )C 2 -^ r +l J21 1 -^ 5 -+K 2 2 -^ 



+V s '-V l '=#. (8) 



We shall now make two assumptions with the object of 

 simplifying the calculation, viz. : — 



(1) That the resistances are negligible : this may be 

 assumed if our object is limited to the calculation of 

 frequencies, initial amplitudes, and the determination of the 



