426 Mr. T. H. Blakesley on the Differential 



Again, from (v.) an 

 by differentiating (iv.), 



dC d 2 V 



Again, from (v.) and (iv.), since — = — K -j-^, obtained 



V + RK^+LK~=0. 



dt dt 2 



This is the differential equation of V. 



Thirdly, differentiating twice the equation 



V+F-RC = 0, 



d*V , d*F p rf 2 G_ n 

 dt* + d* K <fc* ~ U ' 



from (iii.) by differentiation it is seen that 



d?C_ ±dF 



dt* " L <ft ' 

 and from (iv.), 



&Y _ _^dG 



^ 2 " K dp 



IF 



which is further reduced to^ y- by (iii.). 



Hence F d*F R dF _ 



KL + £&" + L ^~ > 



or 



dF <^F 



the differential equation of F. 



It is thus clear that the variables V, F, E, C, all have the 

 same form of differential equation, viz. : — 



E + KEf + KL«-0. 



Of course, to make this equation homogeneous, 



KR is of the order (time) ; 

 KL „ „ (time) 2 . 



KL may be written KR . ^ , or still better —~- . -75-. 



If we write 2L 



KR 



and —=tz, 



t x and t% are time-constants of the circuit, and the differential 





