242 Mr. E. C. Eimington on 



Then 



EBD 2 P K 2 C 



q ~ </>(C + D) + D(B + C)}{G(B + C) + B(C + D)} 



EpK^ 



-(P p B + CuG GC O + DV 



Now the throw is proportional to q^/Q for a galvanometer 

 whose coil-volume is constant. Therefore the throw is pro- 

 portional to 



EpK 2 



/P,f, B + Cyi/G , (VG C + D V 

 VD C + C AD + BD + wg/ 



and this is to be a maximum ; which it obviously is when 



/n B + C__C + D 1 r ,_ B(0 + D) 



ViT -^D"-^D~^7G' ° r U - B + C * 



If A and D are infinite, the higher the resistance of the gal- 

 vanometer the better. Also, in this case, 



_ EpK 2 BpK 2 



Here q is largest when C is largest. 



To find the conditions under which a telephone may replace 

 the galvanometer : — 



In equation (1) we have 



A 2/ =A(C + D)g-(A + B)D^. 



Now, in order to employ a telephone, y must always be zero. 

 Therefore 



A dq-i D dq 2 



A 

 But 



Hence 



Now, since there is no current in the galvanometer, its 

 resistance may be anything : let it be zero. Then K x dis- 

 charges through -r — sgj and K 2 through A ■ tv 



A + B dt ~ 



"C + D dt' 







A 

 A + B" 



D 



= C + D , since 



AC = 



= BD 



dq x _ 



dt ' 



_dq 2 

 dt' 







