14S Louis Schwendler — On Differential Galvanometers. [No. 2, 



andG'^E^ 



N 



where N = (g + w) (g( + to') + f(g + w + g' + w'). 



Thus substituting in I and I ' we get either 



N V m 11 ^/g v,y J / 



or rf»oc*»'»'E^- f( y / + w /) i^ *X (* + «,)\ p 



N V*' y w&'ra' v/y / 



aud either A or A ' is the factor which at balance becomes zero. 



The coefficient j— means, therefore, nothing? else than what is 



m 11 s /g ° 



generally called the constant of the differential galvanometer, i. e., the num- 

 ber by which the total resistance in one branch of the differential galvanometer 

 has to be multiplied, in order to obtain the total resistance in the other branch, 

 when balance is established. This constant of the differential galvanometer 

 is a given function of g and g', the resistance of the coils, and as g andy' 

 are to be determined, by being variable, it cannot be considered a constant 



in' 11 



in this investigation. But the factor is entirely independent of any 



of the resistances, it represents what may appropriately be called the 

 ' mechanical arrangement of the differential galvanometer, and may be 

 designated by p. It must be borne in mind that p represents an absolute 

 number, which theoretically may be anything with the exception of o and oo. 

 If p has a value equal to either of these two limits, the instrument would be 

 a simple galvanometer with a shunt, and not a differential galvanometer. 

 The deflection a may now be written more simply, as follows : — 

 A 



S °aK|(y'+,'-f| (? + «0) = K^f-A I 



r 



K and K ; being independent of g and g ', and also of w and to '. 



N is a known function of all the resistances in the differential circuit. 



A and A ' are similar functions of g and g ', w and w 1 and which functions 

 become both zero at balance. 



For the further investigation, only one of the two possible expressions 

 of a will be used, viz. equation I. 



