Mr. Louis Schvvendler on Differential Galvanometers. 169 



most delicate near balance, when the variation takes place in 

 ic^ , i. e, the external resistance belonging to the coil g\ 



If, instead of differentiating the expression for a with respect 

 to w^ by using the expression (I.), we had done so with respect to 

 w by using the expression (!'.), we should have obtained in a 

 similar way the following relation between g and g\ 



¥-9') [i^-^9) ■\-f{iv + ^^' + 9-9') _. 2 (y + ^^M- /) ,..,. 



which equation, connected with the other, 

 g^ + w' Vg 



P V^' 



+ z^ = A' = 0, .... (1) 



gives all that is necessary to determine g and g', being those 

 values which would make the reading at or near balance most 



X being the undetermined factor. From this equation we have 



p _Q +x«c=0 

 and 



-(P'+Q') + Xi3 = 0; 



or^ X eliminated^ 



_ t^-Q _ P-fQ \ 



eft /3 ' 



but Ave have always 



thus we have as final equatiouj 



a ~ (i' 

 ox, the value for P, P', u, and /3 substituted, we have 

 d^ 2d^ 



dg dg' 



pg\g-w) 2s/gsjg'-p{g + w) 



further substituting 



=g +w 4-/, 

 dg 



d^ , , ^ 



and reducing as much as possible, we have 



{w-g){w'^g')-\-f{w+w'-\-g'-g) _ 2(.y + w+./) 



which is the equation (II.) as given above. 



In quite a similar manner equation (II'.) can be found; it must only be 

 remembered that it is more simple to use expression (I'.) for the purpose 

 than (I.). 



(II.) 



