1S72.] Louis Sclrwendler — On Differential Galvanometers. 151 



would be those which would make the reading most delicate near balance, 

 when the variation takes place ia.w',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 expres- 

 sion I ', we should have obtained in a similar way the following relation 

 between g and g' 



(w' — g<) ( W +g) ±f( w + W ' + g—g>) = 2(g> + w'+f) 



j-(g'-w') 2^V?-^-'' 



which equation connected with the other 



II' 



dcf> 

 dg' 

 further we "will substitute : 





&A 

 ' Ks/g dg ' 

 1 N 2 



{ N 2 



d A 



d g 

 d A 



a 

 a 



= - (P ' + Q ') 



dg' 

 Thus we have the following differential equation : 



(P — q)dg — (F'+Q')dg' + x[ a dgr + d<jr ') = o 



A being the undetermined factor. From this equation we have : 

 P— Q + A a = 

 and — (P ' + Q ') -f A j3 = 

 or \ eliminated : 



_ F ~ Q — P'-t-Q' 



but we have always : 



_Q __Q^ 



thus we have as end-equation : 



P _ _ _Pj[ 

 <x j8 



or the value for P, P ', a and /3 substituted we have : 



2g dN 2 £S 



dg _ d g ' 



pg'(g-w) 2 s/g sjg ' — p (g + «>) 

 further substituting 



[I 



and reducing as much as possible, we have 



(w — g)(w' + g ') -{./ (w + w' + g '—g) __ 2 (g -f- w - f /) 



P (g — w) g' ~ 2 s/g \/g' — i? (g + "0 



which is the equation II as given above. 



In quite a similar manner, equation II y can be found, it must only be remembered 

 that it is more simple to use expression I ' for the purpose than I. 



