Ml'. Louis Schweudlei' on Differential Galvanometers. 165 

 different forms — either 



or 



«o«„.^,(G-'i;i^G') . . : (I.) 



«=aW«Vyg^,gG-G'), . . . (F.) 



which means that any deflections observed may of course be con- 

 sidered due to either coil. In the first form (equation I.) it is 



considered due to the coil a when a current G ;^G' 



mn V g 



flows through it ; in the latter form (equation 1'.) it is considered 



mn y Q 

 due to the coil o' when a current —v-, -^G — G' flows throus;h it. 

 •^ 7?i'/i' s/ g^ ^ 



Now, considering that the same battery E has to supply the 



current to both the coils, we have 



and 



G = L-^ 



G'=E^^^' 

 ^ N ' 



where N = (^ + w) [ij + w^) ^f[g + m; +^' + 1^') • . 

 Thus, substituting in (I.) and (!'.), we get either 



A 



«°OcmnE^(y + ^.'-^^^(^ + ^.)), . . . (I. 

 N \ mn A/g '-^ ^ y ' ^ 



or 



«°o:mWE^((y+«,')£,^,-(^ + t«)); . (I'.) 



The coefficient -^^^ /^ means, therefore, nothing else than 



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



mn ^g 



what is generally called the constant of the differential galvano- 

 meter, i. e. the number 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 galva- 

 nometer is a given function of g and g^ , the resistance of the 

 coils ; and as g and g' are to be determined, by being variable, it 

 cannot be considered a constant in this investigation. But the 



