2 Louis Schwendler — On Differential Galvanometers. [No. 1, 



" mechanical arrangement'' of the differential galvanometer under consider- 

 ation. 



By these three equations, which are independent of each other, y, g' 

 and p can be expressed in terms of w, w' and f. 



By equation I we have at or very near balance : 



p = — y~, winch value substituted in equations II and II ' 



g-Yw ^gi 



gives : 



(,, _ g) (,,/ 4. c,t) ^rf{^o^■ 10' + g' - g) _ 2 {g ^ to + f) ^ ^ 



{g' ■\'iv') {g — w)g' {g' — W) (y-f ^^) 



and 



{w' — g') iii^-^g^^-fiwArii^'^g — g') ^ 2 {g'-¥io'-Vf) ^^, 



{9 +^) {9'—^^')9 (9 — ^) (y'+^O 



and from these two equations g and g' may be developed. 



This is best done by subtracting equation II from equation II' when 

 after reduction we get : — 



(w 'g — wg (w '9 •¥'^^9' "V gg' -^r iviv ') = — f{g +g' -\- tv -^tv') {iv 'g — wg ') 



III 



Now it must be remembered, that with respect to our physical problem, 

 y, w^ w\ g and g' represent nothing else, but electrical resistances, and that 

 they have, therefore, to be taken in any formula as quantities of the same 

 sign (say positive). 



Consequently the above equation III would contain a mathematical 

 impossibility (a positive quantity equal to a negative quantity), whenever 

 the common factor w'g — wg' is diiferent from zero. 



In other words equation III can only be fulfilled if we always have : 



w'g — wg' = IV 



This simple relation between the resistances at which balance arrives 

 and the resistances of the two differential coils, expresses not only the 

 necessary and sufficient condition under which a simultaneous maximum 

 sensitiveness can exist, but it also affords an easy means of getting at once 

 those special values of y, g' and p, which only solve the physical problem. 



Substituting the value of either g or g\ as given by equation IV in 

 equations II and II' and developing g and g' we have : 



the negative signs of the square roots having been omitted since they would 



*g' 



* See note at end. 



