8 Louis Schwendler— O/i Differential Galvanometers. [No. 1, 



The wire used for filling each coil must he invariahly of the same 

 diameter, otherwise a maximum sensitiveness is impossible. 



How the above simple law expressed by equation e would be altered, 

 when the given suppositions were not fulfilled, must be found by further cal- 

 culation, but as the latter is intricate and a more general result is not 

 required in practice, I shall dispense at present with this labour. 



Special Differential Galvanometers. — Here shall be given the special 

 expressions to which the general equations a, h, c and d, are reduced when 

 certain conditions are presupposed. 



\st case. — When to and lo', the two resistances at which balance is 

 arrived at are so large that f the .resistance of the testing battery can be 

 neglected against either of them without perceptible error. Substituting 

 therefore y ^ in equations a, and h, we get : 



10 



^ =3 ^• 



g'=='^ h. 



^ 3 



and the other two remain as thc^.y are namely : 



p^ =— c, 



Q=^ i. 



w 

 2nd case. — When the battery resistance f cannot be neglected against 

 either w or w\ but when the two resistances at which balance is arrived 

 at are invariably equal. 



Thus substituting in the general equation 



w = w^ = IV 

 we get 



/ = 1 ^• 



C =1 ^. 



Srd Case. — When the conditions given under 1 and 2 are both fulfilled 

 or 10 = w^ = w 



and /=0 



then we have 



9=9 =ff-=- 3 ^'*- 



p2 = 1 ^• 



C =1 ^• 



The very same result which was obtained by direct reasoning at the 

 beginning of this paper. 



