Differential Galvanometer for measuring small Resistances. 247 



therefore the current from the battery is 



E _ E _ E(# + r + 2ff) 



b j (x+ff)(r+9) b(x + r + 2g)+(x + g){r+g) 

 x + r-\-2g 



This current divides between the two paths x+g and r-\-g in 

 inverse proportiou to their resistances ; therefore the current in 

 9 is 



x + r + 2g b(x + r + 2g) + {x+g){r+g) 

 and the current in g' is 



G> = B x °° +9 = EQK-fff) 



x + r + 2g b(x + r + 2g) + (x+g){r+g)' 



The effective current (that influencing the needle) will be the 

 difference of G and G', say 



D = ^*) . . (1) 



1 b(x + r + 2g)+(x+g){r+g) * J 



By the second method, the resistance external to the battery is 

 xg rg 



f+9 r+g' 

 therefore the current from the battery is 



E _ E E(*+g)(r+g) 



b | #ff ] r 9 b{x+g){r+g)+gx(g + r)+gr{g + x)' 

 ss+g r+g 



The current in g is 



x ~Ex(g + r) 



G = Bx 



x+g b(x+g){r+g)+gx{r+g) +gr{x+g)' 

 and the current in g 1 



G f = B x _1_ _ Vr{g + x) 



r+g b(x+g){r+g)+gx(r+g)+gr(x+g) 



The effective current will therefore be 



D = G-G'= %(*-*•) 



b{x+g){r+g)+gx(r+g)+gr(x+g) 



Equations (1) and (2) give the effective current in each 

 case ; and we may ascertain the relative sensitiveness of the two 

 methods by comparing D 1 and D 2 . 



D 2 b [x + r + 2g) + (x +g) (r +g) 



B, b(x+g){r+g) +gx{r+g) +gr{x+g) 



*9> 



