208 M. E. Edlund on the Nature of Galvanic Resistance. 

 From this we obtain 



x= 



1 



1 



+ i + 



r, 



1 



which, as is known, agrees with experiment. Let us now ima- 

 gine such an arrangement of the conducting wires as is shown 

 in fig. 2. The conductor divides at a into two branches, which 



Fig. 2. 



again unite at b ; and the branches are con- 

 nected by the bridge c d. At the point c 

 the current divides into two portions, one of 

 which passes through cb t and the other 

 through c db. Then, according to what has 

 just been adduced in reference to the equality 

 of the resistances in the two conductors, we 

 must have the following expression : — 



W=*©r +* 4 r 4 . 



In like manner the current divides at a 

 into two parts. Then the resistance in ad 

 must be just as great as in ac and cd to- 

 gether ; for if the resistance in a d for ex- 

 ample were less, the current-intensity in 

 this conductor must grow until the resist- 

 ance became just as great as in the other two 

 conductors together, so that the current would have the same 

 resistance to overcome in order to arrive at d from a whether it 

 passed through a d or through a cd. wnetnei it 



We thus get 



If we will that no current traverse the bridge cd } therefore 



f-YofH be =0, the ratio which for thfs purpose must 



subsist between the resistances is obtained by dividing the first 



!°I mUla _ by ! h * laS ^ w H lG {t J S t0 be -memWed that i a this 

 ■s 4 . In this way we get 



case s l = s 3 and 



All these formulae are among the oldest known 

 «nffl,° r V, XampleS T n °\ re( * uisite > as those above given are 

 SfrlTanT 6 ^ aPPhCabllity ° f the CX « ** the £ 

 6. It has been remarked above, that, if galvanic resistant i, 



that the eleetnc fluid follows other hydrodynamic laws than those 



