500 OHM ON THE GALVANIC CIRCUIT. 



nitude of its cun-ent, which results fi-om the above-found for- 

 mulae, is 



A 



T V w ' 



L + — + r— 

 am w 



If now a conductor of the length v -^w, and of the power of con- 

 duction X with the same section, being taken instead of the two 

 former, leaves the current of the circuit unchanged, then must 



whence we find 



V vy v + w 



a CO b CO X CO 



_ ab [v +'w) 

 b v-\- aw 



But it is perfectly indiiFerent for the magnitude of the cur- 

 rent, whether the entire length v be situated near the entire 

 length 10, or any number of discs be formed of the two, which 

 are arranged in any chosen order, if only the extreme parts re- 

 main of the same kind, as otherwise a change might result in 

 the sum of the tensions, consequently also in the magnitude 

 of the current. If we extend this law, which holds for every 

 mechanical mixture, likewise to a chemical compound, the above 

 .value found for x evidently gives the conducting power of the 

 compound, where, however, it has been taken for granted that 

 the two parts of the circuit, even after the mixture, still occupy 

 the same volume, for v and lo are here evidently proportional 

 to the spaces occupied by the two bodies mixed with each 

 other. 



If we now apply this result to our subject, and therefore 

 put, instead of v and w, the values z and 1 — z, which express 

 the relations of space of the two constituents in the disc M, we 

 obtain, when a denotes the conducting power of the one consti- 

 tuent A, and b the same for the constituent B ; further, x the 

 power of conduction of the mixture of the two contained in the 

 disc M, the following expression for x, 



_ ab 



a+ [b — a) z' 



37. Having thus determined the power of conduction at each 

 place of the extent in the act of decomposition, there only re- 

 mains to be ascertained the nature of the function u at each 

 such place ; and since all tensions and reduced lengths in the 



