432 OHM ON THE GALVANIC CIRCUIT. 



at its extremities must still always remain a, and consequently 



be 



a a. a. a. 



A " T "^ 77 ^ A"' 

 or 



A ~ A "^ A' "^ A"' 

 which equation serves to determine the value of A, But if this 

 value is known, and we call A the sum of all the tensions in the 

 circuit, and L the reduced length of the non-divided portion of 

 the circuit, we obtain, as is known, for the magnitude of the cur- 

 rent in the last-mentioned circuit 



A 

 L + A' 



which is equal to the sum of the currents occurring in the separate 

 branches. Now since it has already been proved that the cur- 

 rents in the separate branches are in inverse proportion to one 

 another as the reduced lengths of these branches, we obtain for 

 the magnitude of the current in the branch whose reduced 

 length is A, 



A A 



L -F A • A ' 



in the branch whose reduced length is A', 



A A 



L + A • A' ' 



and in the branch whose reduced length is A", 



A A^ 



L + A • A"* 



This remote, and hitherto but slightly noticed peculiarity of the 

 galvanic circuit, I have also found to be perfectly confirmed 

 by experiment*. 



I herewith conclude the consideration of such galvanic cir- 

 cuits which have already attained the permanent state, and 

 which neither suffer modifications by the influence of the 

 surrounding atmosphere, nor by a gradual change in their che- 

 mical composition. But from this point the simplicity of the 

 subject decreases more and more, so that the previous element- 

 ary treatment soon entirely disappears. With respect to those 



* Schweiggei's /«A;'6«c/?, 1S27. 



