of Electrical Conductivities. 83 



galvanometer). Let the resistance of this wire be w. Then 



J 3 =— J 2 , J 4 =— Ji. 



Further, we have, on one hand. 



P 2 — V 3 = ivJ 2 , 

 and, on the other, 



P 2 — P 3 = («21 — «31 ~ a 2i + «3i) Jl + (#22 — #32 — #23 + #33) ^2* 



Putting 



#21 — #31 — #24 + #34 = P; 

 #22 — #32 — #23 + #33 = r ) 



we hence get 



pJ 1 =(w—r)J 2 ' 



The quantity p can be qualified as the value which P 2 ~P 3 

 has in the case that J 2 =— J 3 = 0, and j x =— J 4 =l. If the 

 conductor is a very long thin wire and the surfaces 1 and 2 

 are situated quite close to one end, surfaces 3 and 4 to the 

 other, p is the resistance of the conductor ; with another form 

 of the conductor, p may be named one resistance of it. 



Let us now imagine a second conductor, besides the one 

 above-mentioned, possessing also the properties attributed to 

 that. To the quantities p and r in that, P and R in this may 

 correspond. Electrode surfaces 2 and 3 of the second con- 

 ductor are to be connected to the ends of the second wire of 

 the differential galvanometer, whose first wire touches with its 

 ends the surfaces 2 and 3 of the first conductor; electrode 

 surfaces 1 and 4 of the second conductor are to communicate 

 respectively with the electrode surfaces 4 and 1 of the first, 

 the one by a wire, the other by a galvanic series. An arrange- 

 ment is then produced such as is described at the beginning 

 of this communication. In this arrangement J x has the same 

 value for both conductors ; and the same holds also for J 2 

 when the needle of the galvanometer shows no deflection and 

 this instrument possesses the construction presupposed. Hence, 

 if W is the resistance of the second wire of the galvanometer, 

 we have 



pj 1= (W-R)J 2 , 

 and therefore 



P^-^) = /0 (W-R). 



Now if w r and "W 7 are two other values of the resistances of 

 the two galvanometer-wires at which the needle likewise suffers 

 no deflection, then in like manner is 



therefore also 



P(tc/- w )=p(W / -W). 



G2 



