CALIBRATION OF THE WIRE. 



371 



double or treble that of the first, so that the portions of the wire 

 utilised are near the principal points of the calibration. 



The following arrangement will make the operations easier : 

 The resistances a' and b' are replaced by a second auxiliary 

 wire AjBj (Fig. 193) like the first. The breaks P' and Q' being 

 open, the intervals P and Q are closed one by a plate without 

 resistance, and the other by an auxiliary resistance f equivalent to 

 the nth part of the wire A'B'. Lastly, the connections of the gal- 

 vanometer are both variable, the one at D l and the other at C. 



The contact D 1 being placed at any given point of the wire A^, 

 let a l and b l be the two resistances AA^ and BBjDj, which need 

 not be known, x and x' the readings on the wire A'B' when the 



Fig. 194. 



resistance / is successively inserted at P and at Q, d the total length 

 of the wire including the terminal branches. We have 



and therefore 



^ i- x f+i-x" 



1 



f=x'-x. 



By changing the position of the point D x on the second wire, 

 we might measure the resistance / successively by different portions 

 of the wire comprised between the principal points of the calibration. 

 A series of similar operations, with different auxiliary resistances, will 

 enable us to determine the correction for each division x. 



973. The idea of the following method is due to Von Helm- 

 holtz.* Let us imagine two circuits S and S' (Fig. 194) containing 

 electromotive forces E and E' ; two points A and B of the former 

 circuit are joined respectively to the two points A' and B' of the 

 second; and let i be the intensity in one of the auxiliary wires, BB' 

 for example. 



* GIESE. Wied. Ann., Vol. XL, p. 440. 1880. 

 B B 2 



