368 COMPARISON OF RESISTANCES. 



these resistances respectively from the points A and B to the ex- 

 treme positions of the contacts at the corresponding ends of the wire. 

 Resistances a' and b' are then introduced at P' and Q', the ratio p 

 of which is known, and the position of equilibrium of contact is 

 observed, and then the position x' after inverting the resistances 

 a' and b'. We have 



a' a + x b + l-x' 



x a + x' 

 from this follows 



_- , _ 



Ct " O 



I-p I-/ 



If the ratio / is equal to unity, it follows that x = x', and ex- 

 periment gives simply the difference 



a- b=l- 2x. 



By closing the breaks P and Q by strips of copper without 

 resistance, we thus determine the resistances a and P of the ends 

 AA' and BB', measured to the position of contact of the extreme 

 divisions. 



If the resistance interposed b is less than twice that of the wire, 

 we may work by substitution, inserting and suppressing the resist- 

 ance b. 



970. The resistances a and ^, including their complements a 

 and /?, being known, the resistances to be compared a' and b' will 

 be placed at P' and Q'. It is still advantageous to interchange 

 these resistances, which gives two readings x and x', and we have 



a' a + x b + l-x' a + b + l+(x-x') 

 a + x' 



If the ratio is near unity, we only utilise a very small portion 

 of the wire (x - x'). We may then write 



x - x' a' -b' x x' 



or 



V a + b + l' 



The difference a' - b' is proportional to the distance of the two 

 positions x and x' ; moreover, for the same value of this difference, 



