THE MEASUREMENT OF RESISTANCE 175 



ing resistance coils at the gaps a and b. The effect of these, so 

 far as the balance is concerned, is the same as if the wire had been 

 extended on each side by the addition of such a length as would 

 have the same resistance as the coils. Therefore, the equivalent 

 lengths of these coils in millimeters of the slide wire must be 

 determined. Let m l denote this quantity for the coil at a and 

 m 2 that for the coil at b. Then when measuring X, 

 1,000 - l + n 2 + m z 



** - *^ 7 I * 



I + HI + mi 



The values of mi and m z may be determined as follows: place at 

 c a resistance of E ohms and at d another known resistance of B 

 ohms. Close both a and b by the straps and balance the bridge. 

 Call the reading Zi. Then 



E h + ni 



B 1,000 - Zi + n* 



Now insert at a the coil, the equivalent length of which is desired, 

 and obtain a new balance. Call the reading Z 2 . Then 



E Z 2 4- ni + mi 

 B ~ 1,000- li + n, 



and similarly for m 2 . 



In using equal extension coils, it is necessary to have the 

 known resistance S (at c) so nearly equal to X that the balance 

 point will come upon the slide wire. If the extension coils are 

 unequal, then the ratio of S to X must be such as to accomplish 

 this; or if S is of a fixed value, then the ratio of mi to m 2 must be 

 properly adjusted. If S, mi and m 2 are all fixed, the range 

 of the apparatus is limited. 



With a more elaborate construction, and when used with due 

 precautions to eliminate thermo-currents, contact resistances, 

 etc., the slide wire bridge becomes useful in work of the highest 

 precision. 



Carey Foster Method for Comparing Two Nearly Equal 

 Coils. This method is primarily designed for the comparison of 

 nearly equal resistances; it therefore lends itself readily to the 

 determination of temperature coefficients and to the verification 

 of standard coils. 



