THE MEASUREMENT OF RESISTANCE 195 



Convenience dictates that the second term on the right-hand 

 side of the equation be made zero; this is accomplished if m 



and n are so adjusted that ~ = -jrp In other words, M, N, 



Tl I\ 



ni, n, should fulfil the conditions for the resistances in an ordinary 

 Wheatstone bridge, in which case X is independent of the inter- 

 mediate resistance a and of the auxiliary conductors n and m, 

 as has just been shown in a somewhat less general fashion. 



In the commercial instrument the ratio arms are usually 

 mounted in the same box and are capable of variation, being 



made up of coils so chosen that the relation = -^ is con- 

 veniently attained. If this condition is not exactly fulfilled, the 

 error due to neglecting the last term in (15) will diminish as a is 

 decreased; therefore the resistance of the intermediate con- 

 nection should be made as small as possible, especially when 

 measuring small resistances. One obvious test for the accuracy 



m M 

 of the relation = -TV- may be made by temporarily increasing 



a, or better, by altogether removing the connection, thus breaking 

 the circuit. If the galvanometer remains in balance with a 

 both open and closed the adjustment is correct. 



Best Resistance for a Thomson Galvanometer When Used 

 with a Thomson Bridge. The best resistance for the galvanome- 

 tcr may be found as follows: The resistance a is always made 

 as small as possible; assume that it is negligible in comparison 

 with both m and n, then [ ] in equation (14) reduces to 



and 



(MP - NX) 



(RG + - -} (M + N + X + P) + (M + X)(N + P) 



\ TH, ~\~ ill 



With Thomson galvanometers having coils of equal dimensions 

 the relation between the current, the resistance and the 

 deflection is 



D = K 



If the resistance of the arm P differs from that necessary for 



