USE OF DOUBLE BRIDGE FOR MEASURING SMALL RESISTANCES. 381 



two conductors are joined by a third wire c of very small resistance ; 

 the resistances a', b', a lt and b^ are very great. The two extreme 

 points C and D of the branch of the galvanometer are displaced 

 until the current is null. If 7 is the intermediate resistance AjBj, 

 the ratio of the resistances a' and b' is given by the equation (38). 

 If the resistance 7 were null, we should have the usual ratio 



a a' 

 (43) ~ b = b ,\ 



if the resistance 7 is merely very small, we may write 



+ ! TT- 



As this difference -7 - is very near zero, it will be seen that 

 b a 



.JQJ. 



Fig. 201. 



if 7 is very small compared with the sum a^ + b^, equation (43) is 

 very approximately exact. 



The resistances due to the contacts at A, B, A : and B x have 

 not been taken into account, but the error may be neglected if 

 the auxiliary resistances a' b\ a^ and b^ have been sufficiently 

 large. 



980. The following modification, due to Hockin and Matthies- 

 sen,* eliminates this source of error. X and Y (Fig. 201) are known 



* MAXWELL. Electricity and Magnetism, Vol. I., p. 444. 



