140 



BRIDGMAN, 



connected to a bridfje wire, wliich was tapped by a moving slider. 

 Hence adjustment was made by adding to R3 an appropriate resistance, 

 and at the same time subtracting the same resistance from Ri. 



Let us call the initial resistance for balance with no heating effect 

 (small D.C. or A.C. only) R^ and Ri. To maintain balance under the 

 heavy D.C. with no A.C, R3 must be increased by AR and Ri dimin- 

 ished by AR. A.C. balance with the heavy D.C. flowing is now main- 

 tained by an additional increase of AR' to R3 and decrease of Ri by 

 AR'. The conditions for balance under these three states of current 

 flow are: 



Ro = R2 ^ (5) 



lU 



U. 



R. I + a 



= R-2 



Rs + AR 

 Ri-AR 



Ro\l+a( 



To + n 



'1/ 



R-2 



R3 + AR + AR' 

 Ri - AR - AR' 



(6) 



(7) 



Subtracting (6) from (7) and discarding squares and products of AR 

 and AR' gives 



RoCtTi 



1} _ 1 II 



Ri 



AR'iRs + Ri) 



/?4- - Ri {^AR + AR') 



Also neglecting hii/h compared with Ij/ii, and substituting for Ro 

 its value from (5) gives 



Ri^ 



"^' /i Ri- (AR' -\-2ARy 

 which gives again approximately 



From (6), for the D.C. setting, we get approximately 



Hence finallv we have 



(8) 



(9) 



(10) 



