140 



BRIDGMAN. 



connected to a bridge wire, which was tapped by a moving slider. 

 Hence adjustment was made by adding to R^ 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) R3 and Ri. To maintain balance under the 

 heavy D.C. with no A.C, Rz must be increased by AiJ 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 thi'ee states of current 

 flow are: 



Ro = R2 r, 



Xi4 



Ro 



1 4- 



a\ To 



+ |ti 





= Ro 



R3-\-AR 



Ro 



1 + a To + Ti 





R2 



Ri - AR 



Rs + AR + Ai^^ 

 Ri — AR — AR 



(5) 

 (6) 



(7) 



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

 and AR' gives 



Rf/XTi 



h 





Ri 



AR'iRs + Ri) 



Ri^ - Ri {2AR + AR') . 



Also neglecting ^ii/h compared with I]/ii, and substituting for Ro 

 its value from (5) gives 



Xl4\ 



aTi 



AR'il^ P 

 ti \ R3/ 



h Ri - {AR' -\- -lAR) 

 which gives again approximately 



^1 



an = 7 AR' 



.Rs Ri/ 



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



1 1 \ 



aTo = AR[~ + — 

 \n3 tiii 



Hence finally we have 



To 



h 



AR' 

 AR 



(8) 



(9) 



(10) 



