184 ELECTRICAL MEASUREMENTS 



If the connections are as shown in Fig. 1045, 



I Bt (MP - NX) 





^ = ' ~ Ro(M + N + X+P) + (M + N)(X + P) 

 and 



7 *> - -WTOTTP) nearly enough ' 



" M+N+X+P 



By use of these equations it is easy to determine whether 

 or not any galvanometer will give results of the desired pre- 

 cision, for the maker will furnish a statement of the sensitivity 

 of the instrument that is, the deflection per unit current at a 

 scale distance of 1 meter, the galvanometer being in proper 

 adjustment. 



The Best Resistance for a Thomson Galvanometer When 

 Used with a Wheatstone Bridge. In general terms, the gal- 

 vanometer should have a high or a low resistance depending on 

 whether high or low resistances are to be measured. The 

 magnitudes of the bridge arms being fixed, the galvanometer 

 having the best resistance is that one which will give the great- 

 est deflection when the arm P is changed from the condition of 

 perfect balance by a given amount. It has previously been 

 shown that if the coils of a Thomson galvanometer are always 

 wound on the same bobbin, the galvanometer constant is given 

 by G = K\^RQ, the effect of the insulation being neglected; 

 consequently, if the time, of vibration is kept constant, the 

 deflection may be represented by 



D = K1 Q ^ (3) 



K is seen to be the deflection per ampere for an instrument having 

 a resistance of 1 ohm. Using (1) 



D = K7 V5fc : " ~ (3A) 



R (M + N + (3 



This is to be made a maximum, R G being the only variable. 

 It will be found that 



Hf 7? (M + *> (^ + P ) 



- R = 



Inspection shows that this result corresponds to a maximum 



