156 ELECTRICAL MEASUREMENTS 



Substitution Method. This method is based on the assump- 

 tion that the e.m.f. and resistance of the battery employed are 

 constant. 



With the connections as in Fig. 82 the galvanometer current is 



ER S 



fa +Rh + R R + S R + X) (R G 



If, by means of a switch, S be substituted for X and adjusted 

 until the deflection is the same as before, then obviously 



S = X. 



Any error which might be due to the law of deflection of the 

 galvanometer is eliminated. The shunt R s serves to vary the 



-x 



FIG. 82. Substitution method for measuring resistance. 



sensitivity of the galvanometer to suit different conditions. The 

 resistances of the other parts of the circuit should be small com- 

 pared with S and X] for this reason arrangements should be 

 made so that the number of battery cells may be varied. The 

 substitution method in a modified form is frequently used in 

 dealing with very high resistances (see "Insulation Resistance"). 



Direct-deflection Method. Two resistors which are to be 

 compared may be connected in series and the potential differ- 

 ences between their terminals measured by voltmeters of the 

 proper range. If the current be constant, a single instrument 

 may be used; its deflection should be proportional to the'current 

 and it should be so arranged that the terminals can be quickly 

 transferred from S to X, see Fig. 83. 



R is a variable resistance for changing the range of the volt- 

 meter; if the current taken by the voltmeter be negligible, 



D^ (R r + R 

 ~ *D \R + R 



