204 ELECTRICAL MEASUREMENTS 



the and + poles connected to the core and require that the 

 two results check. 



To measure X the " constant " of the apparatus must first be 

 determined; this is, the number of megohms at X which will 

 correspond to a deflection of 1 mm. on the galvanometer scale. 

 To do this, short circuit X at KI by a piece of wire W ; the resistance 

 of the circuit will then be R + PR, where P R is the resistance of 

 the shunted galvanometer, the leads and the battery. S should 

 be set at its smallest value and the deflection of the galvanometer 

 noted. Now, if necessary, alter S to obtain a good reading; 

 call this D R and let m R be the corresponding multiplying power 

 of the shunt. Then E = I R (R + PR). When X is in place 

 E = I X (X + R -h P x ). As the deflection of the galvanometer is 

 proportional to the current, 



I R = Km R D R , 



I x = Km x D x , 



therefore X = ^f-(R + P*) - (R + PX). 

 m x D x 



In general, R + P x is negligible compared with X, and P R neg- 

 ligible compared with R-, so, 



Rm R D R 



The quantity Rm R D R is the "constant" of the apparatus. As 

 R is expressed in megohms, this is the number of megohms for 

 unit deflection of the galvanometer when the relative multiplying 

 power of the shunt is unity. 



The resistance R is left in circuit continuously, in order that 

 there may be no possibility of a current being sent through the 

 galvanometer of sufficient strength to burn it out. The mag- 

 nitude of R, }/{ o megohm, is so small that no material error is 

 introduced by this procedure, as X is some hundreds or thousands 

 of. megohms. 



Precautions. In order that a measurement of insulation 

 resistance may possess any value, one must be sure that the 

 only current which passes through the galvanometer is that which 

 flows through the insulation of the cable. Therefore, the 

 galvanometer must be connected to the core of the cable and 



