288 ELECTRICAL MEASUREMENTS 



and X is, to a good degree of approximation, 14.35 ohms, and 

 when the battery circuit is closed through a series resistance, B, 

 which is external to the potentiometer the resistance becomes, 

 using a second approximation, 



14.35 - rc. 1 ^ 



where R is the resistance of the potentiometer between T l and 

 TI with the galvanometer circuit open. 



The resistance of the right-hand path between T l and T\ 

 is 990 ohms; that of the left-hand path, 99 ohms; the resistance 

 of the whole apparatus is therefore R = 90 ohms. 



If a storage cell is used and the potentiometer current is 

 0.001 amp., R + B must be approximately 2,000 w; therefore, 

 the maximum variation in the resistance of the galvanometer 

 circuit will be only 0.05 ohm or about 0.3 per cent. This con- 

 stancy of the resistance allows one to obtain the last figure in the 

 P.D. under measurement, by the deflection method, the reading 

 of the last decade, n? , being kept at zero. By properly setting 

 up the apparatus, the full reading of the last decade, n^ = 10, 

 may be made to correspond to 1, 10, or 100 divisions on the 

 galvanometer scale and the necessity for exact balancing may 

 thus be obviated. Where the P.D. to be measured is fluctuating 

 slightly, this is a decided advantage (see page 277, " Brooks 

 Deflection Potentiometer " ) . 



Another advantage, if a moving-coil galvanometer is used, is 

 that the damping remains constant, irrespective of the setting 

 of the potentiometer. 



Effect of Thermo -electromotive Forces. The magnitude of 

 the e.m.f. set up by manipulating any switch is less than 10~ 6 of a 

 volt. 



Any e.m.f s. arising from manipulating / and I' are added to 

 the battery e.m.f. (2 volts) and will be negligible. The effect 

 of a thermo-electromotive force of magnitude , due to moving 

 contact II, will be very small. 



Referring to Fig. 165, by KirchofFs laws the current in the left- 

 hand branch, if I is the total battery current coming to the 

 potentiometer, is 



I (ft + 5) + * 



