106 IOWA ACADEMY OF SCIENCE 



Theory. 



The theory of the method is quite elementary. Consider resistances 

 without appreciable capacity or self-induction to be connected in a 

 "Wheatstone bridge circuit. Suppose the battery resistance to be small 

 compared with the other resistances. Let the balance be disturbed by 

 changing the resistance in the variable arm by a small amount ^t. Then 

 it can be shown that ^x=Cd where ^t is the time that the current flows 



Cd 



At 



through the galvanometer and also the time during which we are con- 

 sidering the change of resistance. The meaning of this equation is that 

 the change of resistance is in the variable arm of the bridge is directly 

 proportional to the deflection of the ballistic galvanometer and to the 

 constant C, and inversely proportional to the interval ^t during which 

 the galvanometer is in the circuit. 



Application to the Measurement of Small Changes of Resistance. 



Ill order to test the linear relation between the deflection and the 

 change of resistance, and between the deflections and the interval ^t 

 known resistances were placed in the Wheatstone bridge circuit. To 

 find the variation of the deflection with the change in resistance, the 

 keys k, and k^ were placed such a distance apart that the interval 

 during which the galvanometer was in the circuit was '^t=.05 sec. The 

 resistance in the variable arm was varied by different amounts previous 

 to each reading. The readings were taken after the pendulum had 

 operated keys k3 and k4. Observations are recorded in the curve 

 Fig II. It will be noted that there is only a small percentage error in 

 any single observation and further that for a change of resistance as 

 large as 800 ohms there is only a slight variation from the linear rela- 

 tion. For changes as large as Ax=200 ohms there is obviously complete 

 agreement between the theory and the experiment. It may be concluded 

 therefor that the deflection is proportional to the resistance. 



Relation Between Deflection and the Time That the Gal- 

 vanometer is in the Circuit. 



Pa order to test the relation between the deflection and the time that 

 the galvanometer was in the circuit the variable resistance was changed 

 a given amount, 15 ohms, from that required for equilibrium and the 



