56 



Kansas Academy of Science. 



MAXWELL'S METHOD OF COMPARING AN ELECTRO- 

 STATIC CAPACITY WITH A SELF-INDUCTANCE. 



By J. A. G. Shirk, Ottawa, Kan. 



TI^HEN direct currents are used in a Wheatstone bridge, there 

 is a balance when the resistances of the four arms of the 

 bridge are proportional, i. e., Ri:Ro = R ; :R4. (Figure 1,) 



F., / 



If three of these resistances are known, the fourth may be de-. 

 termined by adjusting the three known ones until there is a balance,_ 

 and hence no deflection of the galvanometer, as the points A and 

 B will be at the same potential. 



This is the ordinary application of the Wheatstone bridge in 

 measuring the resistance of an unknown conductor. If alternating 

 currents are used there is a balance if the impedances of the four 

 arms are proportional. The impedances consist of the resistances 

 and reactances of the different branches. Let Ri, R2, R3, and R4 

 represent the resistances of the four arms, as before, and let Xi, X2, 

 X3, and X4 represent the reactances of the corresponding arms. 

 Then the impedances of the four arms become: Ri — jXi, Ro — jX-2^ 

 R3 — jX:;, and R4— JX4, where j= V — 1- (This method of represent- 

 ing the impedances of a circuit may be found in chapter V, vol. II, 

 of the "Elements of Electrical Engineering," by Franklin and 

 Esty.) 



If three of the impedances are known, the fourth can be deter- 

 mined by adjusting the three known ones until there is a balance 

 in the bridge. In order to accomplish this result arrange the 

 bridge as in figure 2. For the direct current use a storage coil or 

 a primary battery, the current being reduced to the desired valu& 



