CHAP, vi.] ELECTRICITY AND MAGNETISM. 



319 



branch falls to N, and again falls till it reaches the value 

 at Q. Now if N be the same proportionate distance 



Fig. 130. 



along the resistances between P and Q, as M is along 

 the resistances of the upper line between P and Q, the 

 potential will have fallen at N to the same value as it 

 has fallen to at M ; or, in other words, if the ratio of the 

 resistance C to the resistance D be equal to the ratio 

 between the resistance A and the resistance B, then M 

 and N will be at equal potentials. To find out whether 

 they are at equal potentials a sensitive galvanometer is 

 placed in a branch wire between M and N ; it will show 

 no deflexion when M and N are at equal potentials ; or 

 when the four resistances of the arms " balance " one 

 another by being in proportion, thus : 



A : C : : B : D. 



If, then, we know what A, B, and C are, we can calculate 

 D, which will be ExC 



EXAMPLE. Thus if A and C are (as in Fig. 133) 10 ohms 

 and 100 ohms respectively, and B be 15 o/ims, D will 

 be 15 x 100 -v- 10 = 150 ohms. 



IMS 



