336 COMPARISON OF RESISTANCES. 



adjusting the resistances of the four sides so that no current 

 passes in the galvanometer. 



Let A and B (Fig. 184) be the two summits connected by the 

 battery, C and D those which connect the galvanometer ; a, b, a', and ', 

 the resistances of the four sides AC, CB, AD and DB; a, /?, a', /?', 

 the currents which traverse them respectively; R the resistance of 

 the diagonal of the battery, r that of the diagonal of the galvano- 

 meter or of the bridge ; I and / the intensities of the current in 

 the two diagonals. 



In order that no current shall pass in the galvanometer, it is 

 necessary and sufficient that the two points C and D shall be at 

 the same potential. If V and V are the potentials of the two 

 summits A and B, and suppose that the wire CD is cut; the fall 

 of potential from A to C is 



6' 



I +- 



a 



and the fall from A to D in like manner is 



i 



(V-V) 



The potentials are equal at C and D, and no current will pass in 

 a wire interposed between these two points, if 



b b' 



(17) - = , or ab' = ba' 



a a 



This condition of equilibrium is that which it is usually attempted 

 to produce. 



943. GENERAL PROPERTIES OF A NETWORK OF CONDUCTORS. 

 We shall consider that a net work of linear conductors forms a 

 complete system, when any two points may be connected with each 

 other by a closed circuit taken within the network. The resistances 

 being given, as well as the electromotive forces they contain, the 



* Compare POGGENDORFF. Ann. de Chim. et de Phys. [3], Vol. xvni., 

 p. 489. 1846. BOSSCHA. Pogg. Ann., Vol. civ., p. 460. 1858. LUCIEN DE 

 LA RIVE. Archiv. de Geneve, Vol. xvn., p. 105. 1863. J. RAYNAUD. 

 Journal de Physique, Vol. n., p. 161. 1873. 



