CONDITIONS OF SENSITIVENESS OF WHEATSTONfi'S BRIDGE. 353 



and therefore 



In this case the four sides of the bridge should have equal 

 resistances. 



959. The same kind of discussion no longer applies to the 

 resistances of the galvanometer and the battery, for the galvanometer 

 constant and the electromotive force must be brought in. If the 

 galvanometer and the battery are given, it is clear that any auxiliary re- 

 sistance placed in either of the diagonals diminishes the sensitiveness. 



Let us assume the battery given, as well as the resistances of the 

 four sides, and the channel of the galvanometer coil ; the conditions 

 of maximum sensitiveness are realised (731) when the resistance of 

 the coil is equal to the resistance p of the total network between the 

 two extremities C and D (Fig. 184) of the diagonal in which is the 

 galvanometer. For if V and V are the potentials of these two points 

 when the diagonal r is open, the current / is the same as if the 

 points C and D were the ends of a single conductor of resistance /o, 

 containing an electromotive force equal to V-V. 



On the other hand, given a certain number of identical ele- 

 ments, we get the maximum current when they are arranged so 

 that the resistance of the battery is equal to the resistance of the 

 circuit.* 



In the present case, when the balance has been established, as 

 the two diagonals are conjugate, the external resistance to be con- 

 sidered as that of the battery (947) is that of the two branches 



* If n is the number of cells, e the electromotive force, and r the resistance 



of each ; if they are coupled up in series of p cells, and if the - series thus 



P 



obtained are joined in parallel order, the strength I of the current in an external 

 resistance p t which joins the two poles, is 



pe e 



P r P 



-pr + p -p + - 

 n n p 



The value of/, which makes this expression a maximum, is given by the value 



r p f 



-p-- t or r=p; 

 n p n 



that is to say, when the resistance r of the battery is equal to the external 

 resistance. 



VOL. II. A A 



