34 ELECTRIC LIGHTING. 



2. The number of groups which must be connected for 

 tension is given by the whole number nearest to the square 

 root of the product of the total number of elements in the 

 battery into the resistance of the external circuit, divided by 

 the resistance of a single element. 



One of these determinations will, however, suffice, for if it 

 be known how many elements are to be connected for quan- 

 tity in each group, the total number of elements divided by 

 that of each group will give the number of groups that must 

 be connected for tension. 



The amount of the resistance of the external circuit is 

 ascertained by employing an apparatus known as the Rheo- 

 stat, and a kind of electrical balance which may be a differen- 

 tial galvanometer or a Wheatstone's bridge. These pieces of 

 apparatus, and the mode of using them, being described in 

 all treatises on physics, and particularly in our Expose des 

 applications de P elcctricite, we shall not further occupy our- 

 selves with them : we shall state only that the total resistance 

 of the derivations of a circuit may be obtained by the follow- 

 ing equation : 



i i i i i 



T "~ d + 1' + W + Z* 7 "' &c< 



in which T represents the total resistance, d, #, d" t d'\ &c., 

 the resistances of the several derivations. From this the 

 value of T can be calculated when we know the values of 

 d, d', d", &c., or the value of any one of the derivations can 

 be found when we know that of the rest and'of T. 



I should have wished, in such a work as I am now writing, 

 to avoid mentioning these different calculations, but as 

 they are indispensable if we wish to understand the ques- 

 tion, and besides are very simple, I have considered it my 

 duty at least to indicate them. Further, there is a general 

 principle which is found in nearly all electrical effects capable 

 of a maximum, and which ought always to be present to our 

 minds. It is this : in order to be under the best conditions, 

 the electrical generators must be arranged in such a manner 



