SCIENCE AND PRACTICE. 263 



when the external resistance of the circuit is equal to that of the 

 battery* 



Now, let the given battery consist of N" elements, the 

 resistance of each of which is r units, and the external resist- 

 ance p as before ; to determine the manner in which we must 

 couple them in order to get their maximum intensity we must 



arrange x rows of each - elements parallel. The resistance 

 x 



of each row must therefore be 



P _ rx 



x ' N 



whence the number of rows, 



As a numerical example : We have a galvanometer, the 

 resistance (p) of whose coil is 16 units, and wish to arrange 

 CN"=) 100 elements, each of which has (r=) 4 units resist- 

 ance, in such a way that the galvanometer needle is deflected 

 to the maximum. Inserting these numbers in (XI V., we find 

 for the number of rows, 



and by dividing the total number of elements by the rows, 



JL=- 10 * 



" ~20~~ 



we have the number of elements in each row. 



The practical limits are evidently when #=N and when 

 a?ssl In the first case the elements are all connected up in 

 series, in the other they are all parallel. It very frequently 



* If p represents the surface of a rectangle whose sides are a and t>, p = a b ; 

 and, if one side of another rectangle of the same superficial area = x, the 



remaining side must be , because x = a b. But the sum of the sides of 

 x x 



a rectangle of given surface are least when the sides are equal, as in this case, 

 when x = , which can only occur when a b #2 = p. (Dub. p. 63.) 



