Chap, in.] ASSOCIATION OF CELLS. 31 



Therefore, supposing cells to be joined in series, 

 (1) when there is LITTLE EXTERNAL RESISTANCE, no ad- 

 vantage is gained by a number of cells so joined ; (2) 

 where the' EXTERNAL RESISTANCE is GREAT, the strength 

 of the current increases in direct proportion to the 

 number of cells so joined. 



To summarise the four cases that have been con- 

 sidered : to get increased intensity of current with 

 small external resistance, either use large cells, or join 

 a number of smaller cells in "multiple arc"; with great 

 external resistance join the cells in series, small ele- 

 ments being as good as large. 



Association of cells in groups. Ohm's law 

 shows further, that increased intensity of current 

 may often be obtained not by a regular arrangement 

 of cells, either in "multiple arc," or "in series," but 

 by forming a number of groups, each group being 

 formed by uniting several cells " in multiple arc," 

 and then connecting the groups " in series." It is 

 unnecessary here to detail how this is proved, but the 

 rule is, that the best effect is obtained when the group- 

 ing is such that the total resistance of the elements is 

 equal to the external resistance. That rule is ex- 



T> 



pressed by the formula n '- = r, where R = the 



internal resistance of a cell, m = the number of cells 

 united " in multiple arc " into a group, n the number 

 of groups united "in series," and r = the total external 

 resistance. All that it is necessary to know is the 

 resistance of each cell, and the resistance of the 

 apparatus through which the electricity is to be con- 

 ducted. Thus, suppose it is known that the resistance 

 of each cell is represented by 5 (= R), and the resis- 

 tance in the circuit by 20 (= r), it is easy to calculate 

 how to arrange thirty-six cells in order to give the 



strongest current. 



-p 



In the formula n = r, substitute the values 



m 



