CHAP, vi.] ELECTRICITY AND MAGNETISM. 313 



internal resistance of our battery by linking cells to- 

 gether in parallel branches of a compound circuit, join- 

 ing several zincs of several cells together, and joining 

 also their copper poles together (as suggested in Art. 

 1 8 1 ), a different and better result is attained. Suppose 

 we thus join up four cells. Their electromotive-force 

 will be no more, it is true, than that of one cell, but 

 their resistance will be but ^ of one such cell, or J an 

 ohm. These four cells would give a current of 666 

 milliwebers-per-second through an external resistance of 

 i ohm, for if E = i, R = i, and the internal resistance 

 be J of r, or 1, then 

 C R + r of a weber-per-second, or 666 milliwebers. 



351. Best Grouping of Cells. It is at once 

 evident that if we arrange the cells of a battery in n 

 files of m cells in series in each file (there being m x n 

 similar cells altogether), the electromotive-force of each 

 file will be m times the electromotive -force E of each 

 cell, or ;;zE ; and the resistance of each file will be m 

 times the resistance r of each cell, or mr. But there 

 being n files in parallel branches the whole internal 

 resistance will be only-- of the resistance of any one file, 

 or will be -V, hence, by Ohm's law, such a battery would 

 give as its current 



P _ ?;z E 



-^-^R: 



It can be shown mathematically that, for a given 

 battery of cells, the most effective way of grouping them 

 when they are required to work through a given external 

 resistance R, is so to choose m and n, that the internal 

 resistance ( W V) shall eqital the external resistance. The 

 student should verify this rule by taking examples 

 and working them out for different groupings of the 

 cells. 



352. Long and Short Coil Instruments. The 



