364 Dr. C. 11. A. Wright on the Determination of 



99. It hence results that all methods for determining the 

 E.M.F. of voltaic combinations, or for determining the internal 

 resistance of cells, which depend on the production of currents 

 of different magnitudes by means of the voltaic combination 

 employed, may be erroneous to a considerable extent when it is 

 assumed (as is ordinarily done) that the E.M.F. of the combina- 

 tion is independent of the current generated, and when the vol- 

 taic combination is such that this assumption is untrue, which is 

 the case apparently in all the more common forms of cells, if 

 indeed it is not universally the case. Thus, for instance, in 

 Ohm's method for determining the E.M.F. of a cell, the cur- 

 rent Cx produced by the cell when connected with a galvano- 

 meter, the total resistance in circuit being R 1? is determined ; 

 an additional resistance R 2 is then introduced, and the new 

 current C 2 again determined. If the galvanometer be a sine- 

 galvanometer, and a and ft are the deflections in the two cases 

 respectively, 



Oi=Ksin« and C 2 =K sin/5, 



where K is a constant for the instrument. If the E.M.F. of 

 the cell be supposed to be the same (E) for both currents, then 



E 



and 



whence 



Ci = K sin a •— 

 C 2 = K shift 



R 1 + R 2 



E = K E sm * • sin ft 



2 sin a— -sin ft 



p p sin ft 



= CoRi 



*"3 



sin a— shift 



sin a 



sin a — sin ft ' 



that is, E is known in terms of the currents, the deflections, 

 and the added resistance R 2 . 



But if E be not the same for the two currents, being greater 

 for the smaller by an amount 6\E, the equations become 



Ci = Ksina= ^r-j 



and 



n „ . a E + SE (1 + S)E 



