THE SMITHSONIAN INSTITUTION. 343 



If another battery, whose resistance is )! , witli the resistance V and 

 cd, (quantities corresponding to the I and x above,) produce the same 

 deflection in the galvanometer, we have — 



w 



S' = ^^ • 



A' + i' + ic' ' 

 Hence 



E : E' = (A 4- Z + a;) : (/ + Z' + a/.) 

 Thus by this method the rehation of the electro-motive forces of dif- 

 ferent voltaic combinations to each other can be determined. Jacobi 

 found, in this manner, that the electro -motive force of Daniell's bat- 

 tery is to that of G-rove's as 21 is to 35. 



Wheatstone presented a very beautKul process for determining the 

 electro-motive force of a battery, without having previously found a 

 value for the resistance of the battery. (Pogg. Ann. LVII, 518.) 



A battery whose electro-motive force is E, gives as the force of the 

 current 



S =r — , E being the sum of all the resistances. The electro-motive 

 R 



force of another battery being n times as great, the entire resistance 

 must also be ?^ times as great if the second battery has the same force 

 of current, or produces the same deflection (say 45°) in the galva- 

 nometer ; then we have 



E _ wE 



Adding to the resistance R the resistance r, the force of the current 



Tjl 



will decrease to — ; the needle of the galvanometer will re- 



K -f- r 



cede a given number of degrees, (say 5°,) If it be d-^sired upon insert- 

 ing the second battery to weaken the current exactly so much, and 

 make the needle recede from 45° to 40", the resistance n r must be 



added to the resistance n R ; for if — = . we have also 



R wR R -h r 



"p 



The electro-motive forces of the two batteries are 



n ^ -{- n r 



consequently to each other as the resistances wliich must be added to 

 the resistance already present, to cause the needle to retrograde from 

 a given deflection (say 45°) a given number of degrees, (say 5°.) 



To compare the electro-motive forces of different batteries the fol- 

 lowing process is, therefore, to be adopted. In the conducting circuit 

 of the battery, besides the galvanometer, the rheostat is inserted with 

 so much wire as to produce a deflection of the needle of 45° ; the re- 

 sistance is then increased by turning the rheostat until the deflection of 

 the needle is only 40° ; the number of turns is thus a measure of the 

 electro-motive force of the battery. 



Suppose, for example, the current of a Daniell's element be passed 

 through the rheostat and the galvanometer, and so much wire has 

 been inserted as to produce the deflection of 45°. To reduce the 

 deflection from 45° to 40°, suppose thirty turns of the rheostat must be 



