ON ohm's law. 



Uonce the resistance of this conductor will be 





l+«^+?^ + &c.' 



Now lot us suppose two conductors of the same material but of different 

 dimensions arranged in series and the same current passed through both : 





where the suffixes indicate to which conductor the quantities belong. TIio 

 ratio of the resistances is 



Hence if Ohm's law is not true, and if, therefore, any of the quantities s, s', 

 &c. have sensible values, the ratio of the resistances will depend on the 

 strength of the current. 



Now the ratio of two resistances may be measured with great accuracy 

 by means of Wheatstone's bridge. . ^ . 



We therefore arrange the bridge so that one branch of the current passes 

 first through a very fine wire a few centimetres long, and then through a 

 much longer and thicker wire of about the same resistance. The other 

 branch of the current passes through two resistances, equal to each other, 

 but much greater than the other two, so that very little of the heating-effect 

 of the current is produced in these auxiliary resistances. 



The bridge is formed by connecting the electrodes of a galvanometer, one 

 to the junction of the fine wire and the thick one, and the other to a point 

 between the other two resistances. 



We have thus a method of testing the ratio of the resistances of the fine wire 

 to that of the thick one ; and by passing through the bridge sometimes a feeble 

 current and sometimes a powerful one, we might ascertain if the ratio differed 

 in the two cases. 



But this direct method is rendered useless by the fact that the current 

 generates heat, which raises the temperature of both wires, but that of the 

 thin wire most rapidly ; and this makes it impossible to compare the effects 

 of strong and weak currents through a conductor at one and the same 

 temperature. 



It is also useless to work with weak currents, as the effect dej^ends on 

 the square of the current, and is so small as to have escaped observation in 

 all ordinary experiments. 



Again, if we were to use a single very strong current acting for a very short 

 time, we should not be able to observe the galvanometer "in a satisfactory 

 manner. In fact it was found in the experiment that currents which lasted 

 for a sixtieth part of a second produced a heating-effect which interfered 

 with the measurements. The experiment was therefore arranged so that a 

 strong current and a weak one were passed through the bridge alternately ; 

 and when the bridge was so arranged that the galvanometer was in equili- 

 brium, the direction of the weaker current was reversed. If Ohm's law were 

 not true, the condition of equilibrium for strong currents would be different 



e2 



