ON OHM'S LAW. 535 



The quantity R, which we have defined as the resistance of the conductor, 

 can be determined only by experiment. Its value may therefore, for any thing 

 we know, be affected by each and all of the physical conditions to which the 

 conductor may be subjected. 



Thus we know that the resistance is altered by a change of the tempe- 

 rature of the conductor, and also by mechanical strain and by magnetization. 



The question which is now before us is whether the current itself is or 

 is not one of the physical conditions which may affect the value of the 

 resistance ; and this question we cannot decide except by experiment. 



Let us therefore assume that the resistance of a given conductor at a 

 given temperature is a function of the strength of the current. Since the 

 resistance of a conductor is the same for the same current in whichever 

 direction the current flows, the expression for the resistance can contain only 

 even powers of the current. 



Let us suppose, therefore, that the resistance of a conductor of unit length 

 and unit section is 



where r is the resistance corresponding to an infinitely small current, and 

 c is the current through unit of section, and s, s', &c. are small coefficients to 

 be determined by experiment. The coefficients s, s', &c. represent the deviations 

 from Ohm's law. If Ohm's law is accurate, these coefficients are zero ; also if 

 e is the electromotive force acting on this conductor, 



e = re (1 + so* + s'c 4 + &c.). 



Now let us consider another conductor of the same substance whose length 

 is L and whose section is A ; then if E is the electromotive force on this 

 conductor, and e that on unit of length, 



E = Le. 

 Also if C be the current through the conductor and c that through unit of 



area, 



C=Ac. 



Hence the resistance of this conductor will be 



E Lrf *<?*'<? 



