50 REPORT — 1876. 



current would be spent in this way, would require a far more perfect know- 

 ledge of the dynamical theory of bodies than we at present possess. It is 

 only by experiment that we can ascertain the laws of processes of which we 

 do not understand the dynamical theory. 



"We therefore define, as the resistance of a conductor, the ratio of the 

 numerical value of the electromotive force to that of the strength of the 

 current, and we have to determine by experiment the conditions which affect 

 the value of this ratio. 



Thus if E denotes the electromotive force acting from one electrode of the 

 conductor to the other, C the strength of the current flowing through the 

 conductor, and E. the resistance of the current, we have hy definition 



C 



and if H is the heat generated in the time t, and if J is the dynamical equi- 

 valent of heat, we have by the principle of conservation of energy 



"F" 

 JH=EC<=EC2f=^ t. 



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

 can be determined onlj- 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 temperature 

 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 phj-sical conditions which may affect the value of the resist- 

 ance ; 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 sujjpose, therefore, that the resistance of a conductor of unit 

 length and unit section is 



r (l+sc^+sV + &c.), 



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

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

 determined by experiment. The coefficients s, s' &c. represent the devia- 

 tions from Ohm's law. If Ohm's laAV is accurate, these coefficients are zero ; 

 also if e is the electromotive force acting on this conductor, 



e=rc(l+sc^ + s'c* + &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 ou this con- 

 ductor, and e that on unit of length, 



E = L<'. 



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

 area. 



