RESISTANCE THE INVERSE OF A VELOCITY. 19 1 



Let Vj and V 2 be the values of the potential at two points A and 

 B (Fig 49) at a distance / from each other, and let the point A be 

 the origin of the co-ordinates, we have 



(i) 

 and, consequently, 



The quotient = r is called the resistance of the wire between 



<:S 

 the two points A and B, and the inverse of this resistance is the 



conductivity of this same wire. 



Fig. 49. 



Equations (i) and (2) show that : 



i st. The potential decreases in arithmetical progression along the 

 wire, in the direction of the current; 



2nd. The current between the two points A and B is equal to the 

 quotient of the difference of potential of these two points by the 

 resistance of the intermediate wire. 



These two statements form Ohm's law. 



It may be noticed that the distribution of potential, and the flow 

 of electricity in the case we are considering, are identical with the 

 distribution of temperatures, and with the flow of heat in a homo- 

 geneous wall bounded by two parallel planes kept respectively at 

 constant temperatures. 



205. THE RESISTANCE OF A CONDUCTOR is THE INVERSE OF A 

 VELOCITY. The quantity r, which we have called the resistance of 



the conductor, has the value ; it is proportional to the length of 



o 



the conductor, is inversely as its section, and of the coefficient of 

 conductivity of the medium. 



