2O6 PROPAGATION OF ELECTRICITY. 



if, instead of an unlimited plate, we consider a circular plate 

 having two electrodes on its circumference, or again, any plate 

 comprised between two circular segments passing through the 

 points AJ and A 2 . 



218. RESISTANCE OF A CONDUCTOR OF ANY GIVEN FORM. 

 Whatever be the conductor, it may be always supposed to be divided 

 by two series of surfaces parallel to the lines of flow into infinitely 

 slender tubes, each of which is a tube of flow. Each of these tubes 

 may itself be compared to a conducting wire of varying section, the 

 resistance of which is at each point inversely as the section. The 

 total resistance can be deduced from the resistance of this complex, 

 by the ordinary laws of multiple conductors ; the reciprocal of the 

 total resistance, or the conductivity, will be the sum of the reciprocals 

 of the resistances of all these tubes. 



The calculation will in general be very complicated ; but if the 

 value of the potential on the two electrodes is known, as well as the 

 corresponding flow of electricity, it is easy to determine the total 

 resistance of the conducting medium by Ohm's formula (207). 



Let us take as an example the case of two electrodes A l and A 2 

 in an unlimited medium. We may suppose these electrodes to be 

 small spheres of radius p. Let V x and V 2 be their potentials, and I 

 the absolute value of the flow of electricity corresponding to each of 

 them. If the radius p can be neglected in comparison with the 

 distance A 1 A 2 , we may assume that the potential close to each of 



the electrodes is inversely as the distance r, and is represented by -, 

 which, on the spheres themselves, will give 



The current is then 



'/' 



//v 



- 



dn 



As, on the surface of the sphere, we have 



