174, 175] STEADY FLOW IN CONDUCTOES. 345 



space corresponding to that occupied by the conductor. The case 

 of a straight field, 145, gives 



v _ $ r ,_\S T? _ d 



~' " d ' ~\S' 



as in the case of the uniform wire. The case of flow radially 

 between concentric cylindrical electrodes gives, 144, 



I 2A/7rZ 



o = 



This formula might be used for calculating the resistance of 

 the liquid in galvanic cells where the plates are concentric 

 cylinders. The case of radial flow in a sphere from a spherical 

 electrode of radius R Q ( 142) gives, if the outer electrode is at an 

 infinite distance, 



This formula may be used to find the resistance of the earth 

 between two telegraphic earth-plates. If both earth-plates are 

 equal spheres buried deeply in the earth at a distance apart so 

 great that it may be considered infinite in comparison with their 

 diameters, we may consider the resistance from one to the other as 

 that of two conductors of the last case in series, so that 



If, as would more nearly represent the practical case, the con- 

 ductors are hemispheres, with diametral planes in the surface of 

 the earth, we may consider the space in the preceding problem 

 split along the surface of flow formed by the plane through the 

 centers of the spheres, and take the lower half, whose conductivity 

 will be half of that just found, or 



7T\R Q ' 



In like manner the problem of the ellipsoid and the circular 

 disk will give us the resistance between earth-plates in the form of 

 circular disks laid on the surface of the earth as ?r/2 times that for 

 a hemisphere of the same radius. It is important to notice that 

 in any case of geometrically similar electrodes, the resistance is 

 inversely proportional to the linear dimensions of the earth-plate, 



