112 ON DIELECTRICS. 



sum of the potentials relative to each of the centres, it is clear that 

 the points, whose potential is V p , will be obtained by the intersection 

 of spheres of potentials 



such that 



n + n' + n" 



and that the geometrical locus of all these points will be the level 

 surface of potential V p . 



This is a method of general application, and enables us, in theory 

 at least, to determine the equipotential surface of any system whatever. 



Their representation in a plane could be completely made only 

 in the case of a system of revolution traced on a meridian plane. The 

 force will always be in the plane of the figure, perpendicular at each 

 point to the meridional section of the equipotential surfaces, and 

 inversely as their distance. 



If the system is symmetrical in reference to a plane, we could still 

 have a complete representation of the state of the field in the plane 

 of symmetry In any other case the intersection of a system of equi- 

 potential surfaces by any plane will give a series of curves which are 

 equipotential curves ; the component of the force along the intersecting 

 plane is perpendicular to the curves at every point, and is inversely 

 as their distance ; but the value of the true force is not represented. 



129. The lines of force may give an equivalent representation 

 for the field. Such a line, being perpendicular at every point to the 

 equipotential surface, indicates the direction of the force ; in order to 

 represent the strength at the same time, we agree to divide the field 

 into tubes of force, such that the flow corresponding to each of them 

 has a constant value, unity for instance. 



An equipotential surface being given, it is sufficient to divide it 

 into elements ^S such that F^/S= i, and to take each of these ele- 

 ments as the base of an orthogonal tube. 



The division is an arbitrary one, and in each case that would be 

 chosen which leads to the simplest construction. 



130. UNIFORM FIELD. In the case of a uniform field all the 

 equipotential surfaces are equidistant planes, perpendicular to the 

 direction of the force. The simplest division consists in drawing two 

 series of planes at right angles to each other, and parallel to the direc- 

 tion of the force. The equipotential surfaces will then be cut out 

 in equal rectangles. 



Any section by a plane P, parallel to the direction of the field, 

 will give two systems of equidistant lines of force, which will be the 



