SYMMETRICAL FIELD. 



intersection of the plane of the figure with the two series of planes 

 perpendicular to the equipoteritial surfaces. 



131. FIELD SYMMETRICAL IN REFERENCE TO A PLANE. For 

 all points of the plane of symmetry, the force is perpendicular to the 

 plane ; lines of force may be traced such that the product of the 



Fig. 27. 

 force by the distance dl (Fig. 27) of the consecutive lines is constant 



since we have 



it follows that 



dJ L _dl' 

 dn dri 



The curvilinear rectangles dndl, dridl', formed by the two infinitely 

 near equipotential surfaces L and U, and the two lines of force, are 

 similar. 



The flow of force will only be determined by taking into account 

 the dimensions of the tube perpendicular to the plane of symmetry. 

 If we assume that these dimensions are everywhere the same, the flows 

 will not be equal except in that case in which all the planes parallel 

 to the plane of the figure are identical. This is the case of a cylin- 

 drical distribution, all the bodies of the system being parallel cylinders ; 

 it corresponds to the problem of the propagation in a plane in the 

 theory of heat. The potential, or the temperature, no longer depend 

 on only two co-ordinates x and y, and Poisson's equation reduces to 



o- being the electrical density on the plane. 



i 



