ELECTRICAL IMAGES. 



129 



Now, -^S is the projection ^S x of the element dS on a plane 



P Tq 



perpendicular to p, and ^ is the angle dO under which the element 

 p- 



dS is seen from the point A. 

 We have then 



-<rd$ = dO. 



27T 



If the plane, or the mass m, did not exist, the flow of force 

 from the mass m in the angle dO would be mdO. In the present case 



the flow received by the surface dS is 477 d6 = 2mdO. The dis- 



27T 



tribution of this flow is the same as if the mass m were alone there, 

 but the flow is doubled at each point since all the lines of force meet 

 the plane. 



The plane, on which the mass - m is distributed, being at zero 

 potential, all the space on the left is at zero potential. This is the 



A' 



Fig. 3 6. 



case of an unlimited conducting plane Oy, in connection with the 

 earth, and under the influence of a mass of electricity + m placed at 

 a point A. Such a plane completely intercepts the action of the 

 mass m on points behind it ; it plays the part of an electrical screen. 



Thus, the mass +m being placed at A, in the presence of a 

 conducting plane Oy in connection with the earth, this plane may be 

 replaced, for all points on the right, by a mass - m at the point A' 

 symmetrical with A. 



Sir W. Thomson looks upon the mass - m at A', considered in 

 reference to the plane Oy in connection with the earth, as the image 

 of the mass +m at A. The analogy between the electrical phe- 

 nomenon and the corresponding optical problem is at once evident. 

 If the point A is a source of light and the plane Oy a reflecting 



K 



