ELECTRIC INDUCTION. 287 



surface were abolished, would give rise to the actual state of things in the 

 space on the positive side of the surface. 



The state of things on the positive side of the surface is expressed by a 

 mathematical function, which is different in form from that which expresses the 

 state of things on the negative side, but which is identical with that which 

 would be due to the existence, on the negative side, of a certain system which 

 is called the Image. 



The image, therefore, is what we should arrive at by producing, as it were, 

 the mathematical function as far as it will go ; just as, in optics, the virtual 

 image is found by producing the rays, in straight lines, backwards from the place 

 where their direction has been altered by reflexion or refraction. 



3. The position of the image of a point in a plane surface is found by 

 drawing a perpendicular from the point to the surface and producing it to an 

 equal distance on the other side of the surface. If the image is of the same 

 sign as the point, as it is in hydrokinetics when the surface is a rigid plane, it 

 is called a positive image. If it is of the opposite sign, as in statical electricity, 

 when the surface is a conductor, it is called a negative image. The image of a 

 conducting circuit is reckoned positive when the electric current flows in the 

 corresponding directions through corresponding parts of the object and the image. 

 The image is reckoned negative when the direction of the current is reversed. 



In the case of the plane conducting sheet, the imaginary system on the 

 negative side of the sheet is not the simple image, positive or negative, of the 

 real magnet or electro-magnet on the positive side, but consists of a moving 

 train of images, the nature of which we now proceed to define. 



4. Let the electric resistance of a rectangular portion of the sheet whose 

 length is a, and whose breadth is 2ira, be R. 



R is to be measured on the electro-magnetic system, and is therefore a 

 velocity, the value of which is independent of the magnitude of the line a. 

 [If p denotes the specific resistance of the material of the sheet for a unit 



cube, and if c is the thickness of the sheet, then R = ~ ; and if cr denotes 



the specific resistance of the sheet for a unit (or any other) square, R = .] 



