1872.] Prof. J. C. Maxwell on Electric Induction. 161 



that which would he 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 re- 

 fraction. 



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 corre- 

 sponding parts of the object and the image. The image is reckoned nega- 

 tive 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 electromagnet 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 'lira, be R. 



R is to be measured on the electromagnetic 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 11= — ; and if a denotes 



the specific resistance of the sheet for a unit (or any other) square, 



. ... 



5. Let us begin by dividing the time into ^ 

 a number of equal intervals, each equal to Zt. . - 



The smaller we take these intervals the more 

 accurate will be the definition of the train of 



images which we shall now describe. 



6. At a given time t, let a positive image 

 of the magnet or electromagnet be formed 

 on the negative side of the sheet. J 



As soon as it is formed, let this image begin ' 

 to move awav from the sheet in the direction ' 



! ! 6 



i e © 

 i e © 



of the normal, with the velocity R, its form i © ' 

 and intensity remaining constantly the same as Y i 

 that which the magnet had at the time t. 



