162 



Prof. J. C. Maxwell on Electric Induction. [Feb. 15* 



After an interval It, that is to say, at the time t+ct, let a negative 

 image, equal in magnitude and opposite in sign to this positive image, be 

 formed in the original position of the positive image, and let it then begin 

 to move along the normal, after the positive image, with the velocity R. 

 The interval of time between the arrival of these images at any point will 

 be It, and the distance between corresponding points will be Rctf. 



7. Leaving this pair of images to pursue their endless journey, let us 

 attend to the real magnet, or electromagnet, as it is at the time t + lt. At 

 this instant let a new positive image be formed of the magnet in its new 

 position, and let this image also travel in the direction of the normal with 

 the velocity R, and be followed after an interval of time It by a corre- 

 sponding negative image. Let these operations be repeated at equal in- 

 tervals of time, each of these intervals being equal to ct. 



8. Thus at any given instant there will be a train or trail of images, 

 beginning with a single positive image, and followed by an endless succes- 

 sion of pairs of images. This trail, when once formed, continues un- 

 changeable in form and intensity, and moves as a whole away from the 

 conducting sheet with the constant velocity R. 



9. If we now suppose the interval of time It to be diminished without 

 limit, and the train to be extended without limit in the negative direction, 

 so as to include all the images which have been formed in all past time, 

 the magnetic effect of this imaginary train at any point on the positive 

 side of the conducting sheet will be identical with that of the electric 

 currents which actually exist in the sheet. 



Before proceeding to prove this statement, let us take notice of the form 

 which it assumes in certain cases. 



10. Let us suppose the real system to be an electromagnet, and that its 

 intensity, originally zero, suddenly becomes I, and then remains constant. 

 At this instant a positive image is formed, which begins to travel along the 

 normal with velocity R. After an interval ct another positive image is 

 formed ; but at the same instant a second negative image is formed at the 

 same place, which exactly neutralizes its effect. Hence the result is, that 

 a single positive image travels by itself along the normal with velocity R. 

 The magnetic effect of this image on the positive side of the sheet is equivalent 

 to that of the currents of induction actually existing in the sheet, and the 

 diminution of this effect, as the image moves away from the sheet, accurately 

 represents the effect of the currents of induction, which gradually decay 

 on account of the resistance of the sheet. After a sufficient time, the 

 image is so distant that its effects are no longer sensible on the positive 

 side of the sheet. If the current of the electromagnet be now broken, 

 there will be no more images ; but the last negative image of the train will 

 be left unneutralized, and will move away from the sheet with velocity R. 

 The currents in the sheet will therefore be of the same magnitude as those 

 which followed the excitement of the electromagnet, but in the opposite 

 direction. 



