ELECTRIC INDUCTION. 295 



rapidly. Hence, since we assume an eternity of past time, this is the only 

 solution of the problem. 



This solution expresses P, a function due to the action of the induced 

 current, in terms of P ", and through this of P , a function of the same kind 

 due to the external magnetic system. By differentiating P and P with respect 

 to z, we obtain the magnetic potential, and by differentiating them with respect 

 to t, we obtain, by equation (10), the current-function. Hence the relation 

 between P and P,, as expressed by equation (16), is similar to the relation 

 between the external system and its trail of images as expressed in the descrip- 

 tion of these images in the first part of this paper ( 6, 7, 8, 9), which is 

 simply an explanation of the meaning of equation (16) combined with the 

 definition of P,' in 24. 



NOTE TO THE PRECEDING PAPER. 



At the time when this paper was written, I was not able to refer to two 

 papers by Prof. Felici, hi Tortolini's Annali di Scienze for 1853 and 1854, in 

 which he discusses the induction of currents in solid homogeneous conductors and 

 in a plane conducting sheet, and to two papers by E. Jochmann in Crelle's 

 Journal for 1864, and one in Poggendorffs Annalen for 1864, on the currents 

 induced in a rotating conductor by a magnet. 



Neither of these writers have attempted to take into account the inductive 

 action of the currents on each other, though both have recognised the existence 

 of such an action, and given equations expressing it. M. Felici considers the 

 case of a magnetic pole placed almost in contact with a rotating disk. E. 

 Jochmann solves the case in which the pole is at a finite distance from the 

 pkne of the disk. He has also drawn the forms of the current-lines and of 

 the equipotential lines, in the case of a single pole, and in the case of two 

 poles of opposite name at equal distances from the axis of the disk, but on 

 opposite sides of it, and has pointed out why the current-lines are not, as 

 Matteucci at first supposed, perpendicular to the equipotential lines, which he 

 traced experimentally. 



I am not aware that the principle of images, as described in the paper 

 presented to the Royal Society, has been previously applied to the phenomena 

 of induced currents, or that the problem of the induction of currents in an 



