170 Prof. J. J. Thomson on the 



the same velocity through places of given magnetic force, 

 the momentum it possesses and the electromotive force it 

 produces are proportional to the magnetic permeability of the 

 substance through which it is moving. Hence the expres- 

 sions for the mechanical force on a conductor conveying a 

 current, and the electromotive force arising from electro- 

 magnetic induction, which we have deduced for non-magnetic 

 substances, will be true for magnetic ones if we replace the 

 magnetic force by the magnetic induction. 



When the tubes are moving through a field partly occupied 

 by iron, since the inertia of the tubes on the iron is very 

 much greater than in the air, the flow of the tubes through 

 the field will be affected by the iron in much the same way 

 as the flow of a current of electricity would be affected if 

 the air were replaced by a good conductor of electricity and 

 the iron by a bad one. 



We shall now consider some problems in which iron is in 

 the field, selecting two-dimensional ones, as in these we avoid 

 as much as possible purely mathematical difficulties. 



Let us first take the case when an infinitely long cylinder 

 whose axis is at right angles to the plane of the paper is 

 introduced into a uniform magnetic field, the lines of force 

 being parallel to the plane of the paper and horizontal. The 

 tubes of electrostatic induction which are perpendicular to 

 the plane of the paper were before the introduction of the 

 iron moving vertically. When the bar is introduced they 

 will avoid it, and will spread out so that their paths are like 

 the lines of equipotential surfaces which are given for this 

 case in plate xv. of Maxwell's 'Electricity and Magnetism;' 

 the lines of magnetic force which are at right angles to the 

 lines of flow of the tubes will therefore be the lines of force 

 given in that figure. 



Let us now consider the conditions which must be fulfilled 

 at the surface separating iron from air in the general case 

 when the field is not assumed to be uniform. If R is the 

 velocity normal to this surface of a tube of strength h, then 

 2vAR must be continuous as we cross the surface, otherwise 

 there would be an accumulation or the reverse of tubes at 

 the surface. Now AifZliR, is the tangential magnetic force; 

 thus the tangential magnetic force must be continuous as we 

 cross the surface. Again, the momentum parallel to the 

 surface of a tube will-not be altered as it crosses the surface. 

 The momentum of the tube before crossing the surface is hp, 

 if pis the normal magnetic force in air; after crossing the 

 surface it is hfipi, if p x is the normal magnetic force in the 



