ON PHYSICAL LINES OF FORCE. 483 



The physical meaning of the terms in the expression for the electromotive 

 force depending on the motion of the body, may be made simpler by supposing 

 the field of magnetic force uniformly magnetized with intensity a in the direction 

 of the axis of x. Then if I, m, n be the direction-cosines of any portion of a 

 linear conductor, and S its length, the electromotive force resolved in the direction 

 of the conductor will be 



+ Rn) ........................... (78), 



dz 





that is, the product of pa, the quantity of magnetic induction over unit of area 



multiplied by S ( m " n -3? j , the area swept out by the 'conductor S in unit of 

 \ **/ 



time, resolved perpendicular to the direction of the magnetic force. 



The electromotive force in any part of a conductor due to its motion is 

 therefore measured by the number of lines of magnetic force which it crosses 

 in unit of time ; and the total electromotive force in a closed conductor is 

 measured by the change of the number of lines of force which pass through it ; 

 and this is true whether the change be produced by the motion of the con- 

 ductor or by any external cause. 



In order to understand the mechanism by which the motion of a conductor 

 across lines of magnetic force generates an electromotive force in that conductor, 

 we must remember that in Prop. X. we have proved that the change of form 

 of a portion of the medium containing vortices produces a change of the velocity 

 of those vortices ; and in particular that an extension of the medium in the 

 direction of the axes of the vortices, combined with a contraction in all direc- 

 tions perpendicular to this, produces an increase of velocity of the vortices ; 

 while a shortening of the axis and bulging of the sides produces a diminution 

 of the velocity of the vortices. 



Tliis change of the velocity of the vortices arises from the internal effects 

 of change of form, and is independent of that produced by external electro- 

 motive forces. If, therefore, the change of velocity be prevented or checked, 

 electromotive forces will arise, because each vortex will press on the surrounding 

 particles in the direction in which it tends to alter its motion. 



Let A, fig. 4, p. 488, represent the section of a vertical wire moving in the 

 direction of the arrow from west to east, across a system of lines of magnetic force 



612 



