484 ON PHYSICAL LINES OF FORCE. 



running north and south. The curved lines in fig. 4 represent the lines of fluid 

 motion about the wire, the wire being regarded as stationary, and the fluid as 

 having a motion relative to it. It is evident that, from this figure, we can trace 

 the variations of form of an element of the fluid, as the form of the element 

 depends, not on the absolute motion of the whole system, but on the relative 

 motion of its parts. 



In front of the wire, that is, on its east side, it will be seen that as the 

 wire approaches each portion of the medium, that portion is more and more 

 compressed in the direction from east to west, and extended in the direction 

 from north to south ; and since the axes of the vortices lie in the north and 

 south direction, their velocity will continually tend to increase by Prop. X., 

 unless prevented or checked by electromotive forces acting on the circumference 

 of each vortex. 



We shall consider an electromotive force as positive when the vortices tend 

 to move the interjacent particles upwards perpendicularly to the plane of the 

 paper. 



The vortices appear to revolve as the hands of a watch when we look at 

 them from south to north ; so that each vortex moves upwards on its west side, 

 and downwards on its east side. In front of the wire, therefore, where each 

 vortex is striving to increase its velocity, the electromotive force upwards must 

 be greater on its west than on its east side. There will therefore be a con- 

 tinual increase of upward electromotive force from the remote east, where it is 

 zero, to the front of the moving wire, where the upward force will be strongest. 



Behind the wire a different action takes place. As the wire moves away 

 from each successive portion of the medium, that portion is extended from east 

 to west, and compressed from north to south, so as to tend to diminish the 

 velocity of the vortices, and therefore to make the upward electromotive force 

 greater on the east than on the west side of each vortex. The upward electro- 

 motive force will therefore increase continually from the remote west, where it 

 is zero, to the back of the moving wire, where it will be strongest. 



It appears, therefore, that a vertical wire moving eastwards will experience 

 an electromotive force tending to produce in it an upward current. If there 

 is no conducting circuit in connexion with the ends of the wire, no current will 

 be formed, and the magnetic forces will not be altered ; but if such a circuit 

 exists, there will be a current, and the lines of magnetic force and the velocity 





