ON PHYSICAL LINES OF FORCE. 455 



each, other, so that in both cases they are drawn in the direction of the 

 resultant of the lines of force. 



It appears therefore that the stress in the axis of a line of magnetic force 

 is a tension, like that of a rope. 



If we calculate the lines of force in the neighbourhood of two gravitating 

 bodies, we shall find them the same in direction as those near two magnetic 

 poles of the same name ; but we know that the mechanical effect is that of 

 attraction instead of repulsion. The lines of force in this case do not run 

 between the bodies, but avoid each other, and are dispersed over space. In 

 order to produce the effect of attraction, the stress along the lines of gravi- 

 tating force must be a pressure. 



Let us now suppose that the phenomena of magnetism depend on the 

 existence of a tension in the direction of the lines of force, combined with a 

 hydrostatic pressure ; or in other words, a pressure greater in the equatorial 

 than in the axial direction : the next question is, what mechanical explanation 

 can we give of this inequality of pressures in a fluid or mobile medium ? The 

 explanation which most readily occurs to the mind is that the excess of pres- 

 sure in the equatorial direction arises from the centrifugal force of vortices or 

 eddies in the medium having their axes in directions parallel to the lines of force. 



This explanation of the cause of the inequality of pressures at once suggests 

 the means of representing the dipolar character of the line of force. Every 

 vortex is essentially dipolar, the two extremities of its axis being distinguished 

 by the direction of its revolution as observed from those points. 



We also know that when electricity circulates in a conductor, it produces 

 lines of magnetic force passing through the circuit, the direction of the lines 

 depending on the direction of the circulation. Let us suppose that the direction 

 of revolution of our vortices is that in which vitreous electricity must revolve 

 in order to produce lines of force whose direction within the circuit is the 

 same as that of the given lines of force. 



We shall suppose at present that all the vortices in any one part of the 

 field are revolving in the same direction about axes nearly parallel, but 

 that in passing from one part of the field to another, the direction of the 

 axes, the velocity of rotation, and the density of the substance of the vortices 

 are subject to change. We shall investigate the resultant mechanical effect upon 

 an element of the medium, and from the mathematical expression of this 

 resultant we shall deduce the physical character of its different component parts. 



