143 A COMPARISON OF THE ELECTRIC UMTS 



The electromotive force per unit of length between the surfaces is P = !'.. 





The electric displacement is/=^P. 



The energy in unit of volume and the tension along the lines of force 

 per unit of area is } Pf. 



The attraction X on an area ira* of either surface is 



.(22). 



If this area is separated by a small interval from the rest of the plane 

 surface, as in the experiment, and if this interval is small compared with the 

 radius of the disk, the lines of force belonging to the disk will be separated 

 from those belonging to the rest of the surface by a surface of revolution, 

 the section of which, at any sensible distance from the surface, will be a circle 

 whose radius is a mean between those of the disk and the aperture. This 

 radius must be taken for a in the equation (22)*. 



Let us next consider the magnetic force near a long straight conductor 

 carrying a current y. The magnetic force will be in the direction of a tangent 

 to a circle whose axis is the current ; and the intensity will be uniform round 

 this circle. If the radius is 6, and the magnetic intensity yS, the integral 

 round the circle will be 1irbft = ^iry by (A). 



Hence ^ = 2 f ....................................... ( 23 )' 



Let a wire carrying a current y' be placed parallel to the first at a 

 distance 6, and let us consider a portion of this wire of length I. This portion 

 will be urged across the lines of magnetic force, and the electromagnetic force 

 I' will be equal to the product of the length of the portion, multiplied by 



* [Note added Dec. 28, 1868. I have since found that if a, is the radius of the disk, and a, that of 

 the aperture of the guard-ring, and 6 the distance from the large fixed disk, then we must substitute for 



p the more approximate expression" ' +n- \, where a is a quantity which cannot exceed -^-(o,-o,). 

 -J. C. M.] 



