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surface, depends only on the number of lines of magnetic force which 

 pass through it, and that the total electromotive effect on a conduct- 

 ing wire will always be the same, provided it moves across the same 

 system of lines, in whatever manner it does so. But though the 

 quantity of magnetic action over a given area depends only on the 

 number of lines which cross it, the intensity depends on the force 

 required to keep up the magnetism at that part of the medium ; and 

 this will be measured by the product of the quantity of magnetiza- 

 tion, multiplied by the coefficient of resistance to magnetic induction 

 in that direction. 



The equations which connect magnetic quantity and intensity are 

 similar in form to those which were given for electric currents, and 

 from them the laws of diamagnetic and magnecrystallic induction 

 may be deduced and reduced to calculation. 



We have next to consider the mutual action of magnets and elec- 

 tric currents. It follows from the laws of Ampere, that when a 

 magnetic pole is in presence of a closed electric circuit, their mutual 

 action will be the same as if a magnetized shell of given intensity 

 had been in the place of the circuit and been bounded by it. From 

 this it may be proved, that (1) the potential of a magnetized body on 

 an electric circuit is measured by the number of lines of magnetic 

 force due to the magnet which pass through the circuit. (2) That 

 the total amount of work done on a unit magnetic pole during its 

 passage round a closed curve embracing the circuit depends only on 

 the quantity of the current, and not on the form of the path of the 

 pole, or the nature or form of the conducting wire. 



The first of these laws enables us to find the forces acting on an 

 electric circuit in the magnetic field. Give the circuit any displace- 

 ment, either of translation, rotation, or disfigurement, then the dif- 

 ference of potential before and after displacement will represent the 

 force urging the conductor in the direction of displacement. The 

 force acting on any element of a conductor will be perpendicular to 

 the plane of the current and the lines of magnetic force, and will be 

 measured by the product of the quantities of electric and magnetic 

 action into the sine of the angle between the direction of the electric 

 and magnetic lines of force. 



The second law enables us to determine the quantity and direction 

 of the electric currents in any given magnetic field ; for, in order to 

 discover the quantity of electricity flowing through any closed curve, 

 we have only to estimate the work done on a magnetic pole in passing 

 round it. This leads to the following relations between «j j3j y lt 

 the components of magnetic intensity, and a„ b 2 c 2 , the resolved parts 

 of the electric current at any point, 



a = d ^l~ d ll b = <fy±—— 1 c— detl d ^\ 

 dz dy dx dz' dy dx 



In this way the electric currents, if any exist, may be found when 

 we know the magnetic state of the field. When a x dx + fi^dy + y l dz 

 is a perfect differential, there will be no electric currents. 



Since it is the intensity of the magnetic action which is iramedi- 



