318 Cambridge Philosophical Society :-- 



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 vnW 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 a, jSj y^, 

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

 of the electric current at any point, 



= ^1-.^, b =^^—\ c=^-^. 

 ^ 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.^dx~\-(i^dy-\-yx^^ 

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



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

 ately connected with the quantity of electric currents, it follows that 

 the presence of paramagnetic bodies, like iron, will, by diminishing 

 the total resistance to magnetic induction while the total intensity 

 is constant, increase its quantity. Hence the increase of external 

 effect due to the introduction of a core of soft iron into an electric 

 helix. 



From the researches of Faraday into the induction of electric cur- 

 rents by changes in the magnetic field, it appears that a conductor, 

 in cutting the lines of magnetic force, experiences an electromotive 

 force, tending to produce a current perpendicular to the lines of 

 motion and of magnetic force, and depending on the number of lines 

 cut by the conductor in its motion. 



It follows that the total electromotive force in a closed circuit is 

 measured by the rate of change of the number of lines of magnetic 

 force which pass through it ; and it is indifferent whether this change 

 arises from a motion of this circuit, or from any change in the mag- 

 netic field itself, due to changes of intensity or position of magnets 

 or electric currents. 



This law, though it is sufficiently simple and general to render 

 intelligible all the phaenomena of induction in closed circuits, con- 

 tains the somewhat artificial conception of the number of lines pass- 

 ing through the circuit, exerting a physical influence on it. It 

 would be better if we could avoid, in the enunciation of the law, 

 making the electromotive force in a conductor depend upon lines of 

 force external to the conductor. Now the expressions which we 

 obtained for the connexion between magnetism and electric currents 

 supply us with the means of making the law of induced currents 

 depend on the state of the conductor itself. 



