56 Mr maxwell, ON FARADAY'S LINES OF FORCE. 



same as that of a shell coinciding with the surface, and uniformly magnetized normal to its 

 surface. But by the first law all the currents forming the little circuits will destroy one 

 another, and leave a single current running round the bounding line. So that the magnetic 

 effect of a uniformly magnetized shell is equivalent to that of an electric current round the 

 edge of the shell. If the direction of the current coincide with that of the apparent motion of 

 the sun, then the direction of magnetization of the imaginary shell will be the same as 

 that of the real magnetization of the earth*. 



The total intensity of magnetizing force in a closed curve passing through and embracing 

 the closed current is constant, and may therefore be made a measure of the quantity of the 

 current. As this intensity is independent of the form of the closed curve and depends only on 

 the quantity of the current which passes through it, we may consider the elementary case of 

 the current which flows through the elementary area dydss. 



Let the axis of w point towards the west, ss towards the south, and y upwards. Let wyz 

 be the position of a point in the middle of the area dydss, then the total intensity measured 

 round the four sides of the element is 







/ d(i,dz\ 



-[^^--di^n 



f dy, dy\ 



^v'^--diYn 



Total intensity = (-^ - -jAdy dz. 



The quantity of electricity conducted through the elementary area dydx is a.jdydz, and 

 therefore if we define the measure of an electric current to be the total intensity of magnetizing 

 force in a closed curve embracing it, we shall have 



Oa — — —- — , 



dx dy 



dy, dai 



bi = — -T-> 



< dio das 



dai dfS^ 

 dy d,v 



These equations enable us to deduce the distribution of the currents of electricity whenever 

 we know the values of a, /3, y, the magnetic intensities. If a, jS, y be exact differentials of 

 a function of wyz with respect to ar, y and z respectively, then the values of aj b^ c, disappear ; 



* See Experimental Researches (3265) far the relations between the electrical and magnetic circuit, considered as muiually 

 embracing curves. 



