MOTION OF ELECTRIFIED SYSTEMS OF FINITE EXTENT, ETC. 149 



It is generally more convenient to use the equations for a moving origin. Thus, if 

 the origin moves in the direction of x, so that the displacement from a fixed point at 

 any time is f, the equations become 



y _y_ _ _x v T 



Sy 3z ' Sz fa' fa By) ? 



3Y_aZ 3Z_8X 3X_3Y\ __. o 



3z 3y' a.r 3s' 3y 3*/ C\8 a ' 



y = 



~ ~ ^ ^ "\ u > 



da; o?/ dz 



These equations are exact. 



In the following investigations attention has been mainly directed to perfect 

 conductors, on account of the simplification thereby secured. In later sections it will 

 be shown how insulating bodies may be treated. 



It is thus necessary to consider what conditions must be satisfied in and on the 

 conductor itself. 



Two possible views may be taken about this question. 



In the case of steady motion, THOMSON ('Recent Researches,' p. 18) intrinsically 

 uses the condition that the tangential component of electric force (X, Y, Z) should 

 vanish at the surface of the charged body. Now, the force effective in producing 

 motion of electricity, or the electrodynamic force, is not the electric force (X, Y, Z) 

 but is (X', Y', Z'), where 



x, i/, z, being the components of velocity of the moving point. 



LARMOR (' yEther and Matter,' p. 152) concludes that the tangential component of 

 (X', Y', Z') should vanish at the surface of a conductor in steady motion. Strictly, 

 we have no equations for the interior of a perfect conductor, but we define it as a 

 body incapable of supporting electric stress. It seems to me necessary to make 

 (X, Y, Z) and (a, ft, y] vanish, although from one point of view it might suffice to 

 make (X', Y', Z') vanish throughout the conductor. 



We have next to determine how these quantities inside are related to the similar 

 quantities outside the surface. The fundamental equations integrated through a thin 

 shell in the usual way show that the tangential component of (X', Y', Z') is continuous, 

 but the fact that we have no right to assign the fundamental equations or the above 

 form of (X', Y', Z') to the inside of a conductor raises a doubt. If (X', Y', Z') is 

 continuous as regards tangential components, then the tangential component ot 



