1241 



We shall calculate the tield outside the electric body where we have 



'^'' — i^ —3:1 — 



e z= constant. 



In ordei' to execute the calculation of the (ield we must fix the 

 system of coordinates and w^e do this by putting the condition 



j) z= 1 viz. V ^ r (9) 



Introducing this in (8), the last equation divided by — u gives 



n X e 

 2r-=il , 



d f r\_ X e' 



By integration we obtain 



r a e' 



— = r ~ a -\ , 



u' ^ 8rr r 



where a is an integration constant. To simplify the formulae we put 



and find 



1 a f' 



-^-=1 — f-, (ii: 



This formula expresses ii as a function of r. An expression for 

 IÜ gives us the first formula (8). If in that foi-mula we introduce 



1 



the expression found for and reverse the sign, we obtain 



r r 



A simple calculation gives 



« s' 



2 - 



w' r* r* 



w a 8 



1 -- + 



.5 



Oji the right-hand side the numerator is just the derivative of the 



field can be expressed by e-, m, iv, p, and tlie coordinates. We find that in the 



electro-magnetic field -f ; — corresponds to ?'" and ï^ — , ~ to %/>. For 



8 Tïp2 r* ^ ^r 4 8np' r* ^/ 



the diagonal sum of the components we find identically zero. 



