( fil8 ) 



outside, and by -?.. (t. v llie jiiiulos between tliis normal and the 

 positive axes of eoordinates. 



If now we repeat the above eaU-nhitions, we have to do witli 

 voliinie-intejii-als eonfmed to the spaee witiiin n. and e^•e^v integration 

 hv parts will uive rise to a snrtace-integi'ab 



Tims, to the last member of (9) we shall have to add the term 

 ('OS ).. COS [i, I'os r I 



fib,,. (fO>r f^b-. 

 and the \alnc of (12) will no longei- be d' T, bnt 



cos ).. COS n. cos V 



J' 



lie ot 



J 



<i'T — I <i.,. (I,/, a. 



The last integral of (J T) becomes 



,J(7=(i'T— ||a . rf'l)],. J <J. (U) 



c (iimnl <j . [rot d'bj) r/ ,S = c I {rot ,,nol (f . rl'l)) ,1 N — c\\(rra(Uf . (f b |„ (/(J (15) 



Hei-e the lii-st term on the riglil-liand side is 0, since yv/r/yv/// r/=:(). 

 The li-ansformalion of lh<' last pari of (10) remaining as it was, as 

 we have siipposi>d = in all points of llie siii-face, we iiiiall.v liiid 

 lor ilu" second uKMiiber of ( K^) the additional term 



I j _ |,T . rM)|„ + y bl . <^'-An -\- <■ \'.iro<l (f . rr,)|„ '/o-. 



Ihit, on account of (4), 

 



.It 



[■I • '^''>l/i 4- '•I.'"'""''/ • '''■'!'< -= 



a . 



dd'o 

 öd'b 



-j- \^ . <i'oU + •■ I.'"-'"/ V • '''bj/i = 



- '• I ^ • '^Hi ' 



We get therefore, instead of (13), 



Jö'T 



ffE=öir-r) ^-4 



at 



ad'b . 



^' — d b 



— r-|> .d'h] 'J(J (10) 



§ 9. The following are some examples of the applications that 

 may be made of the formnlae (13) and (16). 



//. Let the virtual changes in the position of the electrons and 

 in the dielecti-ic disi)lacement be proportional to the rates of change 

 in the real motion, i. e. let 



