Potentials,  JEolotropic  and  Isotropic.  571 
potentials,  so  also  is  ^-L.  It  is  more  convenient  to  use  an 
independent  notation  for  the  vector  type,  and  we  take 
=  f  °°  <(**+jy  +  0'£)d\  (2) 
Since  dws  a     .       ,     ,     .  ol  N  dX 
the  surface- discontinuity  is  the  same  as  for  %0,  and  the 
snrf ace-density  is  ^  (<z#  +  c'y  +  &V)-  The  volume-density 
is  —  sp(ax  +  cty  +  bfz)us~1  as  appears  from  the  connexion  with 
yfrs+1  ;  or  by  work  following  closely  the  lines  of  M.  p.  442 
we  show  that 
Ve  Xs  =  ~  V(*»  +  7'//  +  #*)/   V  J 
from  which 
Ve  %s  =  0  externally  and  =  5/0  (a#  +  c't/  +  #~)  u~l  internally. 
§  2.  We  proceed  to  the  formula?  by  which  the  above  are 
transferred  to  wave-forms.  In  the  latter  it  is  more  con- 
venient to  work  with  ^=A,Aa  and  AQ*)  =  A2a  J(\),  identity 
in  final  results  following  from  d/*/  y'A(^)=iX/  y/J.  The 
fundamental  formula  for  transference  is 
X  C(lx  +  ™y  +  nz)2sda>_  f°°    ^      _  f°°<^\ 
2tt 
and  a  particular  case  is 
&saC{lx  +  my  +  nz)2sd<o  _  f° 
2*J  "  uui+1/2  "Jo 
p 
■    ■     (3  6) 
the  general  case  applies  to  external  potentials,  the  particular 
to  internal  potentials,  the  latter  specially  required  for  energy. 
Now  (3)  is  an  immediate  integral,  with  regard  to  /x,  of 
_1   C(Lv  +  my  +  nz)28d(»_       1     (u  V 1_ 
(25  +  l){A(^)} 
2  P  2 
