When  the  axes  have  general  directions  and  the  normal  has
direction  cosines  {I,  m,  n)  the  normal  force  is

[2K{IX  -¥mY-^  nZy  -  KWYSir (110).
As  already  explained  this  normal  force  is  equilibrated  either
by  the  elasticity  of  a  solid  medium,  or,  in  an  uncharged  liquid,
by  additional  hydrostatic  pressure  and  by  surface  tension.
§  53]  STRESSES   IN   MATERIAL   MEDIA.  71

53.  In  a  magnetostatic  field  the  stresses  in  the  ether  are
given  by  §  51  and  consist  of  tensions,

[fj,  (Xa  _  M'  -  N'^)  +  (^  - 1)  {D  +  if «  +  iV'^/STr,  etc.,
and  shears,

[fiMN]l4>7r,  etc.
The  couples  vanish (HI).
These  give  rise  to  an  internal  force  per  unit  volume  given

by

=  TL  +  k{LL:,-}-MLy  +  NL^)  =  TL-\-k.IV7.L (112).
On  a  magnetic  molecule  of  moment  M  we  should,  according
to  Maxwell's  theory,  expect  a  force  MV .  L:  cf.  Electricity  and
Magnetism,  §§  389,  639.  The  formula  for  H  gives  a  force
G'V.X/47r  per  unit  volume  when  the  induced  moment  per  unit
volume  is  Ot'l^tTr :  thus  the  result  is  such  as  might  be  expected
to  follow  from  our  hypothesis  that  the  molecules  behave  as  if
independent  of  each  other.
Further,  at  a  surface  of  rapid  though  continuous  transition
to  which  OX  is  normal,  H  is  large  and  the  normal  force  per
unit  area  is,  by  the  method  of  §  44,

^dxB  =  ^  fdx'  (^^  IfjL  {D  -  M'  -  N^)  +  (fi-l)  {L'  +  ilf^  +  m]

=  {/jL (D -M^-  m)  +  (yL6  -  1)(Z2  +  i/2  +  iV^=^)l?/87r

for  {/.I)?=47n/,     {M]l  =  0,     {N]l  =  0,

where  v  is  the  surface  density  of  permanent  magnetism,  if  any

is  present.
Similarly


/■


/'


dxU  =  {fiLM/^irY,

=  vM,
dxZ  =  vN.
