Prof.  J.  C.  Maxwell  on  Electric  Induction ,  531 
side,  but  consists  of  a  moving  train  of  images,  the  nature  of  which 
we  now  proceed  to  define. 
4 .  Let  the  electric  resistance  of  a  rectangular  portion  of  the  sheet 
whose  length  is  a,  and  whose  breadth  is  2ira,  be  R. 
R  is  to  be  measured  on  the  electromagnetic  system,  and  is  there- 
fore a  velocity,  the  value  of  which  is  independent  of  the  magnitude 
of  the  line  a.  (If  p  denotes  the  specific  resistance  of  the  material  of 
the  sheet  for  a  unit  cube,  and  if  c  is  the  thickness  of  the  sheet,  then 
R=— ;  and  if  a  denotes  the  specific  resistance  of  the  sheet  for 
a  unit  (or  any  other)  square,  R  =  —.) 
5.  Let  us  begin  by  dividing  the  time  q 
into  a  number  of  equal  intervals,  each        .     .     •     • 
equal  to  It,   The  smaller  we  take  these 
intervals  the  more  accurate  will  be  the 
definition  of  the  train  of  images  which  ... 
we  shall  now  describe. 
6.  At  a  given  time  t,  let  a  positive 
image  of  the  maguet  or  electromagnet 
i  ■  e 
i  ©  e 
\  e  © 
I  ©  © 
e  e 
© 
be  formed  on  the  negative  side  of  the 
sheet. 
As  soon  as  it  is  formed,  let  this  image 
begin  to  move  away  from  the  sheet  in 
the  direction  of  the  normal,  with  the 
velocity  R,  its  form  and  intensity  re- 
maining constantly  the  same  as  that 
which  the  magnet  had  at  the  time  t. 
After  an  interval  ct  (that  is  to  say,  at  the  time  £+c£)let  a  nega- 
tive image,  equal  in  magnitude  and  opposite  in  sign  to  this  positive 
image,  be  formed  in  the  original  position  of  the  positive  image,  and 
let  it  then  begin  to  move  along  the  normal,  after  tbe  positive  image, 
with  the  velocity  R.  The  interval  of  time  between  the  arrival  of  these 
images  at  any  point  will  be  ct,  and  the  distance  between  correspond- 
ing points  will  be  R^. 
7.  Leaving  this  pair  of  images  to  pursue  their  endless  journey, 
let  us  attend  to  the  real  magnet,  or  electromagnet,  as  it  is  at  the  time 
t  +  ct.  At  tbis  instant  let  a  new  positive  image  be  formed  of  the 
magnet  in  its  new  position,  and  let  this  image  also  travel  in  the  di- 
rection of  the  normal  with  the  velocity  R,  and  be  followed  after  an 
interval  of  time  St  by  a  corresponding  negative  image.  Let  these 
operations  be  repeated  at  equal  intervals  of  time,  each  of  these  in- 
tervals being  equal  to  it. 
8.  Thus  at  any  given  instant  there  will  be  a  train  or  trail  of 
images,  beginning  with  a  single  positive  image,  and  followed  by  an 
endless  succession  of  pairs  of  images.  This  trail,  when  once  formed, 
continues  unchangeable  in  form  and  intensity,  and  moves  as  a  whole 
away  from  the  conducting  sheet  with  tbe  constant  velocity  R. 
9.  If  we  now  suppose  the  interval  of  time  ct  to  be  diminished 
witbout  limit,  and  tbe  train  to  be  extended  without  limit  in  the  ne- 
2M2 
