﻿368 
  

  

  Mr. 
  N. 
  E. 
  Gilbert 
  : 
  Experiments 
  upon 
  the 
  

  

  any 
  elementary 
  circuit 
  to 
  be 
  proportional 
  to 
  the 
  linear 
  velocity 
  

   and 
  to 
  the 
  length 
  of 
  the 
  circuit, 
  we 
  may 
  find 
  an 
  expression 
  for 
  

   the 
  magnetic 
  intensity 
  at 
  a 
  point 
  on 
  the 
  surface 
  of 
  the 
  earth 
  

   due 
  to 
  such 
  currents 
  in 
  the 
  interior. 
  

  

  The 
  magnetic 
  potential 
  at 
  a 
  point 
  P 
  (fig. 
  2) 
  due 
  to 
  a 
  current 
  

   in 
  an 
  elementary 
  circuit 
  is 
  equal 
  to 
  the 
  value 
  of 
  the 
  current 
  

   multiplied 
  by 
  that 
  of 
  the 
  solid 
  angle 
  subtended 
  at 
  P 
  by 
  the 
  

   circuit. 
  Let 
  represent 
  the 
  centre 
  of 
  the 
  earth 
  and 
  r 
  the 
  

   distance 
  of 
  the 
  circumference 
  of 
  the 
  circuit 
  from 
  the 
  origin, 
  

   8 
  the 
  angle 
  subtended 
  at 
  by 
  the 
  circuit, 
  R 
  the 
  distance 
  

   of 
  P 
  from 
  the 
  origin 
  and 
  X 
  the 
  latitude 
  of 
  P. 
  Then 
  the 
  

   expression 
  for 
  the 
  solid 
  angle 
  at 
  P 
  is 
  

  

  =H5 
  

  

  E 
  riW-^P»WPi 
  

  

  (?«) 
  

  

  + 
  Si'i 
  , 
  i(0)r> 
  

  

  -&roo 
  B 
  tf[^_^P 
  1 
  (#)P 
  1 
  (|+x) 
  

  

  "+^1 
  + 
  ^1 
  

  

  e 
  «)-■]■ 
  

  

  where 
  P 
  x 
  ( 
  ), 
  P 
  2 
  ( 
  ) 
  ? 
  &c. 
  represent 
  zonal 
  harmonics. 
  

  

  To 
  find 
  the 
  current, 
  due 
  to 
  the 
  rotation 
  of 
  the 
  earth, 
  in 
  an 
  

   elementary 
  circuit 
  whose 
  centre 
  is 
  on 
  the 
  axis 
  and 
  whose 
  

   plane 
  is 
  perpendicular 
  to 
  the 
  axis 
  of 
  rotation, 
  — 
  

   let 
  v 
  be 
  the 
  linear 
  velocity 
  of 
  a 
  point 
  on 
  the 
  circumference, 
  

   T 
  be 
  the 
  period 
  of 
  rotation, 
  

   K 
  be 
  the 
  E.M.F. 
  generated 
  in 
  one 
  cm. 
  moving 
  at 
  rate 
  of 
  

  

  1 
  cm. 
  per 
  sec. 
  in 
  direction 
  of 
  its 
  own 
  length, 
  

   E 
  be 
  E.M.F. 
  generated 
  in 
  one 
  circle, 
  

   C 
  be 
  the 
  current 
  generated 
  in 
  one 
  circle, 
  

   p 
  be 
  the 
  specific 
  resistance, 
  i. 
  e. 
  the 
  resistance 
  of 
  1 
  c.c, 
  

   m 
  be 
  the 
  magnetic 
  potential 
  at 
  P 
  due 
  to 
  one 
  circle, 
  

   im 
  be 
  the 
  magnetic 
  potential 
  at 
  P 
  due 
  to 
  whole 
  earth. 
  

  

  