﻿20 
  Maximum 
  Force 
  between 
  Two 
  Coaxial 
  Circular 
  Currents. 
  

  

  when 
  once 
  this 
  is 
  accurately 
  known, 
  the 
  distance 
  between 
  

   the 
  coils 
  and 
  the 
  force 
  exerted 
  at 
  that 
  distance 
  can 
  be 
  found 
  

   by 
  the 
  formulae 
  (1) 
  and 
  (6). 
  

  

  As 
  regards 
  the 
  utility 
  of 
  the 
  solution 
  of 
  the 
  present 
  pro- 
  

   blem, 
  it 
  would 
  be 
  unnecessary 
  to 
  spend 
  words 
  on 
  its 
  bearing 
  

   in 
  the 
  construction 
  of 
  the 
  current-balance 
  for 
  the 
  absolute 
  

   measurement 
  of 
  electric 
  current. 
  The 
  numerical 
  data 
  calcu- 
  

   lated 
  by 
  Grrover 
  are 
  of 
  great 
  value 
  in 
  researches 
  of 
  this 
  kind. 
  

   The 
  solution 
  which 
  I 
  have 
  here 
  given 
  may 
  be 
  of 
  service 
  in 
  

   the 
  direct 
  calculation 
  when 
  the 
  dimensions 
  of 
  the 
  coils 
  are 
  

   given. 
  How 
  far 
  the 
  accuracy 
  o£ 
  the 
  instrument 
  can 
  be 
  

   relied 
  upon 
  is 
  of 
  great 
  interest 
  to 
  me, 
  as 
  I 
  believe 
  that 
  the 
  

   instrument 
  can 
  be 
  used 
  for 
  a 
  purpose 
  totally 
  different 
  from 
  

   the 
  usual 
  measurement 
  of 
  the 
  electric 
  current, 
  and 
  which 
  

   seems 
  not 
  yet 
  to 
  have 
  been 
  well 
  noticed. 
  

  

  The 
  most 
  exact 
  method 
  of 
  measuring 
  relative 
  values 
  of 
  

   gravity 
  is 
  that 
  of 
  comparing 
  the 
  periods 
  of 
  invariable 
  pen- 
  

   dulums 
  at 
  the 
  place 
  of 
  observation 
  with 
  those 
  at 
  the 
  standard 
  

   station. 
  The 
  great 
  inconvenience 
  and 
  difficulty 
  accom- 
  

   panying 
  the 
  method 
  of 
  observation 
  lie 
  in 
  the 
  extremely 
  

   accurate 
  measurement 
  of 
  time 
  ; 
  the 
  rate 
  of 
  the 
  clock 
  must 
  

   be 
  known 
  to 
  l/60th 
  part 
  of 
  a 
  second 
  per 
  day, 
  if 
  the 
  period 
  

   is 
  to 
  be 
  exact 
  to 
  one 
  part 
  in 
  five 
  million. 
  For 
  this 
  we 
  have 
  to 
  

   take 
  a 
  transit 
  instrument 
  of 
  fairly 
  large 
  aperture, 
  and 
  when 
  

   obstructed 
  by 
  bad 
  weather 
  we 
  have 
  to 
  wait 
  for 
  days. 
  In 
  

   addition 
  to 
  this, 
  the 
  occasional 
  change 
  of 
  the 
  clock-rate 
  

   necessitates 
  the 
  unintermittent 
  continuation 
  of 
  observation 
  

   which 
  imposes 
  a 
  great 
  burden 
  on 
  the 
  observer. 
  This 
  

   tedious 
  and 
  unwelcome 
  obstruction 
  to 
  the 
  usual 
  method 
  of 
  

   gravity 
  determination 
  may, 
  to 
  a 
  great 
  extent, 
  be 
  overcome 
  by 
  

   using 
  a 
  current-balance 
  instead 
  of 
  invariable 
  pendulums. 
  

   The 
  strength 
  of 
  the 
  current 
  is 
  to 
  be 
  evaluated 
  by 
  means 
  of 
  

   known 
  resistance 
  of 
  the 
  circuit 
  and 
  the 
  terminal 
  potential 
  

   difference, 
  for 
  which 
  the 
  electromotive 
  force 
  of 
  the 
  cadmium 
  

   cell 
  must 
  be 
  relied 
  upon. 
  It 
  is 
  a 
  question 
  if 
  we 
  can 
  bring 
  the 
  

   constancy 
  of 
  the 
  cadmium 
  cells 
  and 
  of 
  the 
  coils 
  to 
  the 
  same 
  

   order 
  as 
  that 
  of 
  the 
  pendulum 
  and 
  clock. 
  The 
  weight 
  

   counterbalancing 
  the 
  attraction 
  of 
  the 
  coils 
  is 
  an 
  immediate 
  

   measure 
  of 
  the 
  force 
  of 
  gravity 
  at 
  the 
  place 
  of 
  observation 
  . 
  

   For 
  this 
  purpose 
  it 
  is 
  perhaps 
  necessary 
  to 
  design 
  an 
  instru- 
  

   ment 
  anew 
  in 
  a 
  transportable 
  form, 
  and 
  construct 
  the 
  coils 
  

   such 
  that 
  the 
  attraction 
  is 
  of 
  sufficient 
  amount 
  to 
  give 
  the 
  

   desired 
  accuracy. 
  It 
  must 
  however 
  be 
  well 
  noticed 
  that 
  

   the 
  method 
  of 
  current-balance 
  is 
  not 
  free 
  from 
  objections, 
  as 
  

   the 
  current 
  is 
  liable 
  to 
  fluctuations 
  and 
  the 
  coils 
  are 
  heated 
  

   in 
  course 
  of 
  measurement 
  and 
  give 
  rise 
  to 
  convection 
  current; 
  

   moreover, 
  the 
  correction 
  to 
  be 
  applied 
  to 
  such 
  disturbances 
  

  

  