﻿434 
  ON 
  THE 
  RELATIVE 
  HORIZONTAL 
  INTENSITIES 
  

  

  tions 
  just 
  given. 
  One 
  hundred 
  oscillations 
  gives, 
  from 
  the 
  interval 
  

   between 
  the 
  first 
  and 
  second 
  observations, 
  36.2 
  seconds, 
  for 
  the 
  time 
  

   of 
  ten 
  vibrations, 
  while 
  ninety-eight 
  gives 
  36.75 
  seconds, 
  and 
  one 
  hun- 
  

   dred 
  and 
  two, 
  gives 
  35.31 
  seconds 
  for 
  the 
  same 
  time. 
  There 
  is 
  more 
  

   certainty 
  than 
  could 
  have 
  been 
  obtained 
  by 
  counting 
  the 
  whole 
  num- 
  

   ber 
  of 
  vibrations, 
  and 
  quite 
  as 
  much 
  as 
  if 
  each 
  ten 
  had 
  been 
  counted, 
  

   and 
  the 
  time 
  corresponding 
  to 
  it 
  noted, 
  as 
  in 
  the 
  method 
  usually 
  prac- 
  

   tised. 
  

  

  The 
  time 
  of 
  ten 
  vibrations 
  can 
  obviously 
  be 
  found 
  within 
  the 
  re- 
  

   quired 
  limit 
  of 
  accuracy 
  by 
  one 
  or 
  two 
  sets 
  of 
  ten 
  vibrations, 
  counted 
  

   at 
  the 
  beginning 
  of 
  the 
  experiment. 
  When 
  the 
  limit 
  of 
  accuracy 
  is 
  

   fixed, 
  it 
  is 
  easy 
  to 
  determine 
  how 
  many 
  pairs 
  of 
  vibrations 
  the 
  needle 
  

   may 
  make 
  before 
  another 
  observation 
  for 
  the 
  time 
  of 
  passage 
  is 
  neces- 
  

   sary.* 
  

  

  CORRECTIONS 
  FOR 
  TEMPERATURE. 
  

  

  In 
  determining 
  these 
  corrections, 
  we 
  proceeded 
  upon 
  the 
  principle 
  

   usually 
  assumed, 
  that 
  to 
  equal 
  increments 
  of 
  temperature 
  correspond 
  

   equal 
  diminutions 
  in 
  the 
  magnetic 
  force 
  of 
  the 
  suspended 
  needle. 
  

   This 
  is, 
  no 
  doubt, 
  approximately 
  true 
  within 
  a 
  moderate 
  range 
  of 
  tem- 
  

   perature. 
  We 
  also 
  assumed, 
  that 
  the 
  magnetic 
  state 
  of 
  the 
  needle 
  is 
  

   the 
  same 
  at 
  the 
  same 
  temperature. 
  The 
  formula 
  of 
  professor 
  Han- 
  

   steen, 
  based 
  upon 
  these 
  suppositions, 
  is, 
  

  

  t 
  = 
  T' 
  (i 
  — 
  m(*' 
  — 
  1)\ 
  

  

  where 
  T 
  represents 
  the 
  time 
  of 
  making 
  a 
  certain 
  number 
  of 
  oscilla- 
  

  

  * 
  The 
  following 
  simple 
  investigation 
  will 
  serve 
  to 
  determine 
  the 
  greatest 
  admissible 
  num- 
  

   ber 
  of 
  vibrations 
  between 
  two 
  consecutive 
  observations. 
  

  

  Let 
  t 
  = 
  the 
  time 
  of 
  10 
  vibrations 
  ; 
  n 
  = 
  the 
  true 
  number 
  of 
  vibrations 
  in 
  the 
  whole 
  time 
  ; 
  

   e 
  the 
  greatest 
  error 
  in 
  the 
  observed 
  time 
  of 
  10 
  vibrations. 
  

  

  Then, 
  — 
  = 
  the 
  greatest 
  error 
  in 
  estimating 
  the 
  whole 
  time. 
  That 
  there 
  may 
  be 
  no 
  

   10 
  , 
  ne 
  t 
  , 
  t 
  

  

  doubt 
  as 
  to 
  the 
  true 
  value 
  of 
  n, 
  we 
  must 
  have 
  -rr 
  < 
  -rp:> 
  or 
  " 
  < 
  -—■• 
  

  

  To 
  exemplify 
  this, 
  in 
  regard 
  to 
  needle 
  A, 
  suppose 
  t 
  = 
  36 
  seconds, 
  e 
  = 
  .2 
  second, 
  we 
  

  

  36 
  

   must 
  have 
  n< 
  -=< 
  180. 
  

  

  