﻿434 
  Lane 
  — 
  Geothermal 
  Gradient 
  in 
  Michigan. 
  

  

  Art. 
  XLV. 
  — 
  The 
  Geothermal 
  Gradient 
  in 
  Michigan 
  ; 
  by 
  

   Alfred 
  C. 
  Lane. 
  

  

  1. 
  A 
  well 
  has 
  recently 
  been 
  sunk 
  in 
  Bay 
  City 
  to 
  the 
  depth 
  

   of 
  3,508 
  feet. 
  I 
  have 
  had 
  various 
  tests 
  made, 
  and 
  a 
  man 
  

   watching 
  it 
  most 
  of 
  the 
  time. 
  The 
  temperature 
  tests 
  were 
  

   made 
  with 
  Green's 
  self-registering 
  maximum 
  thermometers 
  

   by 
  Prof. 
  C. 
  A. 
  Davis, 
  of 
  Alma 
  College, 
  resulting 
  as 
  follows 
  : 
  

  

  

  

  

  No. 
  of 
  instru- 
  

  

  Calculated 
  

  

  Depth. 
  

  

  Reading 
  °F. 
  

  

  Time 
  Exposed. 
  

  

  nient. 
  

  

  Temperature 
  

  

  3,455 
  

  

  97° 
  

  

  8 
  hours 
  

  

  5688 
  

  

  97'3° 
  

  

  2,934 
  

  

  ( 
  90'1° 
  

   ( 
  90'2° 
  

  

  1 
  hour 
  

  

  5688 
  I 
  

   5690 
  j 
  

  

  89-48° 
  

  

  2,282 
  

  

  I 
  77-° 
  

   177-° 
  

  

  30 
  minutes 
  

  

  5688 
  ) 
  

   5690 
  j* 
  

  

  79-7°' 
  

  

  1,793 
  

  

  71-° 
  

  

  50 
  minutes 
  

  

  4708 
  

  

  72-37 
  

  

  1,304 
  

  

  65-° 
  

  

  1 
  hour 
  

  

  4708 
  

  

  65-03 
  

  

  It 
  is 
  to 
  be 
  regretted 
  that 
  all 
  the 
  work 
  could 
  not 
  be 
  done 
  with 
  

   one 
  thermometer, 
  but 
  two 
  were 
  lost 
  by 
  accident. 
  Still 
  we 
  

   have 
  some 
  valuable 
  results. 
  

  

  The 
  average 
  mean 
  temperature 
  of 
  Bay 
  City* 
  is 
  about 
  45*5° 
  

   and 
  in 
  the 
  early 
  salt 
  well 
  at 
  Saginaw, 
  only 
  ten 
  miles 
  away, 
  a 
  

   strong 
  flow 
  of 
  slightly 
  saline 
  water 
  had 
  the 
  temperature 
  of 
  

   47° 
  at 
  a 
  depth 
  of 
  102 
  feet, 
  at 
  293 
  feet 
  the 
  temperature 
  of 
  the 
  

   flow 
  was 
  50°, 
  at 
  531 
  feet 
  51°, 
  at 
  617 
  feet 
  54°. 
  These 
  latter 
  data 
  

   agree 
  in 
  pointing 
  to 
  a 
  mean 
  surface 
  temperature 
  of 
  45'5° 
  with 
  

   an 
  error 
  of 
  not 
  more 
  than 
  half 
  a 
  degree. 
  We 
  obtain 
  then, 
  for 
  

   the 
  mean 
  gradient 
  to 
  3,455 
  feet, 
  1° 
  F. 
  in 
  67*07 
  feet 
  or 
  very 
  

   nearly 
  3° 
  F. 
  in 
  200 
  feet, 
  or 
  1° 
  C. 
  in 
  36*8 
  meters. 
  We 
  can 
  

   very 
  nearly 
  express 
  the 
  gradient 
  by 
  the 
  formula 
  0-015(<$— 
  102) 
  

   = 
  £—47, 
  (d) 
  being 
  the 
  depth 
  in 
  feet 
  from 
  the 
  surface 
  and 
  (t) 
  

   the 
  temperature 
  Fahrenheit, 
  and 
  from 
  this 
  formula 
  the 
  last 
  

   column 
  of 
  the 
  table 
  is 
  calculated. 
  

  

  It 
  will 
  be 
  noticed 
  that 
  while 
  the 
  agreement 
  with 
  the 
  formula 
  

   is 
  close 
  at 
  3,455 
  and 
  1,304 
  feet, 
  at 
  2,282 
  and 
  1,793 
  feet 
  the 
  

   observed 
  values 
  are 
  low, 
  which 
  result 
  seems 
  to 
  be 
  a 
  sign 
  that 
  

   at 
  those 
  depths 
  the 
  thermometers 
  were 
  not 
  left 
  down 
  long 
  

   enough. 
  

  

  Let 
  us 
  compare 
  with 
  other 
  points. 
  The 
  temperature 
  of 
  the 
  

   Midland 
  brine 
  from 
  a 
  depth 
  of 
  1,205 
  feet 
  has 
  a 
  temperature 
  

   of 
  62*5° 
  F., 
  which 
  agrees 
  exactly 
  with 
  a 
  gradient 
  of 
  1° 
  F. 
  in 
  

   67 
  feet 
  from 
  a 
  mean 
  surface 
  temperature 
  of 
  44*5° 
  F., 
  which 
  is 
  

   that 
  of 
  the 
  place. 
  

  

  The 
  Alma 
  well 
  temperature 
  of 
  98° 
  at 
  2,863 
  feet 
  gives 
  a 
  

  

  * 
  See 
  Water 
  Supply 
  paper 
  No. 
  30, 
  U. 
  S. 
  G-. 
  S., 
  Fig. 
  4. 
  

  

  I 
  

  

  