﻿360 
  PROCEEDINGS 
  OF 
  THE 
  CALIFORNIA 
  

  

  same 
  l)ed 
  ; 
  hence, 
  — 
  varies 
  as 
  f2 
  : 
  and 
  if 
  t 
  is 
  constant, 
  or 
  equal 
  to 
  one 
  hour, 
  r 
  

   vt 
  

  

  varies 
  as 
  v^ 
  or 
  v 
  varies 
  as 
  th 
  ; 
  and 
  hence 
  v 
  = 
  nv'' 
  where 
  n 
  is 
  a 
  coefficient, 
  

   which 
  I 
  have 
  determined 
  in 
  the 
  following 
  manner 
  : 
  

  

  There 
  is 
  the 
  bed 
  of 
  a 
  small 
  stream 
  or 
  river 
  in 
  the 
  vicinity 
  of 
  the 
  pro- 
  

   posed 
  canal. 
  At 
  a 
  distance 
  of 
  about 
  one 
  and 
  a 
  half 
  miles 
  from 
  the 
  shore 
  

   I 
  caused 
  a 
  length 
  of 
  4,148 
  feet 
  to 
  be 
  measured 
  along 
  the 
  bank 
  of 
  this 
  river, 
  

   and 
  further 
  on, 
  another 
  distance 
  of 
  13,040 
  feet 
  in 
  the 
  same 
  direction. 
  I 
  

   caused 
  the 
  flowing 
  tide 
  to 
  be 
  watched, 
  and 
  the 
  time 
  to 
  be 
  noted 
  during 
  which 
  

   the 
  advancing 
  fillet 
  was 
  traversing 
  those 
  latter 
  two 
  distances 
  : 
  the 
  time 
  occu- 
  

   pied 
  in 
  moving 
  over 
  4,148 
  feet 
  was 
  twenty-five 
  minutes, 
  and 
  over 
  the 
  other 
  

   distance 
  one 
  hour 
  and 
  twenty 
  minutes, 
  thus 
  giving 
  a 
  velocity 
  in 
  the 
  former 
  case 
  

   of 
  '2^q\ 
  feet 
  per 
  second, 
  and 
  in 
  the 
  latter 
  of 
  2^^^^'^^ 
  feet. 
  I 
  caused 
  the 
  height 
  to 
  

   which 
  the 
  tide 
  had 
  risen 
  during 
  those 
  times 
  to 
  be 
  noted 
  by 
  means 
  of 
  gauges 
  : 
  in 
  

   the 
  first 
  case 
  it 
  amounted 
  to 
  3 
  ^-^^^ 
  feet 
  ; 
  in 
  the 
  second 
  case 
  it 
  amounted 
  to 
  

   ■'--'• 
  tVo" 
  '^^^ 
  ' 
  *^"®' 
  ^' 
  ^° 
  *^^ 
  ""® 
  ^^^^ 
  ^^ 
  nearly 
  9^^^, 
  and 
  in 
  the 
  other 
  

   about 
  8y50 
  -pi^g 
  g^^3g 
  j,QQ|-g 
  qj- 
  j-j^ggg 
  numbers 
  are 
  nearly 
  in 
  the 
  ratio 
  of 
  '^jq^q 
  

   to 
  2t-VoV' 
  * 
  ^^^^ 
  which 
  goes 
  to 
  corroborate 
  the 
  theory 
  just 
  established 
  ; 
  hence. 
  

  

  ww- 
  = 
  " 
  = 
  '■''''■ 
  

  

  This 
  is 
  an 
  important 
  coefficient, 
  and 
  worthy 
  the 
  attention 
  of 
  engineers 
  who 
  

   may 
  be 
  engaged 
  in 
  similar 
  duties. 
  It 
  is 
  to 
  be 
  hoped 
  that 
  some 
  gentleman 
  will 
  

   try 
  its 
  correctness 
  in 
  some 
  other 
  locality, 
  so 
  as 
  to 
  verify 
  it, 
  or 
  amend 
  it 
  if 
  nec- 
  

  

  It 
  may, 
  perhaps, 
  be 
  objected 
  that 
  the 
  value 
  of 
  n, 
  thus 
  obtained, 
  from 
  the 
  

   movement 
  of 
  the 
  tide 
  up 
  the 
  bed 
  of 
  a 
  river 
  or 
  inclined 
  plane, 
  will 
  be 
  inapplica- 
  

   ble 
  iu 
  determining 
  the 
  velocity 
  while 
  moving 
  along 
  the 
  bed 
  of 
  a 
  horizontal 
  canal. 
  

  

  Let 
  AB 
  represent 
  the 
  bed 
  of 
  the 
  canal, 
  

   A 
  that 
  of 
  the 
  river 
  ; 
  suppose 
  A 
  D 
  the 
  

   velocity 
  of 
  the 
  tide 
  while 
  moving 
  along 
  

   A 
  B, 
  D 
  T 
  being 
  drawn 
  perpendicular. 
  It 
  

   is 
  plain 
  that 
  A 
  T 
  will 
  represent 
  its 
  veloc- 
  

   ity 
  in 
  ascending 
  A 
  C, 
  that 
  is 
  to 
  say 
  : 
  if 
  " 
  " 
  " 
  

   radius 
  represent 
  the 
  velocity 
  in 
  the 
  hor- 
  ^i<5- 
  1- 
  

   izontal 
  direction, 
  the 
  cosine 
  of 
  the 
  inclination 
  will 
  represent 
  the 
  velocity 
  up 
  

   an 
  incline. 
  

  

  The 
  tangent 
  of 
  the 
  inclination 
  of 
  the 
  bed 
  of 
  the 
  river 
  on 
  which 
  I 
  have 
  ex- 
  

   perimented 
  was 
  found 
  to 
  be 
  .00076 
  ; 
  this 
  angle 
  is 
  so 
  small 
  that 
  the 
  cosine 
  may 
  

   be 
  considered 
  equal 
  to 
  radius 
  ; 
  hence, 
  there 
  cau 
  be 
  no 
  difiference 
  between 
  the 
  

   velocity 
  of 
  the 
  tide 
  moving 
  up 
  the 
  bed 
  of 
  this 
  river, 
  and 
  that 
  of 
  the 
  same 
  tide 
  

   moving 
  iu 
  a 
  horizontal 
  canal. 
  Indeed, 
  I 
  may 
  assert 
  generally 
  that 
  the 
  inclina- 
  

   tions 
  of 
  rivers 
  flowing 
  into 
  the 
  sea 
  are 
  so 
  small 
  that 
  the 
  velocity 
  of 
  the 
  tide 
  

   flowing 
  up 
  their 
  beds 
  is 
  the 
  same 
  as 
  it 
  would 
  be 
  on 
  a 
  horizontal 
  plane. 
  

  

  Having 
  now 
  ascertained 
  the 
  means 
  by 
  which 
  to 
  obtain 
  the 
  horizontal 
  velocity 
  

  

  