﻿ACADEMY 
  OF 
  SCIENCES. 
  359 
  

  

  be 
  meaus 
  at 
  hand 
  to 
  fill 
  it 
  sooti 
  again, 
  and 
  maintain 
  its 
  surface 
  at 
  the 
  required 
  

   level 
  for 
  the 
  purposes 
  for 
  which 
  it 
  is 
  intended. 
  

  

  To 
  know 
  the 
  time 
  the 
  tide 
  will 
  take 
  to 
  fill 
  a 
  canal, 
  then, 
  is 
  one 
  of 
  the 
  great 
  

   questions 
  which 
  enter 
  into 
  the 
  discussion 
  of 
  this 
  subject. 
  

  

  The 
  time 
  required 
  to 
  fill 
  a 
  canal 
  or 
  reservoir 
  by 
  tide 
  water 
  to 
  a 
  given 
  height, 
  

   or 
  the 
  quantity 
  poured 
  into 
  it 
  by 
  the 
  tide 
  in 
  a 
  given 
  time, 
  must 
  depend 
  on 
  the 
  

   elevation 
  of 
  its 
  bottom, 
  and 
  on 
  the 
  velocity 
  with 
  which 
  the 
  tide 
  flows 
  into 
  it. 
  

   The 
  science 
  of 
  hydraulics 
  in 
  its 
  present 
  state, 
  so 
  far 
  as 
  I 
  know 
  it, 
  does 
  not 
  afford 
  

   the 
  required 
  assistance 
  in 
  this 
  emergency 
  — 
  new 
  principles 
  must 
  therefore 
  be 
  

   investigated. 
  I 
  propose 
  to 
  do 
  this, 
  and 
  I 
  submit 
  the 
  investigation 
  for 
  your 
  dis- 
  

   cussion. 
  

  

  No 
  comparison 
  can 
  be 
  made 
  between 
  the 
  velocity 
  of 
  the 
  tide 
  at 
  sea 
  and 
  its 
  vel- 
  

   ocity 
  flowing 
  up 
  the 
  bed 
  of 
  a 
  river 
  or 
  through 
  a 
  canal, 
  for 
  the 
  following 
  rea- 
  

   sons 
  : 
  The 
  velocity 
  of 
  the 
  tidal 
  wave 
  in 
  the 
  Atlantic 
  Ocean 
  is 
  stated 
  to 
  be 
  

   about 
  700 
  miles 
  an 
  hour, 
  and 
  yet 
  the 
  depth 
  of 
  the 
  moving 
  tide 
  is 
  insignificant 
  ; 
  

   the 
  tidal 
  wave 
  being 
  only 
  two 
  and 
  a 
  half 
  to 
  three 
  feet 
  high. 
  

  

  The 
  general 
  direction 
  of 
  the 
  tidal 
  wave 
  at 
  sea 
  is 
  from 
  east 
  to 
  west 
  ; 
  and 
  j-et 
  

   on 
  land 
  it 
  is 
  seen 
  in 
  various 
  places 
  to 
  move 
  up 
  the 
  beds 
  of 
  rivers 
  from 
  west 
  to 
  

   east. 
  The 
  Gulf 
  of 
  St. 
  Lawrence 
  and 
  Bay 
  of 
  Fundy 
  are 
  on 
  the 
  east 
  and 
  west 
  

   side 
  of 
  the 
  Isthmus 
  of 
  Chignecto, 
  through 
  which 
  the 
  proposed 
  canal 
  had 
  to 
  

   pass 
  ; 
  they 
  are 
  only 
  some 
  eighteen 
  miles 
  apart 
  at 
  this 
  locality, 
  and 
  yet 
  the 
  tide 
  

   runs 
  to 
  the 
  east 
  up 
  the 
  beds 
  of 
  streams 
  emptying 
  into 
  the 
  Bay 
  of 
  Fundy, 
  

   while 
  it 
  runs 
  to 
  the 
  west 
  from 
  the 
  Gulf 
  of 
  St. 
  Lawrence 
  up 
  the 
  beds 
  of 
  

   streams 
  emptying 
  into 
  the 
  latter. 
  

  

  It 
  is 
  true 
  that 
  high 
  water 
  is 
  earlier 
  at 
  the 
  east 
  side 
  of 
  this 
  isthmus 
  by 
  about 
  

   two 
  hours 
  and 
  thirty 
  minutes 
  than 
  at 
  the 
  west 
  wide 
  ; 
  but 
  it 
  takes 
  about 
  six 
  

   hours 
  to 
  rise, 
  and 
  hence, 
  during 
  the 
  remaining 
  three 
  hours 
  and 
  thirty 
  minutes 
  the 
  

   tide 
  is 
  running 
  in 
  opposite 
  directions. 
  

  

  From 
  these 
  facts 
  it 
  woujd 
  be 
  erroneous 
  to 
  suppose 
  that 
  the 
  velocity 
  of 
  the 
  

   tide 
  at 
  sea 
  is 
  a 
  function 
  of 
  the 
  velocity 
  with 
  which 
  it 
  moves 
  up 
  the 
  bed 
  of 
  a 
  

   river. 
  The 
  inland 
  velocity 
  of 
  the 
  tide 
  must 
  therefore 
  depend 
  upon 
  the 
  

   head 
  or 
  height 
  to 
  which 
  the 
  waters 
  are 
  piled 
  on 
  the 
  adjacent 
  lands 
  which 
  ob- 
  

   struct 
  it 
  in 
  its 
  coarse 
  from 
  the 
  sea, 
  and 
  hence 
  the 
  vertical 
  and 
  horizontal 
  vel- 
  

   ocities 
  of 
  the 
  tide 
  must 
  be 
  coordinates 
  of 
  one 
  another. 
  

  

  Let 
  r 
  = 
  the 
  height 
  to 
  which 
  the 
  tide 
  rises 
  in 
  the 
  time, 
  Z^ec, 
  

  

  Let 
  V 
  = 
  mean 
  horizontal 
  velocity 
  during 
  the 
  same 
  time. 
  

  

  Then 
  we 
  get 
  

  

  vt 
  = 
  horizontal 
  distance 
  advanced. 
  

  

  — 
  = 
  the 
  tangent 
  of 
  the 
  inclination 
  of 
  the 
  thread 
  of 
  the 
  current 
  thus 
  

   generated 
  . 
  

   '['his 
  inclination 
  varies 
  as 
  the 
  square 
  of 
  the 
  velocity, 
  the 
  section 
  and 
  wetted 
  

   perimeter 
  being 
  constant, 
  unless 
  the 
  velocity 
  is 
  exceedingly 
  small. 
  

  

  Now, 
  in 
  the 
  present 
  case, 
  it 
  is 
  the 
  velocity 
  of 
  the 
  advancing 
  fillet 
  we 
  are 
  in 
  

   search 
  of— 
  its 
  wetted 
  perimeter 
  and 
  section 
  do 
  not 
  vary 
  while 
  moving 
  in 
  the 
  

  

  