﻿On 
  the 
  Highest 
  Wave 
  in 
  Deep 
  Water. 
  1053 
  

  

  more 
  than 
  3 
  x 
  10 
  u 
  ohms; 
  with 
  such 
  a 
  resistance 
  a 
  change 
  

   in 
  the 
  current 
  of 
  3 
  X 
  10 
  ~ 
  15 
  amp. 
  can 
  be 
  certainly 
  detected. 
  

   If 
  a 
  higher 
  resistance 
  is 
  taken 
  the 
  conductivity 
  of 
  the 
  insu- 
  

   lation 
  of 
  the 
  apparatus 
  is 
  apt 
  to 
  be 
  comparable 
  with 
  that 
  of 
  

   the 
  resistance, 
  and 
  if, 
  as 
  is 
  usually 
  the 
  case, 
  the 
  currents 
  

   measured 
  are 
  those 
  due 
  to 
  radioactive 
  rays, 
  Schweidler's 
  

   fluctuations 
  prevent 
  any 
  increase 
  in 
  the 
  accuracy 
  of 
  the 
  

   measurement*. 
  

  

  In 
  conclusion 
  it 
  may 
  be 
  pointed 
  out 
  that 
  these 
  high 
  re- 
  

   sistances 
  appear 
  to 
  provide 
  the 
  most 
  convenient 
  means 
  of 
  

   determining 
  small 
  currents 
  of 
  10 
  ~ 
  10 
  amp. 
  or 
  less 
  in 
  absolute 
  

   measure. 
  They 
  are 
  both 
  cheaper 
  and 
  easier 
  to 
  use 
  than 
  

   either 
  standard 
  capacities 
  or 
  quartz 
  piezoelectrics. 
  Perhaps 
  

   some 
  instrument-maker 
  will 
  undertake 
  the 
  construction 
  of 
  

   such 
  standardized 
  high 
  resistances. 
  

  

  Summary. 
  

   Some 
  further 
  information 
  is 
  given 
  as 
  to 
  the 
  high 
  resistances 
  

   made 
  of 
  mixtures 
  of 
  xylol 
  and 
  alcohol 
  contained 
  in 
  glass 
  cells. 
  

   The 
  conclusions 
  important 
  for 
  the 
  practical 
  construction 
  of 
  

   such 
  resistances 
  are 
  given 
  in 
  § 
  5. 
  

   Leeds 
  University, 
  Oct. 
  1913. 
  

  

  XCVII. 
  On 
  the 
  Highest 
  Wave 
  in 
  Deep 
  Water. 
  By 
  J. 
  E. 
  

   Wilton, 
  M.A., 
  B.Sc, 
  Assistant 
  Lecturer 
  in 
  Mathematics 
  

   in 
  the 
  University 
  of 
  She 
  field 
  \. 
  

  

  IT 
  is 
  possible 
  to 
  obtain 
  a 
  fluid 
  motion 
  in 
  two 
  dimensions 
  

   with 
  any 
  given 
  curve 
  as 
  free 
  surface. 
  (The 
  " 
  motion 
  " 
  

   spoken 
  of 
  in 
  this 
  paper 
  is, 
  throughout, 
  to 
  be 
  understood 
  to 
  

   mean 
  steady 
  motion.) 
  

  

  Let 
  the 
  axis 
  of: 
  x 
  be 
  horizontal, 
  that 
  of 
  y 
  vertically 
  upwards. 
  

   Let 
  z 
  = 
  x 
  + 
  ty, 
  w 
  = 
  <p 
  + 
  tijr, 
  

  

  * 
  It 
  seems 
  that 
  some 
  persons 
  who 
  have 
  used 
  such 
  resistances 
  (and 
  

   also 
  Bronson 
  resistances) 
  tor 
  the 
  measurement 
  of 
  currents 
  have 
  estimated 
  

   the 
  current 
  by 
  earthing 
  that 
  end 
  of 
  the 
  resistance 
  which 
  is 
  not 
  attached 
  

   to 
  the 
  quadrant 
  of 
  the 
  electrometer 
  and 
  observing 
  to 
  what 
  potential 
  the 
  

   quadrant 
  rises. 
  A 
  far 
  more 
  convenient, 
  accurate, 
  and 
  rapid 
  method 
  is 
  to 
  

   connect 
  that 
  end 
  of 
  the 
  resistance 
  to 
  a 
  potentiometer 
  and 
  to 
  observe 
  

   to 
  what 
  potential 
  that 
  end 
  must 
  be 
  raised 
  in 
  order 
  that 
  the 
  electrometer- 
  

   needle 
  should 
  not 
  move 
  when 
  the 
  quadrant 
  is 
  insulated 
  disconnected 
  from 
  

   earth. 
  The 
  rapidity 
  of 
  the 
  measurements 
  is 
  then 
  independent 
  of 
  the 
  time 
  

   which 
  the 
  needle 
  of 
  the 
  electrometer 
  takes 
  to 
  come 
  to 
  rest. 
  This 
  method 
  

   would 
  appear 
  specially 
  suitable 
  for 
  observations 
  of 
  radioactive 
  substances 
  

   with 
  a 
  short 
  period 
  of 
  decay. 
  It 
  must 
  be 
  noted 
  that 
  if, 
  as 
  usually 
  happens, 
  

   there 
  is 
  a 
  small 
  " 
  zero 
  E.M.F." 
  (p. 
  1048), 
  its 
  effects 
  can 
  be 
  eliminated, 
  

   either 
  by 
  subtracting 
  it 
  from 
  the 
  potentiometer 
  readings 
  or, 
  more 
  conve- 
  

   niently, 
  by 
  changing 
  the 
  sign 
  of 
  the 
  current. 
  The 
  zero 
  E.M.F. 
  will 
  be 
  

   found 
  to 
  be 
  wonderfully 
  constant 
  over 
  days. 
  

  

  t 
  Communicated 
  by 
  the 
  Author. 
  - 
  

  

  