﻿168 
  Mr. 
  W. 
  H. 
  Johnson 
  on 
  the 
  Action 
  of 
  [Jan. 
  14, 
  

  

  (see 
  Schellbach, 
  ' 
  Die 
  Lehre 
  von 
  den 
  elliptischen 
  Integralen,' 
  1864, 
  

   p. 
  113). 
  In 
  (2), 
  x 
  must 
  be 
  less 
  than 
  ii. 
  

   The 
  two 
  formulae 
  obtained 
  in 
  the 
  memoir, 
  

  

  tanh 
  x+ 
  tanh 
  (x— 
  p) 
  + 
  tanh 
  (x 
  + 
  li)-\-&c. 
  

  

  _ 
  2x 
  2ir 
  f 
  sin 
  2z 
  

  

  f 
  sings 
  + 
  sin4z 
  + 
  &c 
  \ 
  

   [ 
  sinh 
  v 
  sinh 
  2*/ 
  J 
  

  

  coth 
  p 
  -f- 
  coth 
  (x 
  — 
  fx) 
  + 
  coth 
  (# 
  + 
  /u) 
  + 
  &c. 
  

  

  2,37 
  . 
  7T 
  f 
  , 
  , 
  4 
  sin 
  2z 
  . 
  4 
  sin 
  4z 
  „ 
  

  

  = 
  — 
  + 
  - 
  1 
  cot 
  z+ 
  — 
  + 
  — 
  — 
  + 
  <&c, 
  

  

  fx 
  fji 
  I 
  i 
  e 
  4 
  "-l 
  

  

  are 
  considered 
  in 
  some 
  detail, 
  and 
  an 
  algebraical 
  proof 
  is 
  added 
  of 
  Abel's 
  

   identity 
  (' 
  CEuvres,' 
  t. 
  i. 
  p. 
  307), 
  

  

  2 
  -iW 
  + 
  <?)(l 
  + 
  2 
  3 
  )a 
  + 
  2 
  5 
  ). 
  • 
  • 
  =^-(l 
  + 
  ^(l 
  + 
  r 
  3 
  )(l 
  + 
  r 
  5 
  ). 
  . 
  .. 
  

  

  II. 
  " 
  On 
  some 
  remarkable 
  Changes 
  produced 
  in 
  Iron 
  and 
  Steel 
  

   by 
  the 
  Action 
  of 
  Hydrogen 
  and 
  Acids/'' 
  By 
  William 
  H. 
  

   Johnson, 
  B.Sc. 
  Communicated 
  by 
  Prof. 
  Sir 
  WilliamThomson, 
  

   LL.D., 
  F.R.S. 
  Received 
  December 
  7, 
  1874. 
  

  

  Some 
  three 
  years 
  ago 
  my 
  attention 
  was 
  called 
  to 
  a 
  remarkable 
  change 
  

   in 
  some 
  of 
  the 
  physical 
  properties 
  of 
  iron 
  caused 
  by 
  its 
  temporary 
  immer- 
  

   sion 
  in 
  hydrochloric 
  and 
  sulphuric 
  acids 
  . 
  This 
  change 
  is 
  at 
  once 
  made 
  

   evident 
  to 
  any 
  one 
  by 
  the 
  extraordinary 
  decrease 
  in 
  toughness 
  and 
  break- 
  

   ing-strain 
  of 
  the 
  iron 
  so 
  treated, 
  and 
  is 
  all 
  the 
  more 
  remarkable 
  as 
  it 
  is 
  

   not 
  permanent, 
  but 
  only 
  temporary 
  in 
  character, 
  for 
  with 
  lapse 
  of 
  time 
  

   the 
  metal 
  slowly 
  regains 
  its 
  original 
  toughness 
  and 
  strength. 
  "With 
  a 
  

   view 
  of 
  ascertaining 
  the 
  cause 
  and 
  degree 
  of 
  this 
  change, 
  I 
  have 
  from 
  

   time 
  to 
  time 
  made 
  a 
  number 
  of 
  experiments, 
  some 
  of 
  which 
  were 
  carried 
  

   out 
  on 
  a 
  large 
  scale 
  in 
  an 
  iron 
  -works 
  where 
  quantities 
  of 
  sulphuric 
  and 
  

   hydrochloric 
  acids 
  are 
  used 
  to 
  remove 
  the 
  coating 
  of 
  oxide 
  from 
  iron 
  wire, 
  

   preparatory 
  to 
  drawing 
  it. 
  Many 
  of 
  these 
  experiments 
  have 
  been 
  already 
  

   described 
  in 
  a 
  somewhat 
  desultory 
  form 
  in 
  the 
  ' 
  Proceedings 
  of 
  the 
  Lite- 
  

   rary 
  and 
  Philosophical 
  Society 
  of 
  Manchester 
  ' 
  for 
  Jan. 
  7th, 
  March 
  4th, 
  

   Dec. 
  30th, 
  1873, 
  Jan. 
  13th, 
  March 
  10th 
  and 
  24th, 
  1874. 
  

  

  As 
  mentioned 
  before, 
  I 
  first 
  noticed 
  that 
  iron 
  wire 
  became 
  more 
  brittle 
  

   after 
  a 
  few 
  minutes' 
  immersion 
  (half 
  a 
  minute 
  will 
  sometimes 
  suffice) 
  

   in 
  strong 
  hydrochloric 
  or 
  dilute 
  sulphuric 
  acid 
  — 
  a 
  piece 
  breaking 
  after 
  

   being 
  bent 
  once 
  on 
  itself, 
  while 
  before 
  immersion 
  it 
  would 
  bear 
  bending 
  

   on 
  itself 
  and 
  back 
  again 
  two 
  or 
  three 
  times 
  before 
  breaking. 
  But 
  per- 
  

   haps 
  the 
  most 
  remarkable 
  phenomenon 
  was, 
  that 
  if, 
  while 
  still 
  hot 
  from 
  

   the 
  effort 
  of 
  breaking, 
  the 
  fractured 
  part 
  was 
  wetted, 
  it 
  appeared 
  to 
  froth, 
  

  

  