﻿Molecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds. 
  51 
  

  

  There 
  are 
  certain 
  reasons 
  that 
  make 
  it 
  not 
  unlikely 
  that 
  the 
  

   atom 
  with 
  only 
  two 
  electrons 
  best 
  represents 
  hydrogen. 
  

   Eventually 
  all 
  combinations 
  should 
  be 
  calculated 
  ; 
  but 
  the 
  

   labour 
  involved 
  has 
  limited 
  us 
  to 
  a 
  few 
  typical 
  solutions. 
  

   The 
  angles 
  of 
  latitude 
  are 
  given 
  in 
  the 
  figure, 
  that 
  for 
  

   hydrogen 
  being 
  65° 
  50'. 
  The 
  other 
  diatomic 
  molecules 
  

   shown 
  have 
  angles 
  ranging 
  from 
  73° 
  40' 
  for 
  carbon 
  to 
  

   74° 
  45' 
  for 
  fluorine, 
  a 
  small 
  variation, 
  but 
  a 
  small 
  variation 
  

   in 
  this 
  angle 
  is 
  very 
  important 
  in 
  the 
  property 
  of 
  forming 
  

   compounds. 
  

  

  The 
  three-atom 
  molecules 
  shown 
  are 
  drawn 
  to 
  the 
  same 
  

   scale 
  as 
  the 
  two-atom 
  molecules. 
  They 
  represent 
  H 
  3 
  , 
  C 
  3 
  , 
  N 
  3 
  , 
  

   0: 
  ? 
  , 
  HON, 
  C0 
  2 
  , 
  H 
  2 
  0, 
  N 
  2 
  0, 
  and 
  HNO. 
  'The 
  angles 
  of 
  latitude 
  

   are 
  a 
  few 
  minutes 
  of 
  arc 
  less 
  than 
  the 
  corresponding 
  diatomic 
  

   molecules. 
  

  

  If 
  the 
  third 
  atom 
  is 
  located 
  on 
  the 
  same 
  side 
  of 
  the 
  equator 
  

   as 
  the 
  second 
  atom, 
  instead 
  of 
  on 
  the 
  opposite 
  side, 
  as 
  in 
  the 
  

   above 
  molecules, 
  it 
  is 
  evident 
  from 
  fig. 
  9 
  that 
  the 
  second 
  and 
  

   third 
  atoms 
  repel 
  each 
  other 
  with 
  considerable 
  force 
  if 
  they 
  

   should 
  remain 
  in 
  the 
  equilibrium 
  circle 
  of 
  the 
  diatomic 
  

   molecule 
  ; 
  for 
  the 
  second 
  atom 
  is 
  upon 
  the 
  equator 
  of 
  the 
  

   third 
  atom, 
  and 
  the 
  distance 
  between 
  them 
  is 
  not 
  so 
  great 
  as 
  

   the 
  distance 
  to 
  the 
  central 
  or 
  first 
  atom. 
  These 
  circles 
  will 
  

   no 
  longer 
  apply 
  to 
  these 
  molecules, 
  because 
  the 
  atoms 
  separate 
  

   from 
  each 
  other 
  to 
  a 
  greater 
  distance 
  than 
  the 
  diameter 
  of 
  

   the 
  circles, 
  and 
  the 
  distance 
  from 
  the 
  central 
  atom 
  also 
  

   increases. 
  The 
  equations 
  have 
  been 
  obtained 
  by 
  which 
  the 
  

   angles 
  and 
  distances 
  may 
  be 
  found, 
  and 
  it 
  has 
  been 
  proved 
  

   in 
  certain 
  cases 
  that 
  the 
  combination 
  is 
  stable 
  ; 
  but 
  no 
  

   sketches 
  are 
  shown 
  in 
  fig. 
  13 
  as 
  the 
  particular 
  angles 
  and 
  

   distances 
  have 
  not 
  been 
  calculated. 
  

  

  One 
  case 
  has 
  been 
  calculated 
  with 
  four 
  atoms 
  in 
  the 
  mole- 
  

   cule 
  : 
  a 
  ring 
  of 
  three 
  hydrogen 
  atoms 
  with 
  one 
  nitrogen 
  

   atom 
  at 
  the 
  apex 
  of 
  the 
  right 
  cone 
  of 
  which 
  the 
  ring 
  forms 
  

   the 
  base. 
  This 
  represents 
  ammonia, 
  NH 
  3 
  . 
  The 
  addition 
  of 
  

   a 
  third 
  atom 
  in 
  the 
  ring 
  rapidly 
  increases 
  the 
  dimensions 
  of 
  

   the 
  whole 
  molecule, 
  and 
  consequently 
  reduces 
  the 
  degree 
  

   of 
  stability 
  possible. 
  The 
  distance 
  between 
  the 
  nitrogen 
  and 
  

   the 
  hydrogen 
  atoms 
  in 
  this 
  figure 
  is 
  /3r 
  = 
  4 
  , 
  9, 
  as 
  compared 
  

   with 
  J3v 
  = 
  2'§8 
  in 
  the 
  diatomic 
  molecule 
  NH, 
  and 
  the 
  angle 
  

   of 
  latitude 
  is 
  64° 
  31' 
  as 
  compared 
  with 
  71° 
  4b". 
  The 
  distance 
  

   between 
  any 
  two 
  hydrogen 
  atoms 
  is 
  /3v 
  = 
  'd'Go. 
  

  

  If 
  a 
  fourth 
  atom 
  is 
  added 
  to 
  the 
  ring, 
  making 
  a 
  five-atom 
  

   molecule, 
  the 
  equations 
  show 
  that 
  for 
  equilibrium 
  the 
  

   distances 
  are 
  very 
  greatly 
  increased. 
  The 
  combination 
  of 
  

   carbon 
  with 
  a 
  ring 
  of 
  four 
  hvdrogen 
  atoms 
  has 
  beeu 
  

  

  E 
  2 
  

  

  