﻿1875.] 
  

  

  Prismatic 
  Structure 
  of 
  Basalt. 
  

  

  181 
  

  

  indefinitely 
  greater 
  than 
  that, 
  and 
  assuming 
  the 
  material 
  at 
  one 
  tem- 
  

   perature 
  initially, 
  homogeneous 
  and 
  isotropic, 
  and 
  that 
  cooling 
  takes 
  

   place 
  from 
  the 
  top 
  surface 
  only, 
  he, 
  on 
  these 
  data, 
  proceeds 
  to 
  con- 
  

   sider 
  the 
  phenomena 
  that 
  will 
  successively 
  result 
  by 
  contraction 
  in 
  

   cooling. 
  

  

  While 
  the 
  mass 
  remains 
  at 
  its 
  upper 
  part 
  still 
  plastic 
  by 
  heat, 
  contrac- 
  

   tion 
  will 
  be 
  met 
  by 
  internal 
  movements 
  and 
  subsidence 
  of 
  the 
  top 
  surface, 
  

   and 
  no 
  cracking 
  or 
  splitting 
  can 
  take 
  place 
  until 
  the 
  material 
  there 
  has 
  

   become 
  rigid 
  enough 
  to 
  break 
  under 
  tensile 
  strain. 
  He 
  points 
  out 
  that 
  

   this 
  degree 
  of 
  rigidity, 
  or 
  " 
  splitting 
  temperature," 
  is 
  not 
  reached 
  until 
  

   the 
  top 
  surface 
  has 
  fallen 
  to 
  between 
  900° 
  and 
  600° 
  Fahr. 
  

  

  At 
  this 
  temperature 
  the 
  cooling 
  surface 
  begins 
  to 
  separate, 
  by 
  fracture 
  

   penetrating 
  perpendicularly 
  to 
  it, 
  into 
  smaller 
  surfaces. 
  These 
  must 
  be 
  

   similar 
  and 
  equal 
  in 
  area, 
  and 
  such 
  as 
  that 
  their 
  edges 
  in 
  contact 
  can 
  

   make 
  up 
  a 
  continuous 
  superficies. 
  To 
  relieve 
  the 
  orthogonal 
  strains 
  in 
  

   the 
  cooling 
  surface, 
  and 
  to 
  meet 
  the 
  above 
  conditions, 
  only 
  three 
  geo- 
  

   metric 
  figures 
  for 
  the 
  separating 
  surfaces 
  are 
  possible 
  — 
  namely, 
  the 
  equi- 
  

   lateral 
  triangle, 
  the 
  square, 
  and 
  the 
  regular 
  hexagon. 
  

  

  The 
  author 
  then 
  inquires 
  why 
  the 
  last 
  of 
  these 
  is 
  normally 
  the 
  form 
  

   found 
  in 
  nature. 
  He 
  traces 
  this 
  to 
  the 
  law 
  of 
  least 
  action 
  which 
  governs 
  

   the 
  play 
  of 
  all 
  natural 
  forces 
  whose 
  final 
  result 
  is 
  produced 
  by 
  the 
  least 
  

   possible 
  expenditure 
  of 
  force. 
  He 
  shows 
  that, 
  in 
  a 
  contracting 
  surface 
  

   splitting 
  up 
  into 
  equal 
  areas, 
  the 
  expenditure 
  of 
  work 
  will, 
  for 
  the 
  equi- 
  

   lateral 
  triangle, 
  the 
  square, 
  and 
  the 
  regular 
  hexagon, 
  be 
  approximately 
  as 
  

   the 
  numbers 
  1*000, 
  0*680, 
  and 
  0*519. 
  This 
  economy 
  of 
  force 
  decides 
  the 
  

   hexagon 
  as 
  the 
  form 
  found 
  in 
  nature. 
  The 
  diameter 
  of 
  the 
  hexagon, 
  which 
  

   is 
  the 
  upper 
  surface 
  of 
  the 
  inceptive 
  hexagonal 
  prism, 
  is 
  shown 
  to 
  be 
  fixed 
  

   by 
  the 
  relation 
  that 
  subsists 
  between 
  the 
  coefficient 
  of 
  contraction 
  of 
  the 
  ma- 
  

   terial 
  and 
  that 
  of 
  its 
  extension 
  at 
  rupture 
  by 
  a 
  tensile 
  force 
  at 
  the 
  splitting 
  

   temperature. 
  This 
  decides 
  the 
  diameters 
  of 
  the 
  separate 
  prisms. 
  The 
  

   splitting 
  by 
  contraction 
  proceeds 
  into 
  the 
  mass 
  always 
  in 
  a 
  direction 
  per- 
  

   pendicular 
  to 
  the 
  cooling 
  surface 
  ; 
  and 
  at 
  any 
  instant 
  the 
  splitting 
  is 
  limited 
  

   in 
  its 
  progress 
  by 
  the 
  isothermal 
  couche 
  which 
  is 
  at 
  the 
  splitting 
  tempe- 
  

   rature 
  within 
  the 
  mass 
  ; 
  for 
  within 
  that 
  couche 
  the 
  mass 
  is 
  still 
  plastic. 
  

   In 
  the 
  case 
  assumed, 
  the 
  prisms 
  formed 
  are 
  straight 
  and 
  vertical. 
  When 
  

   the 
  splitting 
  has 
  proceeded 
  to 
  some 
  distance 
  within 
  the 
  mass, 
  the 
  further 
  

   cooling 
  of 
  each 
  prism 
  takes 
  place, 
  not 
  only 
  from 
  the 
  top, 
  but 
  from 
  the 
  

   sides 
  ; 
  and 
  the 
  more 
  important 
  conditions 
  influencing 
  the 
  latter 
  in 
  nature 
  

   are 
  pointed 
  out. 
  

  

  Any 
  one 
  prism 
  is 
  coldest 
  at 
  its 
  extremity, 
  and 
  its 
  temperature 
  increases 
  

   along 
  its 
  length 
  to 
  the 
  other 
  end, 
  where 
  the 
  splitting 
  is 
  still 
  proceeding. 
  

   The 
  prism 
  is 
  hotter 
  also, 
  for 
  any 
  transverse 
  section, 
  as 
  we 
  approach 
  its 
  

   axis 
  than 
  about 
  the 
  exterior 
  ; 
  differential 
  strains 
  in 
  the 
  longitudinal 
  

   direction 
  thus 
  take 
  place, 
  by 
  cooling 
  and 
  contraction, 
  between 
  the 
  succes- 
  

   sive 
  imaginary 
  couches, 
  taken 
  from 
  the 
  exterior 
  to 
  the 
  axis 
  of 
  the 
  prism, 
  

  

  