﻿Notices 
  respecting 
  New 
  Books. 
  379 
  

  

  (b) 
  To 
  redetermine 
  the 
  change 
  of 
  temperature 
  on 
  free 
  

   expansion 
  for 
  pure 
  hydrogen, 
  nitrogen, 
  and 
  carbon 
  

   dioxide, 
  over 
  as 
  wide 
  a 
  temperature 
  as 
  possible, 
  paying 
  

   particular 
  attention 
  to 
  the 
  question 
  whether 
  the 
  cooling 
  

   effect 
  is 
  strictly 
  proportional 
  to 
  the 
  change 
  of 
  pressure, 
  

   and 
  to 
  its 
  variation 
  with 
  the 
  temperature 
  : 
  the 
  experi- 
  

   ments 
  on 
  hydrogen 
  being 
  the 
  most 
  important. 
  

  

  XLI. 
  Notices 
  respecting 
  New 
  Books. 
  

  

  Theoretical 
  Mechanics, 
  an 
  Introductory 
  Treatise 
  on 
  the 
  Principles 
  

   of 
  Dynamics, 
  with 
  Applications 
  and 
  numerous 
  Examples 
  . 
  By 
  

   A. 
  E. 
  H. 
  Love, 
  M.A., 
  F.R.S., 
  Fellow 
  and 
  Lecturer 
  of 
  St. 
  Johns 
  

   College, 
  Cambridge. 
  Cambridge, 
  at 
  the 
  University 
  Press, 
  1897. 
  

  

  rPHIS 
  well-printed 
  volume 
  issuing 
  from 
  the 
  Cambridge 
  Univer- 
  

   -*- 
  sity 
  Press 
  seems 
  intended 
  to 
  meet 
  the 
  wants 
  of 
  candidates 
  for 
  

   scholarships 
  or 
  places 
  in 
  the 
  Mathematical 
  Tripos. 
  Its 
  contents 
  

   consist 
  of 
  eighty-four 
  pages 
  of 
  " 
  Preliminary 
  " 
  matter, 
  sixty 
  on 
  " 
  the 
  

   Principles 
  of 
  Dynamics," 
  and 
  two 
  hundred 
  and 
  twenty-six 
  on 
  

   "Methods 
  and 
  Applications": 
  an 
  'Appendix' 
  of 
  five 
  pages 
  on 
  

   " 
  Measurement, 
  Units, 
  and 
  Dimensions 
  " 
  ; 
  finally, 
  an 
  Index. 
  

  

  The 
  terminology 
  of 
  the 
  treatise 
  involving 
  the 
  frequent 
  use 
  of 
  

   the 
  vector, 
  ch. 
  ii. 
  is 
  devoted 
  to 
  " 
  the 
  Geometry 
  of 
  Vectors 
  " 
  ; 
  while 
  

   Force 
  is 
  defined 
  (ch. 
  v.), 
  as 
  " 
  a 
  vector 
  localized 
  at 
  a 
  point 
  " 
  or 
  what 
  

   is 
  represented 
  by 
  a 
  right 
  line 
  drawn 
  from 
  a 
  given 
  point 
  in 
  a 
  

   determined 
  direction, 
  sense, 
  and 
  length. 
  Bodies 
  have 
  ' 
  mass 
  ' 
  and 
  

   * 
  act 
  ' 
  upon 
  one 
  another 
  ; 
  and, 
  in 
  the 
  case 
  of 
  homogeneous 
  bodies, 
  

   the 
  ratio 
  of 
  mass 
  to 
  volume 
  is 
  the 
  density 
  ; 
  the 
  limit 
  at 
  any 
  point 
  

   of 
  course 
  giving 
  the 
  density 
  at 
  the 
  point, 
  where 
  this 
  is 
  variable. 
  

   The 
  differential 
  coefficients 
  introduced 
  are 
  usually 
  printed 
  in 
  the 
  

   fluxional 
  manner 
  with 
  dots, 
  as 
  in 
  Thomson 
  and 
  Tait's 
  treatise 
  : 
  

   axes 
  of 
  coordinates 
  form 
  a 
  ' 
  frame.' 
  ' 
  Gravity 
  ' 
  is 
  the 
  vertical 
  

   action 
  of 
  the 
  particles 
  of 
  the 
  Earth 
  on 
  those 
  of 
  any 
  bcdy 
  "small 
  

   enough 
  to 
  be 
  handled 
  or 
  moved 
  by 
  machinery 
  " 
  ; 
  thus, 
  the 
  neigh- 
  

   bourhood 
  of 
  the 
  Earth 
  is 
  a 
  ' 
  field 
  of 
  force,' 
  and 
  the 
  acceleration 
  

   at 
  any 
  point 
  in 
  the 
  field, 
  i. 
  e. 
  the 
  intensity 
  of 
  the 
  field, 
  is 
  at 
  any 
  place 
  

   vertically 
  downwards 
  and 
  equal 
  to 
  g 
  ; 
  weight 
  being 
  " 
  the 
  resultant 
  

   force 
  on 
  a 
  free 
  falling 
  body 
  in 
  the 
  neighbourhood 
  of 
  the 
  Earth, 
  

   numerically 
  equal 
  to 
  mgp 
  " 
  At 
  any 
  place 
  on 
  the 
  Earth's 
  surface 
  

   the 
  mass 
  of 
  a 
  body 
  is 
  proportional 
  to 
  its 
  weight 
  " 
  is 
  a 
  statement 
  

   which 
  implies 
  an 
  ideal 
  Earth, 
  homogeneous 
  and 
  of 
  spherical 
  form. 
  

   " 
  The 
  tendency 
  of 
  a 
  body, 
  apart 
  from 
  the 
  action 
  of 
  other 
  bodies, 
  

   to 
  persist 
  in 
  its 
  state 
  of 
  motion 
  at 
  any 
  instant 
  is 
  known 
  as 
  its 
  

   inertia 
  " 
  ; 
  which 
  the 
  mass 
  can 
  be 
  taken 
  to 
  measure. 
  

  

  In 
  an 
  historical 
  note, 
  at 
  the 
  conclusion 
  of 
  ch. 
  v., 
  the 
  idea 
  of 
  

   acceleration 
  is 
  assigned 
  to 
  Gah'lei, 
  and 
  that 
  of 
  force 
  as 
  its 
  cauee 
  

   to 
  Newton, 
  of 
  whose 
  Acciomata 
  sive 
  Leges 
  Motus 
  a 
  translation 
  is 
  

   given 
  ; 
  they 
  being 
  regarded 
  as 
  postulates 
  of 
  which 
  the 
  third 
  

   contained 
  what 
  was 
  afterwards 
  known 
  as 
  d'Alembert's 
  Principle. 
  

  

  