﻿8&0 
  Notices 
  respecting 
  JSeiv 
  Books. 
  

  

  In 
  the 
  Preface 
  Mr. 
  Love 
  refers 
  students 
  for 
  the 
  history 
  of 
  

   dynamical 
  ideas 
  to 
  Mach's 
  Science 
  of 
  Mechanics. 
  

  

  The 
  term 
  'kinetic 
  reaction' 
  is 
  used 
  with 
  the 
  definition 
  " 
  a 
  

   vector 
  localized 
  in 
  the 
  line 
  arid 
  with 
  the 
  sense 
  of 
  acceleration 
  of 
  a 
  

   particle 
  and 
  of 
  magnitude 
  equal 
  to 
  the 
  product 
  of 
  its 
  mass 
  and 
  

   acceleration.'' 
  

  

  After 
  a 
  chapter 
  (vi.) 
  of 
  general 
  theorems, 
  in 
  that 
  following 
  the 
  

   deforraability 
  of 
  bodies, 
  regarded 
  as 
  geometrical 
  surfaces 
  filled 
  

   continuously 
  with 
  particles, 
  strain 
  and 
  stress 
  are 
  introduced 
  ; 
  

   as 
  also 
  ' 
  Bodily 
  forces,' 
  ' 
  Surface 
  tractions,' 
  ' 
  Tensions 
  of 
  strings 
  ' 
  

   (iuextensible 
  or 
  extensible) 
  and 
  reactions 
  thereof 
  when 
  in 
  contact 
  

   with 
  surfaces 
  ; 
  finally 
  ' 
  Springs.' 
  

  

  Ch. 
  viii. 
  is 
  devoted 
  to 
  the 
  important 
  subject 
  of 
  ' 
  Work 
  and 
  

   Energy.' 
  A 
  ' 
  conservative' 
  system, 
  the 
  analytical 
  condition 
  for 
  

   it, 
  and 
  its 
  ' 
  Potential 
  Energy 
  ' 
  are 
  explained. 
  A 
  collection 
  of 
  

   Examples 
  of 
  the 
  Calculation 
  of 
  "Work 
  is 
  appended. 
  The 
  subject 
  

   being 
  then 
  resumed, 
  a 
  proof 
  of 
  the 
  constancy 
  of 
  the 
  sum 
  of 
  kinetic 
  

   and 
  potential 
  energy 
  of 
  a 
  conservative 
  system 
  is 
  given 
  ; 
  forces 
  are 
  

   distinguished 
  as 
  ' 
  Positional 
  and 
  Motional,' 
  and 
  it 
  is 
  shown 
  that 
  

   those 
  of 
  rational 
  mechanics 
  may 
  be 
  conditioned 
  as 
  always 
  conserva- 
  

   tive 
  as 
  regards 
  positional, 
  but 
  generally 
  non-conservative 
  as 
  regards 
  

   motional. 
  ' 
  Power 
  ' 
  is 
  defined 
  as 
  the 
  rate 
  per 
  unit 
  of 
  time 
  at 
  which 
  

   work 
  is 
  done 
  by 
  the 
  action 
  of 
  one 
  system 
  on 
  another. 
  The 
  

   kinetic 
  energy 
  produced 
  by 
  impulses 
  ; 
  the 
  principle 
  of 
  virtual 
  

   work 
  or 
  ' 
  virtual 
  moment 
  of 
  a 
  localized 
  vector,' 
  the 
  ' 
  variation 
  

   equation 
  of 
  motion,' 
  and 
  a 
  ' 
  critical 
  note 
  ' 
  — 
  in 
  which 
  a 
  conclusion 
  

   is 
  arrived 
  at 
  that 
  "if 
  we 
  are 
  prepared 
  to 
  abandon 
  pi'ecise 
  definition 
  

   and 
  the 
  purely 
  logical 
  deductive 
  method, 
  as 
  unsuited 
  to 
  a 
  science 
  

   at 
  present 
  incompletely 
  known, 
  we 
  may 
  construct 
  a 
  physical 
  

   theory, 
  indefinite 
  in 
  parts 
  and 
  incomplete 
  in 
  details, 
  but 
  neverthe- 
  

   less 
  available 
  for 
  co-ordinating 
  the 
  results 
  obtained 
  by 
  physical 
  

   investigation, 
  and 
  capable 
  of 
  being 
  itself 
  advanced 
  towards 
  

   perfection 
  thereby 
  " 
  — 
  conclude 
  the 
  first 
  half 
  of 
  the 
  volume. 
  The 
  

   second 
  half 
  is 
  occupied 
  with 
  'Methods 
  and 
  Applications,' 
  largely 
  

   illustrated 
  by 
  a 
  copious 
  collection 
  of 
  examples, 
  some 
  worked 
  out 
  

   in 
  full, 
  attached 
  to 
  each 
  chapter, 
  ' 
  Motions 
  of 
  Eree 
  Particles 
  in 
  

   given 
  Eields 
  of 
  Eorce,' 
  and 
  ' 
  under 
  Constraints 
  and 
  Resistances,' 
  

   form 
  the 
  subjects 
  of 
  chs. 
  ix. 
  and 
  x. 
  devoted 
  to 
  the 
  ' 
  Dynamics 
  of 
  a 
  

   Particle,' 
  The 
  ' 
  Motion 
  of 
  a 
  Rigid 
  Body 
  in 
  Two 
  Dimensions 
  ' 
  

   occupies 
  ch. 
  xi, 
  Impulse 
  and 
  Collision, 
  as 
  far 
  as 
  Impact 
  of 
  

   smooth 
  Spheres, 
  necessarily 
  introduces 
  reference 
  to 
  Elasticity, 
  — 
  

   reminding 
  us 
  of 
  Mr. 
  Love's 
  Treatise 
  on 
  that 
  subject, 
  reviewed 
  in 
  

   this 
  Magazine 
  some 
  few 
  years 
  since. 
  The 
  Impact 
  of 
  Rigid 
  Bodies 
  in 
  

   two 
  dimensions, 
  Initial 
  Movement 
  and 
  the 
  Motion 
  of 
  a 
  Chain 
  are 
  the 
  

   subjects 
  of 
  ch. 
  xii. 
  — 
  one 
  of 
  Examples 
  essentially. 
  A 
  short 
  chapter 
  

   on 
  ' 
  Relative 
  Motion 
  and 
  Universal 
  Gravitation' 
  forms 
  the 
  last. 
  

  

  Erom 
  this 
  abstract 
  of 
  its 
  contents, 
  it 
  will 
  be 
  seen 
  that 
  the 
  

   treatise, 
  within 
  the 
  limits 
  to 
  which 
  it 
  is 
  confined, 
  is 
  quite 
  " 
  up 
  to. 
  

   date 
  " 
  ; 
  and 
  maintains 
  the 
  Author's 
  character 
  as 
  a 
  careful 
  and 
  

   competent 
  teacher 
  of 
  the 
  subjects 
  on 
  which 
  he 
  undertakes 
  to 
  

   instruct. 
  J. 
  J. 
  W. 
  

  

  