﻿Notices 
  respecting 
  New 
  Books, 
  493 
  

  

  volume, 
  many 
  are 
  mere 
  notes 
  ; 
  of 
  the 
  many 
  others 
  which 
  are 
  sub- 
  

   stantial 
  additions 
  to 
  knowledge 
  special 
  mention 
  might 
  be 
  made 
  of 
  

   two. 
  The 
  one 
  is 
  the 
  " 
  Trilogy 
  " 
  on 
  the 
  real 
  and 
  imaginary 
  roots 
  

   of 
  algebraic 
  equations 
  (Phil. 
  Trans. 
  1864), 
  including 
  proofs 
  of 
  

   Newton's 
  rule. 
  The 
  other 
  is 
  the 
  interesting 
  extension 
  of 
  Poinsot's 
  

   representation 
  of 
  the 
  rotation 
  of 
  a 
  solid 
  body, 
  a 
  paper 
  which 
  con- 
  

   tains 
  some 
  very 
  elegant 
  geometrical 
  reasoning. 
  

  

  The 
  most 
  outstanding 
  papers 
  in 
  the 
  French 
  volume 
  are 
  the 
  great 
  

   memoir 
  on 
  the 
  equation 
  of 
  the 
  fifth 
  degree, 
  which 
  was 
  published 
  

   at 
  intervals 
  in 
  the 
  Comjptes 
  Bendus 
  during 
  1865 
  and 
  1866, 
  and 
  the 
  

   essay 
  or 
  so-called 
  Note 
  on 
  the 
  Theory 
  of 
  Elliptic 
  Functions, 
  which 
  

   originally 
  formed 
  part 
  of 
  the 
  6th 
  edition 
  of 
  Lacroix's 
  ' 
  Differential 
  

   and 
  Integral 
  Calculus 
  ' 
  (1862). 
  This 
  second 
  volume 
  is 
  adorned 
  

   Avith 
  a 
  fine 
  and 
  evidently 
  characteristic 
  portrait 
  of 
  Hermite 
  at 
  the 
  

   age 
  of 
  fifty. 
  For 
  their 
  continued 
  labours 
  in 
  editing 
  the 
  writings 
  of 
  

   Sylvester 
  and 
  Hermite, 
  the 
  respective 
  editors, 
  H. 
  F. 
  Baker 
  and 
  

   Emile 
  Picard, 
  deserve 
  the 
  thanks 
  of 
  the 
  whole 
  mathematical 
  world. 
  

  

  An 
  Elementary 
  Treatise 
  en 
  Tlieoretical 
  Mechanics. 
  By 
  J. 
  H. 
  Jea.ns, 
  

   F.R.S. 
  Boston 
  : 
  Ginn 
  & 
  Co. 
  1907. 
  

  

  This 
  is 
  a 
  thoroughly 
  sane 
  book 
  on 
  Dynamics, 
  just 
  such 
  in 
  fact 
  as 
  

   we 
  should 
  look 
  for 
  at 
  the 
  hands 
  of 
  Professor 
  Jeans. 
  The 
  opening 
  

   chapters 
  deal 
  in 
  a 
  clear 
  Newtonian 
  manner 
  with 
  the 
  simple 
  prin- 
  

   ciples 
  at 
  the 
  foundation 
  of 
  the 
  science, 
  and 
  up 
  to 
  the 
  middle 
  of 
  

   Chapter 
  TV. 
  no 
  serious 
  demand 
  is 
  made 
  on 
  the 
  mathematical 
  

   powers 
  of 
  the 
  student. 
  In 
  this 
  chapter, 
  which 
  treats 
  of 
  the 
  

   statics 
  of 
  particles, 
  the 
  equilibrium 
  of 
  the 
  flexible 
  string 
  or 
  chain 
  

   is 
  discussed. 
  This 
  early 
  introduction 
  of 
  the 
  belaying-pin 
  and 
  the 
  

   catenary 
  has 
  much 
  to 
  commend 
  it 
  : 
  — 
  e. 
  g., 
  they 
  give 
  easily 
  realizable 
  

   problems 
  for 
  the 
  first 
  use 
  of 
  the 
  calculus. 
  The 
  next 
  two 
  chapters 
  

   deal 
  with 
  the 
  statics 
  of 
  rigid 
  bodies 
  and 
  centres 
  of 
  gravity 
  ; 
  and 
  

   then 
  in 
  Chapter 
  VII. 
  we 
  have 
  a 
  clear 
  discussion 
  of 
  the 
  principle 
  of 
  

   Work, 
  including 
  virtual 
  work, 
  conservation 
  of 
  energy, 
  and 
  the 
  

   conditions 
  for 
  stable 
  and 
  unstable 
  equilibrium. 
  The 
  treatment 
  is 
  

   admirable. 
  The 
  illustrations 
  are 
  well 
  chosen 
  and 
  sufficient 
  for 
  

   the 
  purpose 
  ; 
  and 
  there 
  is 
  no 
  unnecessary 
  wielding 
  of 
  the 
  mathe- 
  

   matical 
  weapon. 
  The 
  simpler 
  problems 
  of 
  motion 
  under 
  constant 
  

   forces 
  and 
  of 
  motion 
  of 
  systems 
  of 
  particles 
  having 
  been 
  disposed 
  

   of, 
  the 
  remaining 
  chapters 
  are 
  characterized 
  by 
  a 
  distinctly 
  more 
  

   advanced 
  mode 
  of 
  treatment. 
  Towards 
  the 
  end 
  of 
  the 
  book 
  the 
  

   student 
  is 
  not 
  spared, 
  and 
  many 
  a 
  reader 
  who 
  has, 
  so 
  to 
  speak, 
  

   cycled 
  steadily 
  up 
  the 
  incline 
  to 
  Chapter 
  X. 
  will 
  begin 
  to 
  feel 
  a 
  

   steepening 
  gradient 
  as 
  he 
  essays 
  the 
  last 
  two 
  stages. 
  Indeed 
  it 
  is 
  

   not 
  a 
  mere 
  question 
  of 
  a 
  steeper 
  ascent, 
  it 
  is 
  ascent 
  into 
  a 
  

   wholly 
  different 
  atmosphere. 
  The 
  symmetrical 
  spinning 
  top 
  is 
  

   a 
  hard 
  enough 
  nut 
  to 
  crack 
  for 
  a 
  student 
  to 
  whom 
  most 
  of 
  the 
  

   book 
  is 
  new; 
  but 
  the 
  generalized 
  methods 
  of 
  Lagrange 
  and 
  

   Hamilton 
  are 
  a 
  much 
  more 
  severe 
  test 
  of 
  the 
  mathematical 
  

   capacity 
  of 
  the 
  reader. 
  "We 
  are 
  at 
  one 
  with 
  Professor 
  Jeans 
  in 
  

  

  