﻿Notices 
  respecting 
  Neio 
  Books. 
  537 
  

  

  chapter, 
  on 
  Sturm's 
  theorem, 
  is 
  specially 
  interesting. 
  Continued 
  

   fractions 
  and 
  their 
  applications 
  to 
  quadratic 
  irrational 
  numbers 
  

   aud 
  to 
  the 
  Pellian 
  equation 
  are 
  discussed 
  in 
  chapter 
  eleven 
  (with 
  

   some 
  departures, 
  in 
  notation, 
  from 
  Gauss 
  and 
  Dirichlet). 
  In 
  the 
  

   last 
  chapter 
  the 
  elementary 
  parts 
  of 
  the 
  theory 
  of 
  the 
  roots 
  of 
  

   unity, 
  and 
  also 
  the 
  subject 
  of 
  quadratic 
  residues 
  and 
  the 
  law 
  of 
  

   quadratic 
  reciprocity 
  are 
  expounded. 
  

  

  Algebraical 
  quantities, 
  the 
  subject 
  of 
  Book 
  iii., 
  are 
  also 
  handled 
  

   in 
  six 
  chapters. 
  These 
  last 
  200 
  pages 
  constitute 
  the 
  prime 
  portion 
  

   of 
  the 
  banquet 
  provided 
  by 
  our 
  Author. 
  The 
  Galois' 
  Theory 
  is 
  

   discussed 
  in 
  chapters 
  thirteen 
  and 
  fourteen, 
  as 
  to 
  its 
  fundamental 
  

   notions, 
  a 
  more 
  advanced 
  treatment 
  being 
  presented 
  in 
  vol. 
  ii. 
  

   (of 
  the 
  first 
  edition). 
  The 
  account 
  is 
  thoroughly 
  interesting, 
  and, 
  

   we 
  believe, 
  original. 
  Chapter 
  fifteen 
  is 
  on 
  Cyclical 
  Equations, 
  

   chapter 
  sixteen 
  on 
  Cyclotomy, 
  and 
  chapter 
  seventeen 
  contains 
  

   several 
  propositions 
  connected 
  with 
  the 
  Solution 
  of 
  Equations, 
  

   carrying 
  forward 
  the 
  G-alois 
  ' 
  theory, 
  and 
  the 
  last 
  chapter 
  treats 
  

   of 
  the 
  roots 
  of 
  metacyclic 
  equations 
  of 
  prime 
  degrees. 
  We 
  have 
  

   given 
  but 
  a 
  bald 
  account 
  of 
  what, 
  possibly, 
  is 
  an 
  epoch-making 
  

   book. 
  It 
  only 
  remains 
  to 
  say 
  that 
  the 
  printers 
  have 
  done 
  their 
  

   work 
  well, 
  for 
  the 
  typography 
  is 
  all 
  that 
  one 
  could 
  wish. 
  

  

  Die 
  Mechanik 
  des 
  Welt 
  alls. 
  By 
  Dr. 
  L. 
  Zehistdee, 
  Extraordinary 
  

   Professor 
  of 
  Physics 
  in 
  the 
  University 
  of 
  Freiburg 
  i. 
  B. 
  (Freiburg 
  

   i. 
  B., 
  J. 
  C. 
  B. 
  Mohr, 
  1897.) 
  

  

  In 
  this 
  treatise 
  Professor 
  Zehnder 
  contributes 
  another 
  to 
  the 
  

   already 
  numerous 
  theories 
  of 
  aether 
  and 
  matter. 
  He 
  assumes 
  that 
  

   space 
  is 
  infinite 
  and 
  three-dimensional, 
  and 
  that 
  it 
  is 
  filled 
  with 
  

   extremely 
  small 
  material 
  particles 
  which 
  exert 
  a 
  gravitational 
  

   attraction 
  on 
  each 
  other, 
  but 
  move 
  with 
  great 
  velocities.; 
  these 
  

   particles 
  constitute 
  the 
  aether, 
  which 
  therefore 
  behaves 
  as 
  a 
  gas 
  

   and 
  transmits 
  vibrations 
  exactly 
  as, 
  according 
  to 
  the 
  kinetic 
  theory, 
  

   ordinary 
  gases 
  do. 
  The 
  density 
  of 
  this 
  aether 
  and 
  consequently 
  

   the 
  mass 
  of 
  each 
  particle 
  are 
  assumed 
  to 
  be 
  exceedingly 
  small. 
  

   Electricity 
  consists 
  of 
  a 
  vibrational 
  motion 
  of 
  the 
  aether 
  particles, 
  

   positive 
  charges 
  corresponding 
  to 
  translational 
  velocities 
  greater 
  

   than 
  the 
  mean 
  velocity 
  and 
  negative 
  charges 
  to 
  a 
  defect 
  of 
  trans- 
  

   lational 
  motion. 
  Matter 
  is 
  composed 
  of 
  particles 
  much 
  larger 
  

   than 
  the 
  aether 
  atoms 
  but 
  of 
  the 
  same 
  material 
  ; 
  these, 
  by 
  reason 
  of 
  

   their 
  greater 
  mass, 
  attract 
  round 
  themselves 
  a 
  shell 
  of 
  condensed 
  

   aether 
  atoms 
  which 
  serves 
  to 
  communicate 
  the 
  motion 
  arising 
  from 
  

   the 
  impact 
  of 
  the 
  particles 
  to 
  the 
  surrounding 
  free 
  aether. 
  

  

  The 
  author 
  applies 
  his 
  theory 
  to 
  various 
  physical 
  phenomena 
  in 
  

   a 
  general 
  non-mathematical 
  fashion. 
  It 
  is 
  obvious, 
  however, 
  that 
  

   no 
  ultimate 
  theory 
  of 
  aether 
  and 
  matter 
  can 
  lay 
  claim 
  to 
  serious 
  

   consideration 
  which 
  postulates 
  an 
  attractive 
  force 
  without 
  a 
  medium 
  

   for 
  its 
  action, 
  and 
  which 
  assumes 
  the 
  existence 
  of 
  elastic 
  spherical 
  

   atoms 
  without 
  explaining 
  the 
  nature 
  of 
  the 
  elastic 
  forces 
  called 
  into 
  

   play 
  during 
  their 
  impact. 
  J. 
  L. 
  H. 
  

  

  