﻿536 
  Notices 
  respecting 
  New 
  Books. 
  

  

  wavelets, 
  by 
  working 
  in 
  the 
  inverse 
  direction 
  through 
  the 
  

   MacCullagh 
  analysis 
  ; 
  and 
  thus 
  we 
  learn 
  that 
  the 
  more 
  abrupt 
  

   and 
  irregular 
  the 
  hedge-firing, 
  the 
  more 
  abundant 
  will 
  be 
  the 
  

   proportion 
  of 
  rays 
  of 
  ordinary 
  light 
  consisting 
  of 
  spherical 
  

   waves 
  of 
  short 
  wave-length 
  in 
  the 
  radiation 
  from 
  the 
  target. 
  

  

  If, 
  as 
  appears 
  almost 
  certain, 
  these 
  are 
  what 
  we 
  know 
  

   under 
  the 
  name 
  of 
  Rongten 
  rays, 
  it 
  follows 
  that 
  anything 
  

   which 
  increases 
  the 
  intensity, 
  the 
  abruptness, 
  and 
  the 
  irregu- 
  

   larity 
  of 
  the 
  hedge-firing 
  will 
  increase 
  the 
  abundance 
  of 
  the 
  

   Rongten 
  emanations. 
  

  

  Moreover, 
  inasmuch 
  as 
  a 
  certain 
  amount 
  of 
  abruptness 
  and 
  

   irregularitv 
  is 
  present 
  in 
  the 
  emission 
  of 
  light 
  from 
  every 
  

   visible 
  object 
  or 
  luminous 
  source, 
  it 
  follows 
  that 
  Rongten 
  

   ravs 
  — 
  { 
  t 
  e 
  , 
  ra 
  y 
  S 
  of 
  very 
  short 
  wave-length 
  — 
  are 
  present 
  in 
  all 
  

   light 
  throughout 
  nature 
  ; 
  only 
  the 
  quantity 
  present 
  is 
  usually 
  

   inconspicuous. 
  

  

  LVIII. 
  Notices 
  respecting 
  New 
  Books. 
  

  

  Lehrbuch 
  der 
  Algebra. 
  Von 
  Heineich 
  Weber. 
  Zweite 
  Auflage, 
  

   ErsterBaud: 
  pp. 
  xvi 
  + 
  704. 
  (Braunschweig, 
  Vieweg 
  & 
  Sohu, 
  

   1898.) 
  

   T^HIS 
  is 
  no 
  hastily 
  composed 
  treatise. 
  The 
  Author 
  tdls 
  us 
  in 
  

   -*- 
  his 
  Preface 
  (p. 
  v) 
  that 
  he 
  had 
  cherished 
  for 
  some 
  years 
  the 
  

   idea 
  of 
  writing 
  such 
  a 
  work, 
  and 
  the 
  result 
  is 
  the 
  comprehensive 
  

   one 
  before 
  us. 
  He 
  has 
  traversed 
  the 
  field 
  described 
  several 
  times 
  

   in 
  his 
  university 
  lectures. 
  That 
  he 
  has 
  not 
  failed 
  in 
  his 
  attempt 
  

   may 
  be 
  inferred 
  from 
  the 
  fact 
  that 
  the 
  first 
  edition 
  was 
  published 
  

   so 
  recently 
  as 
  1895, 
  and 
  then 
  was 
  limited 
  to 
  654 
  pages. 
  The 
  book 
  

   is 
  clearly 
  conceived 
  in 
  plan, 
  : 
  nd 
  is 
  very 
  thorough 
  in 
  its 
  execution. 
  

   This 
  first 
  volume 
  contains 
  three 
  books, 
  which 
  are 
  prefaced 
  by 
  an 
  

   excellent 
  arithmetical 
  introduction 
  which 
  discusses 
  the 
  theory 
  of 
  

   multiplicities, 
  the 
  theory 
  of 
  rational 
  and 
  irrational 
  numbers, 
  and 
  

   further 
  gives 
  a 
  proof 
  of 
  the 
  continuity 
  of 
  real 
  numerical 
  magnitude. 
  

   Here 
  the 
  author 
  refers 
  mainly 
  to 
  Dedekind 
  ( 
  ' 
  Stetigkeit 
  und 
  

   irrationale 
  Zahien,' 
  and 
  ' 
  Was 
  sindund 
  was 
  sollen 
  die 
  Zahlen 
  ') 
  and 
  

   to 
  G-. 
  Cantor. 
  _ 
  . 
  

  

  The 
  first 
  book, 
  which 
  is 
  headed 
  the 
  Foundations, 
  in 
  six 
  chapters, 
  

   treats 
  of 
  Rational 
  functions 
  of 
  one 
  or 
  more 
  Variables, 
  Determinants, 
  

   the 
  roots 
  of 
  Algebraical 
  Equations, 
  Symmetric 
  functions, 
  Invari- 
  

   ants 
  and 
  Covariants, 
  and 
  the 
  Tschirnhausen 
  transformation 
  (the 
  

   application 
  of 
  which 
  to 
  cubic, 
  biquadratic, 
  and 
  quintic 
  equations 
  is 
  

   shown 
  in 
  chapter 
  iv., 
  and 
  in 
  chapter 
  vi. 
  Hermite's 
  modification 
  

   is 
  introduced). 
  The 
  second 
  book, 
  which 
  is 
  devoted 
  to 
  the 
  

   Roots 
  is 
  also 
  broken 
  up 
  into 
  six 
  chapters, 
  the 
  first 
  four 
  of 
  which 
  

   deal 
  with 
  the 
  reality 
  of 
  the 
  roots 
  of 
  real 
  equations, 
  with 
  their 
  

   number 
  in 
  a 
  given 
  interval, 
  with 
  their 
  superior 
  and 
  inferior 
  limits, 
  

   and 
  with 
  the 
  numerical 
  approximation 
  method. 
  The 
  eighth 
  

  

  