﻿546 
  Notices 
  respecting 
  New 
  Books. 
  

  

  K-eciprocants, 
  which 
  had 
  their 
  start 
  from 
  the 
  inaugural 
  lecture 
  at 
  

   Oxford 
  in 
  1886. 
  Other 
  sustained 
  series 
  of 
  papers 
  are 
  those 
  on 
  

   the 
  theory 
  of 
  Partitions, 
  and 
  on 
  the 
  theory 
  of 
  binary 
  Matrices 
  

   including 
  quaternions. 
  Dr. 
  Baker 
  has 
  enriched 
  the 
  volume 
  by 
  

   an 
  interesting 
  biographical 
  notice, 
  the 
  closing 
  paragraphs 
  of 
  which 
  

   give 
  a 
  brief 
  appreciation 
  of 
  Sylvester's 
  contributions 
  to 
  the 
  

   development 
  of 
  mathematics. 
  It 
  appears 
  that, 
  conjoined 
  with 
  an 
  

   extraordinary 
  fecundity 
  of 
  mathematical 
  thought 
  and 
  an 
  

   exhilarating 
  enthusiasm 
  on 
  whatever 
  problem 
  in 
  analysis 
  or 
  

   geometry 
  he 
  was 
  attacking 
  at 
  the 
  moment, 
  there 
  was 
  a 
  curious 
  

   indifference 
  to 
  certain 
  great 
  fields 
  of 
  mathematical 
  research. 
  

   Nevertheless 
  his 
  "position 
  is 
  secure. 
  As 
  the 
  physicist 
  glories 
  

   in 
  the 
  interest 
  of 
  his 
  contact 
  with 
  concrete 
  things, 
  so 
  Sylvester 
  

  

  loved 
  to 
  mark 
  his 
  progress 
  with 
  definite 
  formulae 
  His 
  work 
  will 
  

  

  endure, 
  according 
  to 
  its 
  value, 
  — 
  mingling 
  with 
  the 
  stream 
  fed 
  by 
  

   innumerable 
  men, 
  — 
  of 
  which 
  the 
  issue 
  is 
  as 
  the 
  source. 
  He 
  is 
  of 
  

   those 
  to 
  whom 
  it 
  is 
  given 
  to 
  renew 
  in 
  us 
  the 
  sanity 
  which 
  is 
  called 
  

   faith." 
  

  

  An 
  Introduction 
  to 
  the 
  Mathematical 
  Theory 
  of 
  Attraction. 
  Vol. 
  II. 
  

   By 
  E. 
  A. 
  Tarleton, 
  LL.l). 
  Longmans, 
  Green 
  & 
  Co. 
  

   London, 
  1913. 
  

  

  This 
  book 
  is 
  in 
  continuation 
  of 
  the 
  first 
  part 
  published 
  some 
  fifteen 
  

   years 
  ago, 
  and 
  begins, 
  in 
  Chapter 
  VIII., 
  with 
  the 
  discussion 
  of 
  

   spherical 
  harmonics 
  and 
  their 
  application 
  to 
  the 
  attraction 
  of 
  

   ellipsoids. 
  Chapter 
  IX. 
  investigates 
  the 
  more 
  elementary 
  parts 
  

   of 
  magnetism, 
  finishing 
  with 
  a 
  brief 
  account 
  of 
  the 
  expression 
  for 
  

   the 
  magnetic 
  potential 
  of 
  the 
  earth. 
  The 
  remaining 
  three 
  chapters 
  

   give 
  a 
  serviceable 
  presentation 
  of 
  Maxwell's 
  theory 
  of 
  electro- 
  

   magnetism. 
  The 
  author 
  recognizes 
  that 
  this 
  is 
  unusual 
  in 
  a 
  book 
  

   devoted 
  to 
  the 
  theory 
  of 
  attractions. 
  But 
  that 
  is 
  after 
  all 
  merely 
  

   a 
  convention, 
  there 
  being 
  as 
  much 
  attraction 
  in 
  the 
  relations 
  of 
  

   currents 
  and 
  magnets 
  as 
  in 
  gravitation 
  itself. 
  The 
  wave 
  surface 
  

   is 
  discussed 
  in 
  considerable 
  detail, 
  but 
  there 
  is 
  no 
  attempt 
  to 
  lead 
  

   up 
  to 
  the 
  more 
  modern 
  theories 
  associated 
  with 
  the 
  names 
  of 
  

   Lorentz, 
  Hertz, 
  and 
  Einstein. 
  As 
  far 
  as 
  it 
  goes, 
  the 
  book 
  

   contains 
  an 
  admirable 
  description 
  of 
  the 
  electromagnetic 
  theory 
  

   of 
  light 
  as 
  it 
  left 
  Maxwell's 
  hands. 
  

  

  Revolving 
  Vectors 
  with 
  special 
  Application 
  to 
  Alternating 
  Current 
  

   Phenomena. 
  By 
  Professor 
  G. 
  W. 
  Patterson. 
  The 
  Macmillan 
  

   Company. 
  New 
  York, 
  1911. 
  

  

  This 
  small 
  book 
  by 
  the 
  Professor 
  of 
  Electrical 
  Engineering 
  in 
  

   the 
  University 
  of 
  Michigan 
  gives 
  clearly 
  and 
  concisely 
  the 
  

   essential 
  features 
  of 
  the 
  graphical 
  representation 
  of 
  complex 
  

   quantities 
  and 
  their 
  application 
  to 
  electrical 
  problems 
  after 
  the 
  

   manner 
  inaugurated 
  by 
  Steinmetz. 
  The 
  author 
  explains 
  the 
  real 
  

   significance 
  of 
  the 
  processes, 
  leading 
  the 
  student 
  from 
  the 
  

  

  