﻿372 
  Notices 
  respecting 
  New 
  Boohs. 
  

  

  Modern 
  Instruments 
  and 
  Methods 
  of 
  Calculation. 
  A 
  Handbook 
  of 
  

   the 
  Napier 
  Tercentenary 
  Exhibition. 
  Edited 
  by 
  E. 
  M. 
  Horsburgh. 
  

   G-eo. 
  Bell 
  & 
  Sons 
  and 
  the 
  Boyal 
  Society 
  of 
  Edinburgh. 
  Price 
  6s. 
  

  

  The 
  Handbook 
  is 
  a 
  mine 
  of 
  information 
  on 
  all 
  questions 
  relating 
  

   to 
  calculations, 
  and 
  the 
  aim 
  of 
  the 
  Editor 
  and 
  the 
  Committee 
  to 
  

   make 
  this 
  volume 
  useful 
  to 
  those 
  engaged 
  in 
  computation 
  has 
  

   been 
  fully 
  realized. 
  Special 
  mention 
  should 
  be 
  made 
  of 
  the 
  list 
  of 
  

   mathematical 
  tables, 
  including 
  tables 
  of 
  logarithms 
  and 
  other 
  

   functions 
  and 
  of 
  the 
  chapters 
  devoted 
  to 
  calculating 
  machines 
  and 
  

   mathematical 
  laboratory 
  instruments. 
  Logarithmic 
  computation 
  

   is 
  being 
  extensively 
  supplemented 
  by 
  that 
  of 
  mechanical 
  calculators, 
  

   and 
  the 
  increasing 
  number 
  of 
  those 
  who 
  use 
  these 
  machines 
  will 
  

   find 
  the 
  descriptive 
  article 
  on 
  this 
  subject 
  of 
  much 
  interest. 
  The 
  

   chapter 
  on 
  instruments 
  gives 
  a 
  detailed 
  account 
  of 
  integrometers, 
  

   planimeters, 
  harmonic 
  analyzers, 
  and 
  other 
  mechanisms 
  required 
  

   for 
  special 
  purposes. 
  Other 
  chapters 
  deal 
  with 
  slide-rules, 
  ruled 
  

   papers, 
  and 
  mathematical 
  models, 
  ihe 
  Handbook 
  forms 
  a 
  fitting 
  

   companion 
  to 
  the 
  Memorial 
  volume, 
  and 
  will 
  be 
  a 
  valuable 
  addition 
  

   to 
  the 
  library 
  of 
  every 
  student 
  of 
  mathematics. 
  

  

  Elliptic 
  Integrals 
  (Mathematical 
  Monographs, 
  No. 
  18). 
  By 
  Pro- 
  

   fessor 
  Harris 
  Hancock. 
  Pp. 
  104. 
  JSew 
  York 
  : 
  John 
  Wiley 
  

   & 
  Sons 
  ; 
  London 
  : 
  Chapman 
  & 
  Hall. 
  1917. 
  Price 
  6s. 
  net. 
  

  

  This 
  excellently 
  produced 
  volume 
  is 
  one 
  of 
  a 
  series 
  of 
  mathe- 
  

   matical 
  monographs 
  now 
  appearing 
  in 
  America. 
  It 
  contains 
  

   an 
  account 
  of 
  the 
  three 
  elliptic 
  integrals, 
  the 
  integral 
  of 
  the 
  

   third 
  kind, 
  however, 
  receiving 
  only 
  passing 
  notice. 
  Starting 
  

   with 
  the 
  definition 
  of 
  elliptic 
  integrals 
  as 
  the 
  integrals 
  of 
  ex- 
  

   pressions 
  when 
  cubics 
  and 
  quartics 
  occur 
  under 
  the 
  root 
  sign, 
  the 
  

   author 
  gives 
  the 
  reduction 
  to 
  Legendre's 
  normal 
  form, 
  and 
  illus- 
  

   trates 
  some 
  of 
  the 
  more 
  obvious 
  properties 
  of 
  the 
  functions 
  with 
  

   excellent 
  graphs. 
  After 
  treating 
  the 
  sn, 
  en, 
  dn, 
  functions 
  and 
  the 
  

   Gudermannian 
  he 
  deals 
  in 
  detail 
  with 
  the 
  reduction 
  of 
  various 
  

   types 
  of 
  integrals 
  of 
  the 
  first 
  kind 
  to 
  Legendre's 
  form, 
  and 
  then 
  

   passes 
  on 
  to 
  the 
  methods 
  of 
  numerical 
  computation 
  of 
  the 
  first 
  

   and 
  second 
  kind 
  of 
  integral. 
  This 
  part 
  of 
  the 
  subject 
  is 
  developed 
  

   at 
  some 
  length, 
  and 
  illustrated 
  with 
  detailed 
  numerical 
  workings. 
  

   After 
  a 
  few 
  well-selected 
  examples 
  and 
  exercises 
  the 
  book 
  closes 
  

   with 
  five 
  place 
  tables 
  of 
  elliptic 
  functions 
  of 
  the 
  first 
  and 
  second 
  

   kind, 
  taken 
  from 
  Levy's 
  well-known 
  work. 
  

  

  The 
  book 
  is 
  well-planned 
  and 
  clearly 
  written, 
  and 
  can 
  be 
  under- 
  

   stood 
  by 
  any 
  student 
  well-grounded 
  in 
  the 
  elements 
  of 
  the 
  calculus. 
  

   It 
  forms 
  an 
  excellent 
  introduction, 
  and 
  will, 
  we 
  think, 
  be 
  welcomed 
  

   by 
  those 
  who, 
  without 
  having 
  much 
  time 
  to 
  devote 
  to 
  the 
  subject, 
  

   wish 
  to 
  possess 
  a 
  concise 
  and 
  accurate 
  account 
  of 
  the 
  fundamental 
  

   properties 
  of 
  elliptic 
  integrals. 
  

  

  