﻿492 
  Notices 
  respecting 
  New 
  Books. 
  

  

  This 
  method 
  has 
  been 
  found 
  to 
  solve 
  most 
  of 
  the 
  difficulties, 
  

   and 
  with 
  the 
  vibrating 
  wire 
  at 
  the 
  sending 
  end 
  of 
  the 
  line 
  

   and 
  at 
  the 
  other 
  end 
  of 
  the 
  line 
  a 
  receiver 
  sounding 
  into 
  a 
  

   transmitter, 
  the 
  latter 
  being 
  connected 
  to 
  a 
  barretter 
  used 
  as 
  

   an 
  alternating 
  current 
  milliammeter, 
  it 
  has 
  been 
  found 
  possible 
  

   to 
  carry 
  out 
  comparative 
  telephonic 
  measurements 
  with 
  greater 
  

   accuracy 
  than 
  with 
  the 
  voice 
  and 
  ear, 
  owing 
  to 
  the 
  elimination 
  

   of 
  the 
  personal 
  equation 
  and 
  the 
  greater 
  sensibility 
  to 
  volume 
  

   variation 
  of 
  the 
  apparatus 
  used. 
  

  

  This 
  method 
  can 
  be 
  used 
  for 
  such 
  diversified 
  tests 
  as 
  

   comparison 
  of 
  loaded 
  with 
  unloaded 
  lines, 
  comparison 
  of 
  

   standard 
  and 
  non-standard 
  apparatus, 
  such 
  as 
  receivers, 
  

   transmitters, 
  induction-coils. 
  

  

  Conclusion. 
  — 
  Apart 
  from 
  telephonic 
  measurements, 
  the 
  

   modified 
  vibrating-wire 
  interrupter 
  may 
  possibly 
  have 
  a 
  

   field 
  for 
  both 
  comparative 
  and 
  absolute 
  electrical 
  measure- 
  

   ments, 
  and 
  especially 
  for 
  use 
  with 
  the 
  vibration 
  galvanometer. 
  

   The 
  ease 
  with 
  which 
  the 
  frequency 
  can 
  be 
  varied 
  together 
  

   with 
  the 
  steadiness 
  of 
  the 
  resulting 
  wave 
  and 
  the 
  simplicity 
  

   of 
  the 
  apparatus 
  are 
  certainly 
  great 
  recommendations. 
  The 
  

   author 
  must 
  express 
  his 
  indebtedness 
  to 
  the 
  National 
  Tele- 
  

   phone 
  Co. 
  for 
  the 
  facilities 
  afforded 
  to 
  him, 
  to 
  Dr. 
  A. 
  Russell 
  

   for 
  great 
  help 
  in 
  the 
  revision 
  of 
  this 
  paper, 
  to 
  Mr. 
  A. 
  Campbell 
  

   for 
  references 
  to 
  humming 
  and 
  vibrating 
  wires, 
  and 
  a 
  tribute 
  

   must 
  also 
  be 
  paid 
  to 
  the 
  oscillograph 
  which 
  has 
  been 
  of 
  such 
  

   great 
  assistance 
  in 
  these 
  investigations. 
  

  

  XLIII. 
  Notices 
  respecting 
  New 
  Books. 
  

  

  The 
  Collected 
  Mathematical 
  Papers 
  of 
  J. 
  J. 
  Sylvester. 
  Volume 
  II. 
  

   (1854-1873). 
  Cambridge 
  : 
  At 
  the 
  University 
  Press. 
  1908. 
  

  

  Oeuvres 
  de 
  Charles 
  Hermite. 
  Tome 
  II. 
  (1858-1872). 
  Paris 
  : 
  

  

  Gauthier-Villars. 
  1908. 
  

   T 
  T 
  is 
  fitting 
  that 
  these 
  important 
  continuations 
  of 
  the 
  collected 
  

   ■*- 
  papers 
  of 
  two 
  great 
  contemporaries 
  should 
  be 
  noticed 
  together. 
  

   To 
  a 
  large 
  extent 
  they 
  worked 
  along 
  the 
  same 
  lines 
  of 
  analysis 
  ; 
  and 
  

   in 
  the 
  papers 
  of 
  each 
  there 
  are 
  frequent 
  references 
  to 
  the 
  re- 
  

   searches 
  and 
  results 
  of 
  the 
  other. 
  It 
  is 
  needless 
  to 
  point 
  out 
  

   in 
  these 
  days 
  the 
  great 
  influence 
  exercised 
  on 
  mathematical 
  

   development 
  by 
  both 
  Sylvester 
  and 
  Hermite. 
  The 
  former 
  was 
  

   characterized 
  by 
  an 
  extraordinary 
  exuberance 
  of 
  mathematical 
  

   imagination. 
  Who 
  but 
  a 
  Sylvester, 
  for 
  example, 
  could 
  have 
  dis- 
  

   covered 
  in 
  the 
  arduous 
  course 
  of 
  discussing 
  the 
  equation 
  of 
  the 
  

   fifth 
  degree, 
  that 
  Music 
  might 
  be 
  " 
  described 
  as 
  the 
  Mathematic 
  

   of 
  sense, 
  Mathematic 
  as 
  Music 
  of 
  the 
  reason 
  — 
  the 
  soul 
  of 
  each 
  the 
  

   same 
  ! 
  " 
  Of 
  the 
  110 
  papers 
  which 
  fill 
  the 
  English 
  mathematician's 
  

  

  