﻿SJiarpiiess 
  of 
  Resonance 
  under 
  Sustained 
  Forcing. 
  127 
  

  

  doubled, 
  and 
  the 
  permissible 
  changes 
  of 
  length 
  for 
  a 
  given 
  

   effect 
  on 
  the 
  resonance 
  much 
  more 
  than 
  doubled. 
  It 
  was 
  

   also 
  easy, 
  with 
  the 
  longer 
  pendulums, 
  to 
  keep 
  all 
  the 
  

   vibrations 
  small 
  in 
  angular 
  amplitude 
  (and 
  so 
  practically 
  

   isochronous) 
  though 
  still 
  of 
  ample 
  linear 
  dimensions. 
  Thus, 
  

   this 
  increased 
  length 
  of 
  the 
  pendulums 
  vastly 
  improved 
  the 
  

   conditions 
  as 
  regards 
  facility 
  in 
  tuning. 
  

  

  The 
  individual 
  pendulums 
  were 
  then 
  each 
  of 
  the 
  order 
  

   4 
  metres 
  in 
  length, 
  the 
  upper 
  bob 
  was 
  of 
  solid 
  iron, 
  

   6*3 
  cm. 
  diam., 
  suspended 
  by 
  a 
  wire, 
  the 
  lower 
  bob 
  was 
  of 
  

   hollow 
  celluloid, 
  6 
  cm. 
  diam., 
  suspended 
  from 
  the 
  other 
  by 
  

   a 
  fine 
  plaited 
  silk 
  line 
  and 
  adjusted 
  in 
  length 
  by 
  a 
  tightener 
  

   (as 
  adopted 
  for 
  tent 
  ropes). 
  With 
  this 
  arrangement 
  a 
  

   slight 
  motion 
  of 
  the 
  upper 
  iron 
  bob 
  quickly 
  produced 
  a 
  con- 
  

   siderable 
  motion 
  in 
  the 
  lower 
  celluloid 
  bob, 
  originally 
  at 
  

   rest, 
  and 
  maintained 
  its 
  motion 
  without 
  any 
  sign 
  of 
  beats, 
  

   although 
  over 
  seventy 
  vibrations 
  were 
  counted. 
  The 
  lower 
  

   pendulum 
  was 
  in 
  turn 
  lengthened 
  and 
  shortened 
  by 
  about 
  

   8 
  centimetres 
  without 
  any 
  appreciable 
  change 
  in 
  the 
  

   character 
  of 
  the 
  resonance, 
  the 
  same 
  number 
  of 
  vibrations 
  

   being 
  counted 
  as 
  before 
  without 
  the 
  appearance 
  of 
  beats. 
  

  

  The 
  bobs 
  then 
  in 
  use 
  were 
  those 
  which 
  previously 
  failed 
  

   to 
  avoid 
  beats 
  when 
  on 
  the 
  pendulums 
  of 
  1 
  metre 
  long. 
  

   To 
  make 
  a 
  further 
  test, 
  the 
  celluloid 
  shell, 
  in 
  use 
  for 
  the 
  

   lower 
  bob, 
  was 
  next 
  replaced 
  by 
  one 
  of 
  solid 
  box-wood, 
  each 
  

   pendulum 
  still 
  being 
  about 
  4 
  metres 
  long. 
  But 
  this 
  gave 
  

   beats 
  numbering 
  only 
  about 
  five 
  vibrations 
  in 
  the 
  cycle 
  from 
  

   start 
  to 
  zero 
  amplitude. 
  It 
  thus 
  became 
  evident 
  that 
  the 
  

   large 
  damping 
  coefficient 
  (k\2) 
  and 
  the 
  small 
  frequency 
  

   {p\2if) 
  were 
  both 
  needed 
  to 
  give 
  a 
  range 
  of 
  resonance 
  

   which 
  was 
  large 
  enough 
  to 
  permit 
  of 
  ready 
  tuning 
  of 
  sufficient 
  

   accuracy 
  to 
  avoid 
  beats. 
  

  

  The 
  theory 
  is 
  accordingly 
  corroborated, 
  and 
  furnishes 
  the 
  

   necessary 
  clue 
  to 
  the 
  conditions 
  to 
  be 
  adopted 
  for 
  the 
  double 
  

   pendulum 
  in 
  order 
  that 
  it 
  should 
  give 
  a 
  good 
  illustrative 
  

   experiment 
  of 
  maintained 
  forced 
  vibrations. 
  It 
  may 
  be 
  

   remarked 
  that 
  it 
  would 
  be 
  still 
  better 
  if 
  the 
  upper 
  bob 
  were 
  

   of 
  lead 
  and 
  of 
  even 
  greater 
  size 
  than 
  the 
  lower 
  bob, 
  instead 
  

   of 
  being 
  (as 
  in 
  the 
  above 
  experiment) 
  of 
  iron 
  and 
  of 
  about 
  

   the 
  same 
  size 
  as 
  the 
  lower 
  one. 
  

  

  Meldes 
  Experiment 
  icith 
  Constant 
  Tension. 
  — 
  This 
  experi- 
  

   ment 
  lends 
  itself 
  most 
  readily 
  to 
  a 
  hasty 
  qualitative 
  illustration 
  

   of 
  the 
  increase 
  of 
  range 
  of 
  resonance 
  with 
  period 
  when 
  the 
  

   damping 
  coefficient 
  remains 
  unchanged. 
  

  

  It 
  was 
  at 
  first 
  tried, 
  as 
  indicated 
  above, 
  with 
  the 
  tension 
  

  

  