﻿586 
  Prof. 
  Pollock 
  and 
  Mr. 
  Vonwiller 
  : 
  Experiments 
  

  

  6. 
  For 
  what 
  class 
  of 
  surfaces 
  may 
  v' 
  lie 
  in 
  the 
  tangent 
  

   plane 
  ? 
  

  

  7. 
  For 
  what 
  class 
  of 
  surfaces 
  is 
  % 
  self-conjugate 
  ? 
  (Tait, 
  

   § 
  332).^ 
  

  

  8. 
  Discuss 
  the 
  pure 
  and 
  the 
  rotational 
  parts 
  of 
  the 
  strain 
  ^. 
  

  

  9. 
  Prove 
  the 
  identities 
  : 
  — 
  

  

  (a) 
  x 
  2 
  v 
  = 
  V 
  . 
  ^Wv-SVv 
  . 
  %v, 
  

  

  10. 
  Discuss 
  the 
  pure 
  strain 
  % 
  + 
  %'. 
  

  

  11. 
  Interpret 
  TWv 
  and 
  J^-UVVv. 
  (Tait, 
  §§ 
  299, 
  300.) 
  

  

  12. 
  Show 
  by 
  (11) 
  of 
  Art. 
  5 
  that 
  V 
  2 
  is 
  the 
  negative 
  of 
  

   Laplace's 
  operator. 
  

  

  13. 
  Show 
  that 
  -r- 
  and 
  -tj 
  are 
  commutative 
  when 
  applied 
  

  

  to 
  P, 
  h 
  being 
  parallel 
  to 
  Y^v. 
  

  

  14. 
  With 
  everything 
  as 
  in 
  Art. 
  4, 
  prove 
  

  

  V(ctt) 
  = 
  Vo" 
  .t— 
  V 
  t 
  -°"— 
  2#'0-. 
  

  

  15. 
  Show 
  by 
  (7) 
  that 
  VVx 
  v 
  lies 
  in 
  the 
  tangent 
  plane. 
  

  

  16. 
  Use 
  (6) 
  of 
  the 
  same 
  article 
  to 
  find 
  Vv(vSV^ 
  + 
  %0- 
  

  

  LXVIII. 
  Some 
  Experiments 
  on 
  Electric 
  Waves 
  in 
  Short 
  Wire 
  

   Systems, 
  and 
  on 
  the 
  Specific 
  Inductive 
  Capacity 
  of 
  a 
  Specimen 
  

   of 
  Glass. 
  By 
  J. 
  A. 
  Pollock, 
  Professor 
  of 
  Physics, 
  and 
  

   0. 
  U. 
  Yonwillek, 
  Deas-jLhomson 
  Scholar 
  in 
  Physics 
  in 
  the 
  

   University 
  of 
  Sydney 
  *. 
  

  

  THE 
  experiments 
  described 
  in 
  the 
  following 
  paper 
  include 
  

   observations 
  of 
  the 
  waves 
  along 
  free 
  wires, 
  and 
  also 
  of 
  

   the 
  vibrations 
  in 
  the 
  two 
  systems 
  formed 
  when 
  the 
  wires 
  are 
  

   bridged 
  at 
  various 
  points. 
  In 
  the 
  former 
  case 
  it 
  is 
  shown, 
  

   that 
  when 
  the 
  electrical 
  vibrations 
  of 
  the 
  wire 
  system 
  are 
  

   forced, 
  they 
  are 
  in 
  that 
  mode 
  whose 
  free 
  period 
  is 
  near 
  to 
  that 
  

   of 
  the 
  vibrator 
  oscillation, 
  and 
  therefore 
  the 
  distance 
  between 
  

   the 
  nodes 
  along 
  the 
  wires 
  does 
  not 
  vary 
  continuously 
  with 
  

   change 
  of 
  the 
  period 
  of 
  the 
  condenser 
  discharge 
  In 
  the 
  

   other 
  case 
  an 
  explanation 
  is 
  found 
  which 
  accounts 
  for 
  the 
  

   varying 
  heights 
  of 
  the 
  maxima 
  deflexions 
  observed 
  when 
  

   the 
  bridge 
  is 
  moved 
  along 
  the 
  wires. 
  A 
  method 
  for 
  finding 
  

   the 
  specific 
  inductive 
  capacity 
  of 
  solid 
  dielectrics 
  with 
  

  

  * 
  Communicated 
  by 
  the 
  Authors. 
  /. 
  

  

  