﻿324 
  Prof. 
  Rutherford 
  and 
  Mr. 
  Richardson 
  : 
  Analysis 
  

  

  enclosed 
  inside 
  a 
  four-dimensional 
  parallelotope, 
  bounded 
  by 
  

   the 
  spaces 
  : 
  

  

  _^*, 
  y=±J^, 
  *=±^, 
  tt 
  =±J^ 
  

  

  CC 
  U 
  

  

  ,V 
  X 
  ,vy 
  ,V 
  Z 
  .~ 
  U 
  

  

  By 
  the 
  variability 
  of 
  the 
  a's 
  the 
  circumscribed 
  parallelotope 
  

   also 
  changes 
  ; 
  the 
  vertices 
  move 
  backward 
  and 
  forward 
  

   between 
  two 
  extreme 
  positions 
  along 
  a 
  wrung 
  curve 
  ; 
  this 
  

   curve 
  lies 
  on 
  a 
  hyperellipsoid 
  whose 
  axes 
  lying 
  along 
  the 
  

  

  axes 
  of 
  coordinates 
  are 
  proportional 
  to 
  — 
  : 
  — 
  : 
  — 
  : 
  — 
  . 
  The 
  

  

  n 
  x 
  ^ 
  7ty 
  n 
  z 
  n 
  u 
  

  

  form 
  of 
  the 
  Lissajous 
  wrung 
  curve 
  in 
  a 
  definite 
  parallelotope 
  

   depends, 
  as 
  is 
  found 
  by 
  a 
  change 
  of 
  the 
  origin 
  of 
  time, 
  on 
  the 
  

   quantities 
  : 
  

  

  2^03,-A,), 
  2n^8 
  y 
  -£,), 
  2n 
  z 
  (/3 
  z 
  -l3 
  u 
  ). 
  

  

  For 
  the 
  osculating 
  curves 
  in 
  the 
  extreme 
  parallelotopes 
  we 
  

   have 
  : 
  

  

  2n 
  x 
  (/3 
  x 
  - 
  A) 
  + 
  2rc 
  y 
  ( 
  /3 
  S 
  - 
  /3„) 
  ± 
  2n,(J3 
  z 
  - 
  ft) 
  = 
  fcr. 
  

  

  Furthermore, 
  there 
  is 
  again 
  a 
  periodic 
  case 
  and 
  an 
  asym- 
  

   ptotic 
  case 
  (§ 
  24). 
  

  

  XIX. 
  Analysis 
  of 
  the 
  7 
  Rays 
  from, 
  Radium 
  D 
  and 
  Radium 
  E. 
  

   By 
  Professor 
  E. 
  Rutherford, 
  F.R.S., 
  and 
  H. 
  Richardson, 
  

   M.Sc* 
  

  

  IN 
  a 
  previous 
  paper 
  f 
  we 
  have 
  given 
  the 
  results 
  of 
  the 
  

   analysis 
  of 
  the 
  7 
  radiation 
  from 
  radium 
  B 
  and 
  radium 
  0. 
  

   The 
  radiation 
  from 
  the 
  former 
  was 
  shown 
  to 
  consist 
  of 
  three 
  

   types 
  varying 
  widely 
  in 
  penetrating 
  power, 
  and 
  the 
  latter 
  

   essentially 
  of 
  one 
  penetrating 
  type. 
  In 
  the 
  present 
  paper 
  the 
  

   7 
  radiation 
  from 
  radium 
  D 
  and 
  radium 
  E 
  has 
  been 
  examined 
  

   by 
  a 
  similar 
  method. 
  These 
  radioactive 
  substances 
  are 
  of 
  

   unusual 
  interest 
  and 
  importance 
  in 
  considering 
  the 
  problem 
  

   of 
  the 
  connexion 
  between 
  /? 
  and 
  7 
  rays, 
  since 
  the 
  7 
  rays 
  

   emitted 
  by 
  radium 
  D 
  and 
  radium 
  E 
  together 
  are 
  exceedingly 
  

   feeble 
  in 
  intensity 
  compared 
  with 
  the 
  ft 
  rays. 
  In 
  this 
  respect 
  

   they 
  are 
  in 
  marked 
  contrast 
  to 
  the 
  products 
  radium 
  B 
  and 
  

   radium 
  C, 
  where 
  the 
  7 
  rays 
  are 
  relatively 
  intense 
  and 
  com- 
  

   parable 
  in 
  energy 
  with 
  the 
  /9 
  rays. 
  

  

  In 
  consequence 
  of 
  the 
  short 
  period 
  of 
  transformation 
  

  

  * 
  Communicated 
  by 
  the 
  Authors. 
  

  

  t 
  Rutherford 
  and 
  JRichardson, 
  Phil. 
  Mag. 
  xxv. 
  p. 
  722 
  (1913). 
  

  

  