﻿Hodographic 
  Treatment 
  of 
  Planetary 
  Motion. 
  181 
  

  

  Fig. 
  3 
  shows 
  the 
  mean 
  of 
  the 
  writer's 
  results 
  and 
  Nutting's 
  

   results 
  on 
  the 
  five 
  subjects 
  who 
  served 
  as 
  observers 
  in 
  both 
  

   experiments. 
  The 
  average 
  maximum 
  visibility 
  found 
  by 
  the 
  

   writer 
  is 
  *555, 
  and 
  by 
  Nutting 
  *554. 
  

  

  This 
  work 
  was 
  carried 
  out 
  at 
  the 
  suggestion 
  of 
  Dr. 
  P. 
  Gr. 
  

   Nutting, 
  and 
  the 
  writer 
  wishes 
  to 
  thank 
  him 
  and 
  the 
  other 
  

   members 
  of 
  the 
  laboratory 
  for 
  their 
  assistance. 
  

  

  Author's 
  Note. 
  — 
  This 
  paper 
  had 
  been 
  completed 
  before 
  a 
  

   paper 
  by 
  Coblentz 
  and 
  Emerson* 
  appeared, 
  so 
  that 
  their 
  

   latest 
  data 
  have 
  not 
  been 
  included. 
  

  

  XX. 
  On 
  the 
  Hodographic 
  Treatment 
  and 
  the 
  Energetics 
  of 
  

   undisturbed 
  Planetary 
  Motion. 
  By 
  Professor 
  Andrew 
  

   Gray, 
  F.R.SA 
  

  

  1. 
  r 
  | 
  1 
  HE 
  following 
  bit 
  of 
  Newtonian 
  dynamics 
  was 
  sug- 
  

   J- 
  gested 
  by 
  some 
  passages 
  in 
  a 
  recent 
  discussion 
  

   in 
  the 
  Philosophical 
  Magazine. 
  It 
  sets 
  forth 
  a 
  mode 
  of 
  

   dealing 
  with 
  the 
  elementary 
  theory 
  of 
  planetary 
  motion 
  

   which 
  may 
  have 
  some 
  novelty, 
  and 
  states 
  certain 
  results, 
  

   which 
  I 
  think 
  are 
  interesting, 
  with 
  regard 
  to 
  the 
  energetics 
  

   of 
  such 
  motion. 
  Into 
  problems 
  of 
  relativity 
  I 
  do 
  not 
  at 
  

   present 
  enter. 
  

  

  As 
  a 
  matter 
  of 
  scientific 
  history 
  there 
  would 
  seem 
  to 
  be 
  

   no 
  doubt 
  that 
  the 
  first 
  idea 
  of 
  the 
  hodograph 
  is 
  due 
  to 
  

   August 
  Ferdinand 
  Mobius, 
  the 
  inventor 
  of 
  the 
  barycentric 
  

   calculus. 
  In 
  § 
  22 
  of 
  his 
  book, 
  Die 
  Elemente 
  der 
  Mechanih 
  

   des 
  Himmels, 
  which 
  was 
  published 
  in 
  1843, 
  Mobius 
  specifies 
  

   a 
  point 
  H 
  which 
  moves 
  so 
  that 
  its 
  distance 
  OH 
  from 
  a 
  fixed 
  

   point 
  is 
  continually 
  equal 
  in 
  length 
  to, 
  and 
  in 
  the 
  same 
  

   direction 
  as, 
  the 
  line 
  which 
  represents 
  the 
  velocity 
  of 
  a 
  

   particle 
  moving 
  in 
  a 
  given 
  path. 
  He 
  derives 
  the 
  result 
  

   that 
  the 
  acceleration 
  of 
  the 
  particle 
  in 
  the 
  path 
  is 
  repre- 
  

   sented 
  in 
  magnitude 
  and 
  direction 
  by 
  the 
  velocity 
  of 
  the 
  

   point 
  H. 
  This 
  of 
  course 
  is 
  the 
  whole 
  idea 
  of 
  the 
  hodo- 
  

   graph 
  very 
  clearly 
  stated. 
  So 
  far 
  as 
  I 
  have 
  been 
  able 
  

   to 
  see, 
  Mobius 
  does 
  not 
  make 
  any 
  particular 
  use 
  of 
  the 
  

   idea 
  ; 
  and 
  he 
  does 
  not 
  seem 
  to 
  be 
  aware 
  that 
  the 
  curve 
  

   described 
  by 
  the 
  point 
  H 
  is, 
  for 
  a 
  planet 
  moving 
  in 
  a 
  conic 
  

   section, 
  a 
  circle, 
  with 
  as 
  an 
  eccentric 
  point 
  within 
  it. 
  

  

  * 
  Coblentz, 
  TV. 
  W., 
  Emerson, 
  W. 
  B. 
  " 
  Relative 
  Sensibility 
  of 
  the 
  

   Average 
  Eye 
  to 
  Light 
  of 
  Different 
  Colors 
  and 
  some 
  Practical 
  Appli- 
  

   cations 
  to 
  Radiation 
  Problems.'' 
  Scientific 
  Paper 
  303, 
  Bureau 
  of 
  

   Standards, 
  issued 
  Sept. 
  12, 
  1917. 
  

  

  t 
  Communicated 
  bv 
  the 
  Author. 
  

  

  