﻿182 
  Prof. 
  A. 
  Gray 
  on 
  Hodographic 
  Treatment 
  and 
  

  

  2. 
  Apparently 
  Hamilton 
  was 
  ignorant 
  of 
  the 
  work 
  of 
  

   Mobius 
  when 
  he 
  published 
  his 
  paper 
  on 
  " 
  The 
  Law 
  of 
  the 
  

   Circular 
  Hodograph" 
  in 
  the 
  Proceedings 
  of 
  the 
  Royal 
  

   Irish 
  Academy 
  in 
  1847. 
  More 
  than 
  ten 
  years 
  after, 
  in 
  

   a 
  letter 
  of 
  date 
  March 
  3, 
  1858, 
  to 
  De 
  Morgan, 
  he 
  says 
  : 
  — 
  

   "Do 
  you 
  know 
  much 
  about 
  Mobius 
  and 
  his 
  works? 
  . 
  . 
  . 
  

   He 
  wrote 
  to 
  me 
  a 
  couple 
  of 
  years 
  ago 
  . 
  . 
  . 
  that 
  he 
  had 
  been 
  

   lecturing 
  on 
  my 
  theory 
  of 
  the 
  circular 
  hodograph, 
  to 
  which 
  

   he 
  might, 
  very 
  plausibly, 
  have 
  put 
  in 
  a 
  sort 
  of 
  claim, 
  or 
  

   at 
  least 
  a 
  claim 
  to 
  the 
  general 
  conception/'' 
  [Graves, 
  ' 
  Life 
  

   of 
  Hamilton,' 
  vol. 
  iii. 
  p. 
  543.] 
  

  

  That 
  the 
  hodograph 
  for 
  the 
  motion 
  of 
  an 
  undisturbed 
  

   planet 
  is 
  a 
  circle, 
  was 
  of 
  course 
  the 
  great 
  discovery, 
  and 
  

   without 
  doubt 
  this 
  discovery 
  was 
  Hamilton's, 
  and 
  Hamilton's 
  

   alone. 
  That 
  a 
  name 
  was 
  given 
  to 
  the 
  curve 
  may 
  have 
  bad 
  

   something 
  to 
  do 
  with 
  the 
  progress 
  of 
  discovery. 
  When 
  the 
  

   curve 
  had 
  thus 
  been 
  endowed 
  with 
  a 
  kind 
  of 
  personality,, 
  

   such 
  questions 
  naturally 
  presented 
  themselves 
  as 
  ; 
  What 
  

   is 
  the 
  nature 
  of 
  the 
  hodograph 
  of 
  a 
  planet? 
  What 
  is 
  the 
  

   hodograph 
  of 
  an 
  unresisted 
  projectile 
  ? 
  and 
  so 
  on. 
  The 
  

   names 
  given 
  to 
  electric 
  and 
  magnetic 
  quantities 
  have 
  

   certainly 
  helped 
  to 
  distinguish 
  sharply 
  between 
  one 
  idea 
  

   and 
  another 
  closely 
  related 
  to 
  it, 
  and 
  led 
  to 
  the 
  evaluation 
  

   of 
  the 
  individualities 
  which 
  the 
  names 
  emphasized. 
  

  

  3. 
  I 
  was 
  surprised 
  to 
  see 
  Professor 
  Eddington's 
  statement 
  

   in 
  the 
  Philosophical 
  Magazine 
  for 
  October 
  that 
  the 
  theorem 
  

   of 
  the 
  resolution 
  of 
  the 
  orbital 
  velocity 
  of 
  a 
  planet 
  into 
  two 
  

   components 
  of 
  constant 
  amount, 
  one 
  of 
  them 
  also 
  in 
  a 
  

   constant 
  direction, 
  seemed 
  to 
  be 
  overlooked 
  in 
  dynamical 
  

   textbooks. 
  It 
  was 
  given 
  in 
  Frost's 
  'Newton 
  - 
  ' 
  in 
  1854, 
  and 
  

   is 
  stated 
  on 
  p. 
  147 
  of 
  the 
  fourth 
  edition. 
  It 
  is 
  to 
  be 
  found 
  

   in 
  Routh's 
  ' 
  Dynamics 
  of 
  a 
  Particle,' 
  § 
  397, 
  and 
  in 
  a 
  book 
  

   on 
  Dynamics 
  by 
  Dr. 
  J. 
  G. 
  Gray 
  and 
  myself, 
  § 
  134. 
  In 
  the 
  

   last 
  mentioned 
  work 
  there 
  is 
  a 
  rather 
  full 
  treatment 
  of 
  the 
  

   subject 
  referred 
  to 
  recently 
  in 
  the 
  Phil. 
  Mag. 
  — 
  the 
  motion 
  

   of 
  bodies 
  of 
  varying 
  mass. 
  

  

  The 
  existence 
  of 
  these 
  two 
  components 
  of 
  velocity, 
  one 
  of 
  

   constant 
  amount 
  i\, 
  say, 
  and 
  constant 
  direction, 
  the 
  other 
  

   of 
  constant 
  amount 
  v 
  2 
  , 
  directed 
  always 
  forward 
  at 
  right 
  

   angles 
  to 
  the 
  radius 
  vector, 
  affords 
  the 
  most 
  elegant 
  mode 
  

   of 
  passing 
  from 
  the 
  circular 
  hodograph 
  to 
  the 
  orbit. 
  I 
  shall 
  

   show 
  first 
  that 
  the 
  hodograph 
  is 
  a 
  cirrle, 
  and 
  then 
  pass 
  from 
  

   the 
  hodograph 
  to 
  the 
  orbit. 
  

  

  Let 
  the 
  planet, 
  denoted 
  by 
  P 
  and 
  supposed 
  to 
  be 
  of 
  unit 
  

   mass, 
  be 
  acted 
  on 
  by 
  a 
  force 
  directed 
  towards 
  a 
  fixed 
  point 
  S, 
  

   and 
  varying 
  inversely 
  as 
  the 
  square 
  of 
  the 
  distance 
  SP. 
  If 
  

  

  