320  Intelligence  and  Miscellaneous  Articles, 
appear  in  the  yellow  ;  and  no  others  are  distinguished  in  the  rest  of 
the  spectrum. 
This  system  of  lines,  very  different  from  that  of  chlorine,  is  ana- 
logous to  those  of  bromine  and  iodine ;  but  it  differs  from  that  of 
iodine  by  the  absence  of  bands  superposed  to  the  fine  lines  in  the  green, 
and  also  because  the  lines  of  chloride  of  iodine  begin  to  show  them- 
selves notably  nearer  the  extreme  red  than  do  those  of  iodine,  and 
cover  only  a  much  less  extensive  region  of  the  spectrum. — (Joniptes 
Bendus  de  V Acad,  des  Sci.  1872,  No.  10. 
ON  THE  MEAN  MOTIONS  OF  JUPITER,  SATURN,  URANUS,  AND  NEP- 
TUNE.      BY  PROFESSOR  DANIEL  KIRKWOOD. 
The  recent  note  of  Professor  Peirce  *,  announcing  his  discovery 
of  some  interesting  relations  between  the  mean  motions  of  the  four 
outer  planets,  has  recalled  my  attention  to  a  number  of  similar  coin- 
cidences detected  by  myself  several  years  since,  while  engaged  in  a 
somewhat  laborious  examination  of  the  planetary  elements.  Of 
these,  the  following  may  be  worth  putting  on  record  for  future  dis- 
cussion : — 
2rcv  —   3rcvi  —  1  lrcviii  =0, (1) 
2rcvi  —  21rcvii  +  30wviii  =0, ;..    (2) 
3nv  —   8nyi  —   2«vii  +  7wviii=0 (3) 
With  the  values  of  wv,  wvi,  and  »vii  adopted  in  the  American  Ephe- 
meris,  the  value  of  wviii  obtained  from  either  of  the  above  equations 
differs  by  less  than  one  second  from  the  latest  determination  f.  The 
second  equation  was  submitted  some  two  years  since  to  Professor 
Newcomb  of  the  U.S.  Coast  Survey.  That  distinguished  astro- 
nomer was  inclined,  however,  to  regard  the  coincidence  as  merely 
accidental.  Be  this  as  it  may,  I  have  strong  confidence  in  the  ac- 
curacy of  the  third.  The  reexamination  of  this  last  has  recently  led 
to  the  discovery  of  two  others,  viz. 
68ravi— 425wvii+  257wviii=0,    (4) 
257wv-844/^+587rcvii=0 (5) 
both  of  which,  I  believe,  are  accurately  true.  The  fifth,  however, 
is  not  an  independent  equation,  but  is  derived  from  the  third  and 
fourth.  By  means  of  these  equations  I  have  found  the  remarkable 
cycle  of  11657*24  Julian  years,  which  separates  the  epochs  at  which 
the  planets  Jupiter,  Saturn,  Uranus,  and  Neptune  return  to  the  same 
relative  positions.  It  is  obvious,  moreover,  from  the  same  equations 
that  no  three  of  the  four  outer  planets  can  ever  be  in  conjunction  at  the 
same  time. — Silliman's  American  Journal  for  March  1872. 
*  Silliman's  Journal  for  January  1872.  It  will  be  observed  that  Pro- 
fessor Peirce's  third  equation  is  identical  with  that  discovered  by  Professor 
Newcomb  in  1857.     See  Gould's  Astr.  Jour.  vol.  v.  p.  101. 
t  Newcomb's  '  Orbit  of  Neptune/  p.  76. 
i 
