466     M.  P.  Zollner  on  the  Origin  of  the  Earth's  Magnetism, 
"  I  have  extended  my  researches  over  all  three  elements ;  and 
from  the  discussion  of  the  observations  made  during  several 
years  at  Prague,  Vienna,  and  other  places,  it  follows  that  the 
changes  of  each  of  the  three  elements  of  the  constant  force  indi- 
cate a  period  of  about  26^-  days, — a  periodicity  which  can  be 
scarcely  explained  otherwise  than  by  the  action  of  the  sun." 
Hornstein  next  explains  the  method  he  has  pursued  in  dis- 
cussing the  observations,  and  continues  (p.  10)  with  the  follow- 
ing words  : — 
"  The  existence  of  an  oscillation  taking  place  in  nearly  twenty- 
six  days  has  therefore  been  proved  almost  beyond  doubt ;  and  I  do 
not  hesitate  to  regard  it  as  an  action  of  the  sun.  I  was  therefore 
obliged  to  take  into  account  the  above-mentioned  great  irregu- 
larity, which  is  shown  in  all  periodical  phenomena  of  the  sun 
and  the  phenomena  connected  with  it.  Indeed  the  mode  of 
proceeding  which  I  have  pursued,  and  which  would  give  the  more 
exact  results  the  more  regular  and  continuous  the  periodical  ap- 
pearances are,  would  only  yield  moderate  results  if  we  were,  for 
instance,  to  employ  it  for  the  more  accurate  determination  of 
the  eleven-year  period  of  the  sun-spots.  I  therefore  first  in- 
quired whether  I  was  justified  in  assuming  that  the  mean  condition 
of  the  sun  during  a  series  of  rotations  is  constant  enough  to  give 
accurate  results.  I  have  therefore  separated  the  observations  for 
Prague  extending  from  the  19th  of  April  to  the  end  of  August 
1870,  and  containing  five  periods,  from  the  observations  of  Sep- 
tember 1,  1870,  to  the  beginning  of  1871  (containing  four 
periods).  Each  of  these  two  sets  of  observations  was  treated 
graphically.  I  arrived  at  the  following  numbers  for  the  oscilla- 
tion : — 
(April  to  August)  0-8  sin  (#  +  90°) ;  a?=0on  the  6th  of  May. 
(Sept.  to  Dec.)     .  0*8  sin  (#  +  90°) ;  x  =  0  on  the  14th  of  Sept. 
The  amplitude  therefore  remained  constant  during  many 
months.  The  period,  however,  found  in  this  way  is  somewhat 
shorter,  viz.  T= 26*20  days.  This  result  is  in  part  favourable  to 
the  assumption  of  the  constancy  of  the  sun's  condition  during  a 
longer  period. 
<l  The  calculation  of  the  periodic  course  of  the  declination  for 
later  or  earlier  years  with  the  aid  of  the  results  of  1870  would 
be  more  decisive.  In  order  to  arrive  at  this  I  first  derived  a 
mean  value  for  T.     I  found, 
each  point  of  the  sun  to  come  to  the  same  position  with  respect  to  the 
earth.  As  the  movement  of  the  latter  corresponds  with  the  direction  of 
rotation  of  the  sun,  the  synodic  time  of  revolution  is  of  course  greater  than 
the  sidereal  or  absolute  one.  Taking  the  above  value  for  the  absolute  time 
of  rotation,  the  synodic  time  would  be  about  26*33  days. 
