388     Royal  Society : — Messrs.  De  La  Hue  Stewart,  and  Loewy 
observers  comparable  with  each  other.  This  will  obviously,  in  addi- 
tion to  the  sources  of  error  to  which  our  own  method  is  liable,  intro- 
duce an  amount  of  uncertainty  arising  from  errors  of  estimation  and 
the  possibility  of  using  for  a  whole  series  an  erroneous  factor  of  re- 
duction. Nevertheless  we  shall  find  a  very  close  agreement  in 
various  important  results ;  and  this  seems  a  sufficient  proof  of  the 
great  value  and  reliability  of  M.  Wolf's  "relative  numbers,"  espe- 
cially for  times  previous  to  the  commencement  of  regular  sun  obser- 
vations. 
6.  The  following  is  a  comparison  of  the  data  of  periodic  epochs, 
as  fixed  by  ourselves  and  M.  Wolf : — 
I.  II.  III.  IV. 
Minima  (  De  La  Rue,  Stewart,  1  1833.92  1843.75  1856-31  1867*12 
,      <      and  Loewy     .     .  j 
epocns.  [RudolfWolf      #     m     1833.8     1844.0     1856.2     1867-2 
I.  II.  HI. 
Maxima  (Be  La  Sue,  Stewart,  and  Loewy  1836-98  1847*87  1859-69 
epochs.  \  Rudolf  Wolf 1837'2     1848-6     1860-2 
It  will  be  seen  from  this  comparison  that  only  one  appreciable  dif- 
ference occurs,  viz.  in  the  maximum  of  1847,  which  M.  Wolf  fixes 
nearly  one  and  a  quarter  years  before  our  date. 
The  mean  length  of  a  period  is  found  by  us  to  be  11  -07  years, 
which  agrees  very  well  with  M.  Wolf's  value,  viz.  11' 1  years. 
7.  We  found  the  following  times  for  the  duration  of  increase  of 
spots  during  the  three  periods,  and  for  the  corresponding  decrease, 
or  for  ascent  and  descent  of  the  graphic  curve,  beginning  with  the 
minimum  of  1833 : — 
Time  of  ascent. 
Time  of  descent 
I.... 
.  ..     3-06 
years. 
677 
years. 
II. . . . 
.  ..     4-12 
»> 
8-44 
>> 
III. . . . 
.  . .     3-37 
}t 
7-43 
>> 
Mean 3'52     „  7*55     „ 
Professor  Wolf  gives  3*7  years  and  7*4  years  for  the  ascent  and 
descent  respectively  ;  and  considering  that  he  derived  these  numbers 
only  from  an  investigation  of  a  portion  of  each  period,  the  agreement 
is  indeed  surprising,  and  would  by  itself  suggest  that  the  times  of 
ascent  and  descent  are  connected  by  a  definite  law. 
8.  M.  Wolf  has  expressed  in  general  terms  the  following  law  with 
reference  to  this  relation  of  increase  and  decrease  of  spots  : — 
"  The  character  of  a  single  period  may  essentially  differ  from  the 
mean  behaviour ;  but  on  the  whole  it  appears  that  a  i         ?     .   ,  i 
rr  [  accelerated  J 
descent  corresponds  to  a  {  J^^  }  ascent." 
We,  on  the  other  hand,  have,  by  an  inspection  of  our  curves  (vide 
