on  some  recent  Researches  in  Solar  Physics. 
387 
or  the  average  duration  of  an  ascent  is  3*7  years,  that  of  a  descent 
7*4  years. 
(3)  The  character  of  a  single  period  may  essentially  differ  from 
the  mean ;  hut  on  the  whole  it  appears  that  a   -J         .  ,  \  de- 
[  accelerated  J 
scent  corresponds  to  a  \     -  _  >   ascent.     Thus  the  minimum 
[  accelerated  J 
of  1844*0  hehavedvery  normally,  but  that  of  1856*2,  and  still  more 
that  of  1823*2,  shown  in  the  above  diagram,  presents  a  retarded 
ascent  and  descent;  on  the  other  hand,  in  the  minimum  of  1833*8, 
and  still  more  in  that  of  1867*2,  also  shown  in  the  diagram,  both 
ascent  and  descent  are  accelerated. 
4.  Finally,  Professor  Wolf  arranged  in  the  manner  shown  in  the 
following  Table  the  successive  minima  and  maxima,  in  order  to  arrive 
at  some  generalization  which  might  enable  him  to  foretell  the  general 
character  aud  length  of  a  future  period.  Taking  the  absolute  differ- 
ences in  time  of  every  two  successive  maxima,  and  the  mean  differ- 
ences of  every  two  alternating  minima,  he  shows  that  the  greatest 
acceleration  of  both  maximum  and  minimum  happens  together.  This 
result  strengthens  our  own  conclusions,  to  be  immediately  stated, 
by  new  evidence,  as  it  is  derived  from  observations  antecedent  to  the 
time  over  which  our  researches  extend. 
Differences  of 
Differences 
Minima. 
alternating 
Means. 
Maxima. 
of  successive 
Minima. 
Maxima. 
1810*5 
1816*8 
1823*2 
23*3 
11*65 
1829*5 
12*7 
1833*8 
20*8 
10*4 
1837*2 
7'7 
1S44-0 
22*4 
11*2 
1848*6 
11*4 
1856*2 
23*2 
11*6 
1860*2 
11*6 
1867*2 
From  this  Professor  Wolf  predicts  for  the  present  period  a  very 
accelerated  maximum — a  prediction  which  seems  likely  to  be  fulfilled. 
5.  Comparing,  now,  M.  Wolf's  results  with  our  own,  it  must 
not  be  overlooked,  in  judging  of  the  agreement  or  discrepancy  of 
these  two  independently  obtained  sets,  that  our  facts  have  been  de- 
rived from  the  actual  measurement  and  subsequent  calculation  of  the 
spotted  area  from  day  to  lay  since  1833  recorded  by  Schwabe, 
Carrington,  and  the  Kew  solar  photograms,  which  measurements 
are  expressed  as  millionths  of  the  sun's  visible  hemisphere,  while  the 
conclusions  of  M.  Wolf  are  founded  on  certain  "  relative  numbers," 
which  give  the  amount  of  observed  spots  on  an  arbitrary  scale,  chiefly 
designed  to  make  observations  made  at  different  times  and  by  various 
2  C  2 
