on  some  recent  Researches  in  Solar  Physics.  389 
Phil.  Trans.  1870,  p.  393),  been  induced  to  make  the  following  re- 
mark on  the  same  question  : — 
"  We  see  that  the  second  curve,  which  was  longer  in  period  as  a 
whole  than  either  of  the  other  two,  manifests  this  excess  in  each  of 
its  branches,  that  is  to  say,  its  left  or  ascending  branch  is  larger 
as  a  whole  than  the  same  branch  of  the  other  two  curves,  and  the 
same  takes  place  for  the  second  or  descending  branch.  On  the  other 
hand,  the  maximum  of  this  curve  is  not  so  high  as  that  of  either 
of  the  other  two  ;  in  fact  the  curve  has  the  appearance  as  if  it  were 
pressed  down  from  above,  and  pressed  out  laterally  so  as  to  lose  in 
elevation  what  it  gains  in  time." 
Although  both  statements  appear  to  lead  up  to  the  same  con- 
clusion, viz.  that  ascent  and  descent  are  connected  by  a  law,  still  they 
differ  essentially  in  this  respect,  that  if  A,  B,  0  represent  the  three 
following  consecutive  events,  descent,  ascent,  descent,  ProfessorWolf's 
law  refers  to  the  connexion  between  A  and  B,  while  our  remark 
refers  to  B  and  C.  We  consider  two  successive  minima  as  the  begin- 
ning and  end  of  a  single  period,  while  M.  Wolf,  at  least  in  this  par- 
ticular research,  places  the  minimum  within  the  period,  and  compares 
the  descent  from  the  preceding  maximum  with  the  ascent  to  the 
next  one. 
9.  We  have  considered  the  connexion  thus  indicated  of  sufficient 
importance  to  apply  to  it  the  following  test.  If,  using  the  previous 
notation,  a  definite  relation  exists  between  A  and  B,  the  ratio  of 
the  times  which  the  events  occupy  in  every  epoch  ought  to  be  ap- 
proximately constant ;  similarly  with  respect  to  B  and  C  ;  and  this 
ratio  should  not  be  influenced  by  the  absolute  duration  of  the  two 
successive  events.  It  is  clear  that  the  greater  uniformity  of  these 
ratios  will  be  a  test  for  their  interdependence.  The  following  is  the 
result  of  the  comparison  : — 
a.  Professor  Wolf's  law  :  comparison  of  A  and  B. 
Duration  of  Duration  of 
Periods.  descent  (A).  Periods.  ascent  (B). 
I.     1829*5  to  1833-8     4*3  years     1833'8  to  1837*2     3-4  years. 
II.      1837-2  to  1844-0     6-8     „         1844-0  to  1846-6     2-6     „ 
III.      1846-6  to  1856-2     9'6     „         1856-2  to  1860-2     4*0     „ 
a  10  B*  Difference  from  mean. 
1 1-265  1  -0-728. 
II 2-615  V  Mean  2'093  +0-522. 
Ill 2-400  J  +0-307. 
These  differences  from  the  mean  are  so  considerable,  that  in  the 
present  state  of  the  inquiry  a  connexion  between  any  descent  and  the 
immediately  succeeding  ascent  appears  highly  improbable.  A  very 
new  and  apparently  important  relation  seems,  however,  to  result  from 
a  similar  comparison  of  any  ascent  and  the  immediately  succeeding 
descent,  or  between  B  and  C. 
