386     Royal  Society: — Messrs.  De  La  Rue,  Stewart,  and  Loewy 
3.  In  a  Table  he  gives  the  mean  numbers  expressing  the  solar 
activity,  arranged  in  various  columns,  and  arrives  at  the  following 
results : — 
(1)  It  is  shown  now,  with  greater  precision  than  was  previously 
possible,  that  the  curve  of  sun-spots  ascends  with  greater  rapidity 
than  it  descends.  This  fact  is  shown  in  the  subjoined  diagram, 
which  it  may  be  of  interest  to  compare  with  the  curves  given  pre- 
viously by  ourselves  in  the  above-mentioned  place.  The  zero-point 
in  this  diagram  corresponds  to  the  minimum  of  each  period;  the 
abscissae  give  the  time  before  and  after  it,  viz.  two  and  a  half  years, 
or  thirty  months;  the  ordinates  express  the  amount  of  spot-pro- 
duction in  numbers  of  an  arbitrary  scale.  The  two  finely  dotted 
curves  are  intended  to  show  the  actual  character  of  a  portion  of  two 
periods  only,  viz.  those  which  had  their  minima  in  18232  and 
1867*2;  the  strongly  dotted  curve,  however,  gives  the  mean  of  all 
periods  (five)  over  which  the  investigation  extends. 
(2)  Denoting  by  x  the  number  of  years  during  which  the  curve  as- 
cends and  presuming  that  the  behaviour  is  approximately  the  same 
throughout  the  whole  period  of  1 1  *  1  years  as  during  the  five  years 
investigated,  we  have  the  proportion 
whence 
*:  ]1-1  -«::  1  :  2, 
x=  3'7, 
