454     M.  F.  Zollner  on  the  Origin  of  the  Earth's  Magnetism, 
spots,  we  find  from  the  outside  numbers  for  the  length  of  the 
mean  period :— 
[1860-a±0-2]-[17500±l-0]  =n.02±0.10j 
[1856-2±0-2]-  [1755-7+0-5]  =n.17±0.06 
y 
These  results  agree,  within  the  limits  of  errors  of  observations, 
with  the  previously  deduced  period  of  11^  years." 
"  Considering,  secondly,  the  period  of  magnetical  variations, 
we  shall  see  that  it  agrees  with  the  period  of  sun-spots,  and  that 
the  parallelism  of  the  two  appearances  has  been  proved  the  more 
strikingly t  as  not  only  the  mean  period  is  exactly  the  same,  but 
even  the  anomalies  of  one  are  exactly  found  again  in  the  other, 
"  This  agreement  induced  me  already,  more  than  three  years 
ago,  to  express  the  opinion  that  there  exists  such  a  connexion 
between  the  two  phenomena  that  the  intensity  of  the  common 
cause  could  be  read  off  in  both  as  on  two  different  scales.  It 
would  then  be  possible  to  calculate  the  magnitude  v  of  the  mag- 
netic variation  from  the  relative  number  r  of  the  year  in  question 
by  a  formula  of  the  form 
v=a  +  b  .r. 
I  found,  for  instance,  at  that  time  for  Munich  the  formula 
fl'=6'-273  +  (H)51r, 
which  represented  more  exactly  the  variations  of  declination  for 
the  years  1835-1850  as  observed  by  Lamont  than  the  formula 
which  had  been  found  directly  by  himself"*. 
It  must  be  said  in  conclusion  that  Professor  R.  Wolf  had  de- 
duced such  a  formula  for  Prague.  He  remarks  on  its  agree- 
ment with  observation,  in  a  recent  publication,  as  follows  f  : — 
"  The  value  9'#44,  which  I  had  calculated  in  No.  26  from  the 
sun-spots  for  the  variation  for  Prague  in  1869,  is  sensibly 
larger  than  that  found  by  observation  2h-20h,  8'*69;  but  it 
agrees  exactly  with  that  flowing  from  the  minimum  and  maxi- 
mum values,  viz.  9'*44." 
A  connexion  which  is  not  less  astonishing  is  that  found  to 
exist  between  the  frequency  of  the  aurora  borealis  and  that  of 
the  sun-spots.  I  take  the  epochs  deduced  from  a  great  number 
of  European  and  American  observations  by  Professor  Loomis  in 
a  paper  published  in  1865  in  the  '  Annual  Report  of  the  Board 
*  As  to  the  differences  of  opinion  between  Lamont  and  Wolf,  which, 
however,  seem  to  be  decided  in  favour  of  the  latter,  I  refer  to  the  two  cited 
papers  in  Poggendorff's  Annalen,  1862. 
t  Vierteljahrsschrift  der  naturforschenden  Gesellschaft  zu  Zurich,  De- 
cember 1870,  p.  253. 
