and  the  Magnetic  Relations  of  the  Heavenly  Bodies.       495 
ness  of  the  instrument,  and  the  surety  with  which  we  can  ob- 
serve deviations  of  only  0*001  second  of  arc,  even  with  a  time  of 
vibration  of  14*44  seconds.  The  above  would  be  the  value  cor- 
responding, according  to  the  above  relation  between  one  division 
of  the  scale  of  the  horizontal  and  one  of  the  vertical  pendulum, 
to  about  0*1  division  of  the  former. 
We  can  easily  increase  to  four  or  five  times  the  sensitiveness 
of  the  instrument  by  raising  the  foot  with  the  adjusting-screw  d; 
but  for  this  the  stability  of  the  pillar  and  its  surrounding  parts 
was  not  sufficient,  in  spite  of  all  precautions.  A  railway-train 
passing  at  a  distance  of  about  H  kilometre  caused  undulatory 
motions  of  the  ground,  which  called  forth  periodic  variations  of 
the  position  of  equilibrium  of  the  horizontal  pendulum. 
Such  observations  are  therefore  best  made  in  deep  and  quiet 
mines,  where  the  variations  of  temperature  and  shakings  of 
the  earth  are  absent,  and  all  those  influences  can  therefore  be 
determined  quantitatively  which  are  caused  either  directly  by 
volcanic  movements  of  the  ground,  or  indirectly  by  magnetical 
induction  through  changes  in  the  velocity  of  the  streaming 
masses  on  the  inner  part  of  the  earth. 
Besides  the  generation  of  an  inner  tidal  and  pressure-wave, 
the  sun  and  moon  exert  a  direct  influence  on  the  position  of  the 
instrument,  because  they  attract  with  different  intensity  the 
centre  of  gravity  of  the  earth  and  the  centre  of  gravity  of  the 
pendulum .  The  magnitude  of  the  deviation  of  the  plumbline  has 
been  made  the  subject  of  an  interesting  research  by  C.  A.  F. 
Peters*. 
The  mean  deviation  which  the  moon  can  generate  in  its  most 
favourable  position  amounts,  according  to  the  deductions  of 
Peters,  to  0"*0174;  that  which  the  sun  generates  under  the 
same  conditions  amounts  to  0"*0080. 
If  the  horizontal  pendulum  is  put  up,  as  mine  is,  so  that  the 
position  of  equilibrium  lies  in  the  plane  of  the  meridian,  it  is  clear 
that  the  above  maximum  values  of  deviation  must  have  opposite 
signs,  according  as  the  heavenly  body  is  to  the  east  or  to  the 
west  of  the  meridian;  the  angular  difference  will  therefore  be 
doubled  in  both  cases — that  is, 
For  the  lunar  influence  =  0"*0348, 
For  the  solar  influence  =  0"*0160. 
The  inaccuracy  of  the  observations  given  above  would  therefore, 
after  one  reading,  amount  to  -^  of  the  amount  to  be  measured  in 
*  "  On  the  small  Deviations  of  the  Plumbline  and  Level  which  are  caused 
by  the  Attraction  of  the  Sun,  the  Moon,  and  some  Terrestrial  Bodies. 
By  Dr.  C.  A.  F.  Peters,"  Bulletin  de  la  Classe  physico-mathematique  de 
I  Acad.  Imp.  des  Sciences  de  St.  Petersbourg,  tome  iii.  No.  14.  Petersburg, 
1844. 
