and  the  Magnetic  Relations  of  the  Heavenly  Bodies.        493 
paratus,  represented  in  Plate  III.  which  accompanies  this  paper 
not  quite  one  sixth  of  its  natural  size.  In  place  of  the  thin 
wires,  on  which  the  known  changes  in  the  position  of  equilibrium 
acted  disturbingly,  I  used  thin  watchsprings,  a,  a',  which  were 
held  in  continual  tension  by  the  weight  A  with  the  mirror  c  in 
front. „  I  preferred  to  give  to  the  instrument  the  greatest  pos- 
sible dimensions  and  wTeight,  as  the  influences  of  sudden  changes 
in  temperature  and  the  currents  of  air  accompanying  those 
changes  were  diminished  accordingly.  The  stand  is  made  of 
iron;  and  the  feet  of  the  tripod  are  as  long  as  possible,  in  order 
to  effect  very  small  changes  in  the  position  of  the  points  of  sus- 
pension with  regard  to  the  direction  of  gravitation  by  the  slow 
movement  of  the  screws. 
The  screw  d,  which  is  situated  as  nearly  as  possible  in  the  ver- 
tical plane  passing  through  the  two  points  of  suspension  c  and 
(/,  allows  us  to  change  as  required  the  sensitiveness  of  the  in- 
strument, as  by  the  relative  position  of  the  points  c  and  cf  the 
time  of  vibration  of  the  horizontal  pendulum  is  determined.  A 
time  of  vibration  of  30  seconds  (half  a  period)  is  easily  accom- 
plished. B  is  a  counterpoise  to  A.  Before  the  oscillating  mass 
A  and  the  parts  belonging  to  it  were  placed  in  the  rings,  which 
fit  into  small  incisions  cut  into  the  cylindrical  axis,  it  was  set 
into  vibration  by  the  direct  action  of  gravity  round  a  knife- 
edge  occupying  provisionally  the  place  of  the  turning-point. 
The  time  of  oscillation  amounted  to  nearly  0*25  second.  By 
means  of  a  known  relation,  the  ratio  of  the  moments  of  direction 
are  thus  easily  obtained  which  are  exerted  by  gravity  on  the  vi- 
brating mass  in  the  horizontal  and  vertical  directions. 
The  theory  of  the  instrument  for  very  small  elongations, 
which  alone  need  be  here  considered,  is  very  simple ;  so  that  I 
shall  content  myself  with  communicating  a  few  values  obtained 
from  the  numerous  series  of  observations  which  have  been  made 
during  the  years  1870  and  1871,  in  order  to  enable  the  reader 
to  judge  of  the  applicability  and  sensitiveness  of  the  instrument. 
I  must,  however,  first  make  some  remarks  on  the  setting-up 
of  the  instrument.  As  the  disturbances  in  the  centre  of  the 
town  were  too  frequent,  it  was  transported  into  a  little  dome 
built  in  the  garden  of  the  observatory  for  astrophysical  researches. 
Close  to  it  I  had  a  massive  pillar  of  sandstone  erected,  covered  in 
its  whole  extent  by  an  insulated  case,  which,  similarly  to  all  re- 
frigerators, was  provided  with  thick  walls  filled  with  bad  con- 
ductors of  heat  j  on  the  inner  side  the  walls  were  covered  with 
tin.  The  case  was  surrounded  by  a  small  wooden  structure, 
with  an  interval  of  about  half  a  foot,  allowing  the  air  to  circulate 
freely,  but  protecting  the  first  box  from  any  direct  influence  of 
radiant  solar  heat.     On  one  side  of  the  building  doors  were  in- 
