and  the  Magnetic  Relations  of  the  Heavenly  Bodies.        491 
an  instrument*,  the  principles  of  which,  as  I  learned  afterwards, 
had  already  been  proposed  seven  years  previously  by  Perrot  to 
the  French  Academy  for  the  same  purpose  f. 
I  have  not  heard  any  thing  about  the  actual  employment  and 
exact  carrying-out  of  the  principle  until  now.  I  therefore  take 
the  liberty  to  describe  the  instrument,  which  has  proved  good 
in  numerous  experiments,  and  hitherto  the  most  convenient  for 
the  measurements  made  by  it.  In  order  to  explain  the  purpose 
of  the  apparatus  and  its  relations  to  the  present  question,  I  take 
the  liberty  to  reproduce  a  passage  from  my  paper  cited  below*. 
"  The  methods  hitherto  employed  for  measurements  of  attrac- 
tive and  repulsive  forces  maybe  divided  into  two  classes: — the  first 
one,  in  which  the  forces  act  on  masses  allowed  to  turn  round  a 
horizontal  axis,  as  in  the  case  of  the  pendulum,  different  electro- 
meters, and  similar  apparatus ;  and  a  second  one,  in  which  the 
masses  may  turn  round  a  vertical  axis,  as,  for  instance,  in  the 
different  torsion-balauces.  The  apparatus  of  the  first  class  have 
one-armed  levers ;  those  of  the  second  class  have  two  arms,  and 
are  therefore  only  applicable  for  forces  which  are  not  parallel. 
The  instruments  of  the  first  class  are  not  liable  to  this  restriction, 
but  can  only  be  employed  if  the  forces  to  be  measured  do  not 
differ  much  from  the  force  of  gravity,  as  this  is  the  force  set 
against  them.  The  instruments  of  the  second  kind  may  be  em- 
ployed for  very  weak  and  not  parallel  forces,  as  the  momentum 
of  direction  may  be  diminished  indefinitely. 
"  If  we  could  devise  a  method  which  would  possess  the  advan- 
tages of  both  of  these  classes,  it  would  become  of  great  import- 
ance in  astronomy,  as  we  should  be  enabled  by  it  to  measure 
even  those  small  forces  which  are,  for  instance,  produced  by  the 
difference  in  distance  between  any  point  on  the  earth's  surface 
from  sun  or  moon  and  the  distance  of  the  earth's  centre  of  gra- 
vity, or  by  difference  in  the  centrifugal  force  of  two  points  at 
different  distances  from  the  earth's  surface/' 
I  explained  the  principles  of  such  a  method  and  its  practicabi- 
lity in  an  apparatus  for  which  I  proposed  the  name  of 
"  Horizontal  Pendulum," 
in  order  to  distinguish  it  from  other  pendulum-like  instruments, 
also  suspended  by  two  threads.     I  gave  the  description  of  this 
pendulum  with  some  remarks  about  its  sensitiveness  in  the  fol- 
lowing words : — 
"  The  end  of  a  thin  rod  of  glass  210  millims.  long  is  joined 
to  the  end  of  a  fine  steel  wire  of  170  millims.  length ;  the  other 
*  Proceedings  of  the  Royal  Saxon  Society  of  Sciences,  November  27, 
1869,  "  On  a  new  Method  for  the  Measurements  of  Attractive  and  Repul- 
sive Forces." 
t  Comptes  Rendus,  vol.  liv.  p.  728. 
