Force  in  the  Contact  of  Metals.  93 
therefore  necessary  to  ascertain  that  the  index  was  sufficiently 
free  in  this  respect.  Supposing  it  to  move  with  perfect  freedom , 
a  difference  of  pressure  of  Y 2 g0 0 0  of  an  atmosphere  would,  ac- 
cording to  what  precedes,  be  sufficient  to  remove  it  one  division 
of  the  scale.  This  quantity  corresponds  to  a  difference  of  pres- 
sure of  0*4)  milligramme  on  the  two  extremities  of  the  index.  I 
satisfied  myself  in  the  following  manner  that  an  index  composed 
of  a  mixture  of  alcohol  and  water  really  moves  under  this  differ- 
ence of  pressure  : — I  used  for  the  experiment  an  index  of  2  cen- 
tims.  length.  Its  weight,  taking  09  for  the  specific  gravity  of 
the  mixture,  was  88  milligrammes.  Now,  for  the  angle  {x) 
which  the  tube  must  make  with  the  horizontal  in  order  that  in 
virtue  of  its  own  weight  the  index  may  receive  in  one  of  the 
directions  a  pressure  of  the  amount  above  indicated,  we  evidently 
obtain  88  sina7=0'4,  whence  «r=15'*5.  It  was  shown,  at  the 
time  of  the  experiments,  that  the  index  commenced  moving  at 
an  angle  of  inclination  which  was  only  a  small  fraction  of  the 
calculated  angle.  It  may  therefore  be  admitted  that,  with  an 
index  of  this  nature,  the  apparatus  evidently  indicated  at  least 
the  half  of  a  thousandth  of  a  degree — a  sensitiveness  which,  as 
special  experiments  demonstrated,  was  not  diminished  with  an 
index  of  several  centimetres  length.  On  the  other  hand,  an 
angle  of  inclination  of  several  degrees  was  required  for  the  com- 
mencement of  motion  of  a  sulphuric  acid  index  of  the  same 
length;  so  the  employment  of  this  liquid  could  not  be  thought 
of.  All  the  following  experiments  were  made  with  an  index  of 
the  alcoholic  mixture  above  mentioned. 
§3. 
As  we  know,  the  cooling  of  a  body  in  the  air  is  not  propor- 
tional to  the  excess  of  its  temperature,  but  increases  more  rapidly 
than  the  latter.  It  is  only  when  the  excess  is  a  minimum  that 
the  cooling  can  be  regarded  as  proportional  to  it.  In  the  fol- 
lowing experiments,  the  excess  of  temperature  of  the  air  of  the 
copper  cylinders  above  the  temperature  of  the  zinc  jacket,  and 
above  that  of  the  air  between  the  jacket  and  the  cylinder  was  at 
the  most  1  or  2  degrees ;  and  consequently  the  excess  of  tem- 
perature of  the  cylinders  themselves  was  still  less.  Let  A  be 
the  quantity  of  heat  which  the  copper  cylinders  lose  by  radiation 
and  the  contact  of  the  external  air,  t  the  excess  of  temperature 
of  the  copper  sides,  and  a,  and  b{  constants,  we  may  then  put* 
A  =  atr  +  fyr2. 
*  According  to  Dulong  and  Petit,  the  formula  of  cooling  is 
Mae(ar-1)  +  Nr  1233, 
where  6  is  the  temperature  of  the  surrounding  bodies,  t  the  excess  of  tcm- 
