504  -Mr.  de  luc  on  
apply  them  to  the  temperatures  in  which  oneprecifely 
wants  the  moil  exact  proportions.  One  likewife  may 
fee  that  the  difference  of  fpirituofity  only,  occaiions  very 
feniible  ones  in  the  progreflions  of  the  two  fpirituous 
liquors,  and  that  confequently  one  would  commit  a dou- 
ble error,  if  one  were  to  coniider  the  intermediate  rela- 
tions as  proportional  to  the  total  relation,  eftabliihed 
between  quickiilver  and  one  of  thefe  liquors,  only  by 
obfervations  made  in  very  different  temperatures. 
If,  on  the  contrary,  the  fundamental  experiments  had 
been  made  at  the  probable  limits  of  the  obfervations, 
that  is  at  o and  at  1 o°  of  the  Thermometer,  having  then 
the  real  dilatation, between  thefe  two  temperatures,  of  the 
fpirituous  liquor  which  ferved  for  the  experiment,  there 
would  be  only  thefe  fmall  deviations,  expreffed  by  the 
companion 
raifon,  quand  on  vient  a les  appliquer  aux  temperatures  ou  Ton  avoit  befoin 
precifement  des  rapports  les  plus  exacts.  On  voit  auffi  que  la  difference  feule  de 
fpirituofite,  en  produit  de  tres  fenfibles  dans  la  marche  des  deux  liqueurs  fpi- 
ritueufes;  et  que  par  confequent  ont  tomberoit  doublement  dans  Perreur,  en 
regardant  ces  rapports  hitermediaires  comme  proportionnels  au -rapport  total, 
etabli  entre  le  mercure  et  une  feule  de  ces  liqueurs  par  des  obfervations  a de 
.grandes  differences  de  temperature. 
Si  au  contraire  on  efk  fait  les  experiences  fondamentales  aux  limites  probables 
des  obfervations,  cleft  a dire  a o et  a 26°  du  Thermometre;  ayant  alors  la  dila- 
tation reelle,  entre  ces  deux  temperatures,  de  la  liqueur  fpiritueufe  qui  eut  fervi 
a Inexperience,  on  n’auroit  a craindre  que  les  ecarts  exprimes  par  les  rapports  des 
nombres 
