348 Carnot on the Theory of 



Evanefcent quantities, as being equal to nothing, ought to 

 be neglected in the calculation, when they are connected, by 

 addition or fubtraftion, to any real, effective quantity. But 

 they have, neverthelefs, as we have feen, relations very 

 important to be known, relations which are determined 

 by the law of continuity, to which the fyfteqa of auxiliary 

 quantities is fubjected in its mutations. Now, in order 

 to difcover this law of continuity, it is eafy to perceive, 

 lhat we are obliged to confider thefe evanefcent quantities at 

 fome diftance from the limit where they entirely vanifh, 

 otherwife they prefent only the indefinite ratio of o to Q; 

 hut this diftance is arbitrary, and hath no other object but to 

 enable us to judge more eafily of the ratios or relations which 

 exift between thefe evanefcent quantities. Thefe are the 

 ratios which we have in view, when we confider infinitely 

 fmall quantities as abfolute nullities, and not thofe ratios 

 which exift between the quantities which are not yet arrived 

 at their limit, or the term of their annihilation. Thefe laft 

 quantities, which I have called indefinitely fmall, are not 

 themfelves defigned to enter into the calculus confidered in 

 the prefent point of view ; but are only employed to affift the 

 imagination, and to indicate the law of continuity which de- 

 termines the ratios and relations, whatever they may be, of 

 the correfponding evanefcent quantities. 



According to this hypothefis, the quantities reprefented by 

 MZ and RZ, in the proportion MZ : RZ::TP : MP, are 

 fuppofed abfolutely equal to nothing. But, as it is their 

 ratio that is required, in order to perceive it's equality to 



TP 



XF5TJ tne indefinitely fmall quantities, which anfwer to thefe 



nullities, muft be confidered, not that they themfelves may be 

 introduced into the calculation, but that the vanifhing quan- 

 tities, which are their ultimate values, may enter into it, 

 under the denominations of MZ and RZ. 



45. Thefe expreflions therefore, MZ and RZ, here repre- 

 fent nullities, and are ufed under the forms of MZ and RZ, 

 rather than under the common form o, becaufe, if they were 

 ufed under this laft form, it would no longer be poffible, in. 

 the operations wherein they are mixed, to diftinguifh their 

 different origins, or, in other words, to diftinguifh the dif- 

 ferent 



