78 CARNOT. 



these gaps should be altogether neglected ? Such was 

 not Carnot's view. "We have already seen him devoting 

 the short moments of repose which his Directorial duties 

 left him to the metaphysics of the Infinitesimal Calculus ; 

 the suppression of the Tribunate will permit him to sub- 

 mit to similar investigations an equally arduous question 

 that of negative quantities. 



It often happens that, after having reduced a problem 

 to the form of an equation, analysis offers you some neg- 

 ative numbers amongst the solutions sought for ; for 

 example minus 10, minus 50, minus 100 ; these solutions 

 the ancient analysts did not know how to interpret. 

 Vieta himself neglected them as absolutely useless and 

 insignificant. By degrees they got into the habit of re- 

 garding negative numbers as quantities less than zero. 

 Newton and Euler gave no other definition of them 

 ( Universal Arithmetic, and Introduction to Infinitesimal 

 Analysis). This notion has in modern times introduced 

 itself into the vulgar tongue : the merchant on the most 

 petty scale understands exactly the position of a corre- 

 spondent who announces to him negative profits ; poetry 

 has also given its sanction to the same thought, as we 

 see in these two verses, by which Chenier stigmatized 

 his political enemies, the editors of the Mercure de 

 France : 



" Which these lettered dwarfs have done, who without literature, 

 Beneathtnonentity. sustain the Mercure." * 



Well, Gentlemen, it is a notion thus supported by the 

 authority of the greatest geometers of modern times, 

 consecrated by the assent of one who has, they say, more 



* " Qu'ont fait ces nains lettre"s qui, sans litte"rature, 

 Au-des&ous du neant, soutiennent le Mercure." 



