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. 
Viéta himself neglected them as absolutely useless anid 
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 Chénier stigmatized 
his political enemies, the editors of the Mercure de 
France :— 
‘““ Which these lettered dwarfs have done, who without literature, 
Beneath nonentity, 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 lettrés qui, sans littérature, 
Au-dessous du néant, soutiennent le Mercure.” 
