nized victory" in fourteen armies, he was a
simple captain.

Carnot was elected one of the five Directors in November 1795, and
continued to direct the war department during the campaign of 1796. Late
in 1796 he was made a member (1st class) of the Institute, which he had
helped to establish. He was for two periods president of the Directory,
but on the _coup d'etat_ of the 18th Fructidor (1797) was forced to take
refuge abroad. He returned to France after the 18th Brumaire (1799) and
was re-elected to the Institute in 1800. Early in 1800 he became
minister of war, and he accompanied Moreau in the early part of the
Rhine campaign. His chief work was, however, in reducing the expenses of
the armies. Contrary to the usual custom he refused to receive presents
from contractors, and he effected much-needed reforms in every part of
the military administration. He tendered his resignation later in the
year, but it was long before the First Consul would accept it. From 1801
he lived in retirement with his family, employing himself chiefly in
scientific pursuits. As a senator he consistently opposed the increasing
monarchism of Napoleon, who, however, gave him in 1809 a pension and
commissioned him to write a work on fortification for the school of
Metz. In these years he had published _De la correlation des figures de
geometrie_ (1801), _Geometrie de position_ (1803), and _Principes
fondamentaux de l'equilibre et du mouvement_ (1803), all of which were
translated into German. His great work on fortification appeared at
Paris in 1810 (_De la defense de places fortes_) and was translated for
the use of almost every army in Europe. He took Montalembert as his
ground-work. Without sharing Montalembert's antipathy to the bastioned
trace, and his predilection for high masonry caponiers, he followed out
the principle of retarding the development of the attack, and provided
for the most active defence. To facilitate sorties in great force he did
away with a counterscarp wall, providing instead a long gentle slope
from the bottom of the ditch to the crest of the glacis. This, he
imagined, would compel an assailant to maintain large forces in the
advanced trenches, which he proposed to attack by vertical fire from
mortars. Along the front of his fortress was built a heavy detached
wall, loop-holed for fire, and sufficiently high to be a most
formidable obstacle. This "Carnot wall," and, in general, Carnot's
principle of active defence,