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'état_ 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 corrélation des figures de géométrie_ (1801), _Géométrie de position_ (1803), and _Principes fondamentaux de l'équilibre et du mouvement_ (1803), all of which were translated into German. His great work on fortification appeared at Paris in 1810 (_De la défense 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, played a great part in the rise of modern fortification.