The velocity of a current increases with the slope and decreases with the winding of the riverbed.
The volume of a river is in proportion to the width of its bed, the slope and the depth of the water being equal.
The slope and width being equal, the speed of the current is greatest in the deepest part of the river.
The excavation force increases at the narrowest section of the river.
Because of the grumbling of the military commanders at what they considered a waste of time, Machiavelli had to intervene with the Signoria before Leonardo was sent out again with documents of authority to continue with his plans. He spent well into the fall surveying the Arno and in October he was back in Florence.
Meanwhile the fighting between Pisa and Florence had been lessened by two political changes. In August Pope Alexander VI had died and his son Cesare Borgia became seriously ill. The Republic of Florence was now free of its most dangerous enemies—the Borgias. The city relaxed in its new security and the hostilities between Florence and Pisa died down to an uneasy armed watch.
Leonardo quickly took advantage of the situation to present an early dream of his to the Signoria. He again put forth his idea of a commercial canal to the sea and made mention of the great advantages there would be for all the mills, lumber yards, forges and other commercial interests in utilizing the water power that would be available from his project. Piero Soderini, the governor of the city-state of Florence, was impressed and thought of the glory it would bring to Florence and himself. He told Leonardo he would present it to the Signoria.
Leonardo now plunged into a winter of great activity. Forced to draw from his savings, he had rejoined the guild of painters in October of 1503, and then applied for the commission of painting the murals in the council chamber of the Palace of the Signoria. It had been planned to decorate this great hall with scenes commemorating famous Florentine victories, and Leonardo chose the battle of Anghiari where the soldiers of Florence defeated the Milanese in 1440. In addition to working on the “Mona Lisa” and continuing with the canal project—for which he was now designing great suction pumps to lift rivers from one level to another—he turned again to astronomy and geology.