Leonardo da Vinci, Pathfinder of Science

8 The French

The noonday sun was baking the deserted streets of Milan as Leonardo hurried across the drawbridge of the castle. The guard dozing in the entrance arch started to his feet, but when he saw who it was he sat down again, muttering about a madman. Taking the shortest way, Leonardo arrived at the monastery gate and pulled on the bellcord. When the gate opened Leonardo brushed past the startled monk and made directly for the scaffolding in the refectory. He looked at his almost completed painting for a moment, took a brush and mixed a color swiftly on the large palette. Then he climbed the scaffolding and very quickly applied three or four strokes. With this he sighed and smiled. Then, just as abruptly, he put away his brushes and, without a backward glance, he left, making his way back to the castle in the hot sun.

For three years, Leonardo had been working this way on the “Last Supper.”

Sometimes he would work from dawn to dusk forgetting to eat; other times, he would stay away for days and then run back just to add a touch. Once he arrived and, with his arms folded across his chest, he stood in front of it for two hours just studying what he had done.

Now, in 1498, the painting was nearing completion and the only faces still left blank were those of Christ and Judas. Leonardo had drawn hundreds of sketches, taking his models wherever he found them—once he sketched a man just for his hands. Now that his name had become well known he always had an audience while he worked. His pupils, the monks, visiting nobility, church officials, and frequently Ludovico himself watched him as he painted the “Last Supper.”

But Leonardo, as usual, was involved in many different tasks. He was supervising the installation of a hydraulic pump over seventy feet high beside a stream which would use the power of the stream itself to pump water into the castle. Mindful, too, of the uncertainty of court patronage, he was designing commercial machinery, hoping thereby to secure an income outside the court. Among the most notable of these were an olive press, an automatic file-cutter, a hydraulic saw, and a needle sharpener. This latter was a forerunner of modern sharpeners with their mass-production methods. With it, Leonardo dreamt of sharpening four hundred needles at a time, or forty thousand an hour so that in twelve hours one person could sharpen four hundred and eighty thousand needles! The needles were arranged successively on a moving belt of leather and brought against a rotating grindstone. This grindstone was set in such a way that the needles were sharpened into curvilinear points rather than the usual triangular points.

In his travels to Vigevano and other parts of the countryside around Milan, Leonardo had studied flour mills. He had talked with the workmen, asked the prices of grain, and noted the time that it took to do the milling. Then he made calculations on ways to cut down the time, and, in fact, redesigned the entire mill. He mounted twelve cylindrical millstones in rows of four on one side of a canal and another twelve on the other side. In the canal were hydraulic wheels or paddlewheels. Each wheel was attached to a rod that ran underneath four millstones. Geared to the one rod were four grinding levers to the stones above. In this way it was possible to have twenty-four millstones operating at the same time.

But most fascinating to Leonardo now was the construction of his flying machine. His first models involved the principle of an air-screw mounted on a platform on which a man stood. But where would the necessary power come from to lift his machine from the ground? At first he thought of operating his air-screw by means of a steel spring coiled around a drum, but this he apparently abandoned. Later, however, Leonardo did design another model on this principle which has been called the forerunner of the modern helicopter. It was to be operated by four men standing on a platform. Each man would hold a bar which wound a spring-driven mechanism, much as in a modern clockworks. The air-screw was a broad blade spiraling about a vertical shaft—the ancestor of the modern propeller.

The model that Leonardo wanted to construct now, however, was of a different principle. Instead of an air-screw he substituted a pair of wings fashioned after those of the birds. There was still a platform on which the flyer stood and two springs were still the essential “motor” to raise and lower the wings. But as Leonardo worked on his apparatus he began to realize that it would be too much at the mercy of a sudden gust of wind or a violent updraft. It was necessary to return to his study of the air and its currents.

With all of this activity in mechanical devices Leonardo had reawakened his interest in mathematics. During this time he was introduced to a man at Ludovico’s court who became his friend and collaborator. He was a Franciscan monk named Fra Luca Pacioli who had been appointed a professor of mathematics by Ludovico. He, too, came from Florence, and in 1496, when he met Leonardo, he was forty-six years old and the author of Summa di Arithmetica, the first printed scientific work of his time. Pacioli was now at work on a book of geometry to be entitled De Divina Proportione and he enlisted Leonardo’s aid in drawing the plates for his book. As Leonardo had already made a study of human proportions, the association with Pacioli was of benefit to them both. Among Leonardo’s best known drawings of human proportion is a beautifully rendered figure-study of a standing man with his arms at his sides and then outstretched, his legs together and then apart, inscribed within a square and a circle. It was made to illustrate a passage from Vitruvius on the proportions of a human figure and demonstrated, among other things, “the span of a man’s outstretched arms is equal to his height.”

Moreover, Leonardo found with Pacioli confirmation of many of his own observations and experiments and in turn Pacioli gave to Leonardo a confidence in his own methods. Pacioli also helped Leonardo with his arithmetic, a subject that Leonardo had neglected in his impatience to study geometry. The association also helped to free him further from the cobwebs of medieval beliefs. For Pacioli, the friendship with Leonardo was a revelation. Although Pacioli was a learned mathematician, Leonardo demonstrated to him that the application of his science encompassed all sciences—even art—for Leonardo later wrote, “Let no one read me who is not a mathematician....”

Legend relates that Leonardo became so absorbed in his studies that the prior of the monastery complained to Ludovico that the “Last Supper,” although nearly completed, still lacked the faces of Christ and Judas. Ludovico summoned Leonardo to court and laid the complaint before him. Leonardo, however, was quick to reply.

“The good prior is an esteemed man, your Grace, but he is a monk and not a painter. Little does he know that I spend at least two hours a day on my painting.”

“But Master, he says he never sees you there, so how do you explain these two hours a day?”

“Excellency, the figure of Judas must be of incomparable evil. Every day I search for this face in the criminal quarter, and every day I fail to find the evil that I am looking for. If I cannot find this man, however, I can use the head of the prior—it would do admirably, but I have hesitated for fear of hurting his feelings.”

Ludovico slapped his knees and roared with laughter. There were no more complaints.

Finally, in 1498, the scaffolding was removed from the painting and Leonardo’s masterpiece was revealed. The twelve apostles grouped at the table are shown each responding in his own way to the words of Christ, “One of you shall betray me.” Again hundreds flocked to see this latest marvel of Leonardo’s. Its striking influence was felt by generations of painters. Even now, more than four hundred and fifty years later, the world still comes to stand before the genius of Leonardo da Vinci in the refectory of Santa Maria delle Grazie.

The clouds of war were gathering again over Italy. In April of 1498, Charles VIII of France died and his successor was Louis of Orleans, who became Louis XII. The new King of France laid claim to the Dukedom of Milan, and Ludovico again tried to form an alliance against him. But the years of juggling enemy against enemy and friend against friend were now coming to an end. No one trusted Il Moro any more, and suddenly he realized that he was to be alone in this new fight. After nearly twenty years of power sustained by powerful alliances, Ludovico was forced to turn to his own people of Lombardy. Frantically he tried to correct the injustices of years. The people had been cruelly taxed to support the extravagances of the Sforza court, and, in addition, they had been badly treated by petty government officials. Ludovico now sought to repay the past miseries of his people and to rally them to his support. In such a spirit he remembered his court painter, Leonardo da Vinci, and gave him a vineyard and considerable piece of land not far from the Porta Vercellina.

Now, for the first time in his life, Leonardo knew financial security. With the income from the vineyard, and in the peace of his estate, he was left free to follow his own researches. He took no notice that his “peace” was surrounded by the threat of war. Indeed, he remained aloof from politics and court intrigues as much as was possible for a man living in the midst of such chaotic times.

Leonardo now had the opportunity to follow up an early interest—the study of plants. He made many beautiful drawings; no plant was too small to catch his eye. His notes on botany began to grow. With his genius for observation and analysis of nature, Leonardo made some extraordinary discoveries of botanical laws entirely unknown before his time. He wrote of the phenomenon of heliotropism, or the movement of plants toward or away from the sunlight. In addition, he described the phenomenon known as geotropism, or the growth of plants according to gravitational law, as for example, roots growing downward and shoots growing upward. He also defined the laws of phyllotaxis, which describe the system or order of leaf arrangement on a plant’s stem. That is, leaves are arranged spirally around a stem so that the third leaf above grows out over the third leaf below on one type of plant; or, on another type, the two third leaves are over the two third leaves below. The same natural laws apply to the branches of plants as well; they occur so that every leaf and branch can receive sufficient air and light. Amazingly enough, these laws, which Leonardo described so completely, were not rediscovered until almost two centuries later!

Leonardo went even further in his botanical studies. He experimented with gourds, planting them in various aqueous solutions; this anticipated modern methods of growing plants in chemicals. He also tested the actions of arsenic and mercury poisons in plants. He reproduced the shape and form of leaves by pressing them on paper coated with lampblack, a method that was not used again until the nineteenth century. Carefully noted, too, in his writings was the rising of sap from the roots to the branches by capillary action; this, too, was not rediscovered until much later—in the eighteenth century. Leonardo also extracted oils and essences from flowers and studied the influences of altitude on the development of vegetation. Indeed Leonardo’s very approaches to a systematic classification of plants were the forerunners of modern methods of classifying.

In the seclusion of his own home, as he continued his studies of geometry with Pacioli, Leonardo again turned to his observations of the heavens. On the roof of his house he had set up a small observatory for watching the sky at night. Often he looked at the stars through a pinhole in a sheet of paper. Leonardo did this to stop the “twinkling” of the stars which he recognized as an optical illusion. Moreover, by looking at the stars in this manner, he noticed that some were larger than others, and imagined to himself how our own earth might look from them. Would we not be but another “star” in a vast collection of stars? And if that were true—how could the earth be the center of the universe? By the same imaginary reasoning, he speculated on how we must look to someone on the moon. Realizing that the moonlight on earth faintly illuminates the dark side of the earth, he reasoned that then there must be an “earthlight” doing the same on the moon. Thus he was the first to explain the dim reflected light on the dark side of the moon. Moreover, Leonardo is known to have looked at the moon through a convex lens, and perhaps even a form of telescope. Indeed, he had built telescopic-type tubes with lenses in them and had written directions for their use. It seems certain that at about this time Leonardo became convinced of the heliocentric theory, the theory that states the sun is the center of our universe. On a sheet of mathematical notes Leonardo wrote in large letters, “the sun does not move.”

During this time he continued to seek out books on astronomy. Leonardo was familiar with Aristotle’s Meteorology, Archimedes’ On the Center of Gravity, and with Problems in Aristotle’s Books of the Sky and the World, a work by Albert of Saxony. This last book Leonardo had to read with the help of a Latin dictionary, because his Latin was not good. He had already read Plutarch, who had defined the moon as a solid. Plutarch had written further that the “spots” on the moon were the result of shadows cast by irregularities on its surface. This theory, that was apparently abandoned during the Middle Ages, supported the conclusions that Leonardo had reached by his own observations. But he still struggled against a mistaken idea of his own. For a long while he maintained that there were seas and waters upon the moon which accounted for the sunlight being reflected so brilliantly.

Meanwhile, in July of 1499, the French army had reached Lombardy. Ludovico was now in a state of desperation. He tried to appeal to the people of Milan, explaining that their heavy taxes had been due to the constant threats from abroad. But, however hard he tried to arouse their sense of loyalty to him, the public of Milan turned a deaf ear. They had not forgotten how Ludovico had allied himself with Charles VIII—a foreign king! Ludovico now had to put his trust in his army commander, Galeazzo da Sanseverino, despite warnings that this was a man of doubtful loyalty. Moreover, to make matters worse, Louis XII had succeeded in forming an alliance against Ludovico; and, among his allies was a powerful cardinal, son of Pope Alexander VI—the notorious Cesare Borgia.

From a note on a page of designs for supplying and heating a bath we know that Leonardo continued his quiet life, only vaguely disturbed by the political upheaval taking place around him. His note reads, “On the first day of August 1499 I wrote here of movement and weight.” He had made many experiments and calculations concerning the movement and weight of objects. He had drawn, for example, the flight of an arrow to describe motion through air and although he wrote no specific formula, he marked the three stages of its trajectory—the initial push, the slowing and the steeper downward path as the arrow’s momentum was overcome by the resistance of the air. He also defined the law of movement on an inclined plane and he arrived at the root principle of Newton’s law of gravitation when he wrote, “every weight tends to fall toward the center by the shortest way.”

A diagram of this period is probably the first scientific graph. Leonardo had experimented with two balls dropped from a height. First he dropped them together and then one after the other. In attempting to solve the mathematical problems presented by these falling bodies he drew a graph of vertical and horizontal lines. The times it took for the balls to fall were marked on the horizontal lines and the distances on the vertical lines—thus, he could trace their relationship.

But this peaceful time of productive work was running out for Leonardo. Ludovico’s commander, Galeazzo, had yielded the fortress of Alessandria to the French at the first battle. Ludovico himself had sent his sons and his treasure to his brother, Cardinal Ascanio, in Germany. When he saw that his cause was lost, he turned the Sforza castle over to Bernardino da Corte, a trusted commander, making certain that it was fully supplied with arms and food. Then in sorrow, Ludovico Sforza, Duke of Milan, left his city for the last time as ruler of Lombardy. The gates of Milan were opened to the French in October of 1499, and Bernardino da Corte surrendered the Sforza castle.

French soldiers now occupied Milan as conquerors and the people of the city were in a state of confusion. Those who could made their peace with the French; but others, who had been supporters of Ludovico, fled to avoid arrest. Leonardo, who would be suspect to the French, packed up his few possessions—although he did manage to retain his estate—and left, together with Pacioli and an apprentice, for Mantua.

Leonardo had to flee Milan.

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