The success of this entertainment so pleased Ludovico that Leonardo was encouraged to present another amusing idea. This one was an “alarm clock” and it utilized what we call today the mechanical relay principle. When a small power is suddenly switched over, the power is reinforced. The “alarm” clock worked by placing a shallow basin of water at one end of a tubed lever. At the other end was another empty basin. Water was led drop by drop into the second basin and as this slowly filled the increasing weight lowered the lever. The shallow basin of water at the first end was suddenly emptied and the immediate switch in weight flipped the lever up and this in turn pushed up the sleeper’s feet. Leonardo decided to withdraw from the competition for the cathedral dome. Although the cathedral authorities were pleased with his design, they could not decide to whom the commission should be awarded. In the summer of 1490 Ludovico was called upon to settle the issue and he decided in favor of Antonio Amadeo from Milan. But the work that Leonardo had done so impressed Ludovico that he sent him to Pavia in company with an architect from Siena, Francesco di Giorgio Martini, to inspect the work on the cathedral of that city. Leonardo, who had his own workshop and apprentices now, took along one of them, Marco d’Oggionno, a young boy of twenty. In Pavia one of the greatest libraries in all of Italy was in the ducal palace. Here Leonardo wandered among shelves of books and illuminated manuscripts bound in rich velvets and gold-embossed leather all bound to their places with silver chains. One book that he records in his notes was written in the thirteenth century by Witelo, a Polish scholar, who wrote extensively on perspective. Leonardo, by the necessity of his art, had solved many problems in perspective. He had invented a pair of proportional compasses, the forerunners of those used today for the transfer of a drawing from one scale to duplicate the same drawing in a larger scale. Leonardo had also designed in very careful detail a parabolic compass for drawing a parabola in one continuous movement. He now determined to write his own book on perspective and, as the subject was so close to his studies of the eye, he would entitle it _Introduction to Perspective, or the Function of the Eye_. Leonardo submitted a number of plans for the completion of the cathedral to the authorities in Pavia and then returned to Milan. He worked through the rest of the summer on the equestrian statue and at the same time he continued to expand his notes on anatomy, light and shade, and perspective.