The Pendulum Swings Again: A Mathematical Reassessment of Galileo's Experiments with Inclined Planes

 After over 300 years of scrutiny, the subject of Galileo continues to be pursued with unabating intensity. Dava Sobel's Galileo's Daughter points to the popular interest in the man and his legacy. The Catholic Church, understandably interested in dispelling the notion that its censure of Galileo centuries ago is proof positive that religious faith and science as well as ecclesiastical authority and free pursuit of scholarship are irreconcilable, continues to offer explanations. New books, articles and conferences probe both in breadth and in depth the magnetic field charged by Galileo, science, and the Church. Galileo's analysis of the physics of motion has also received considerable attention. In particular, a great deal has been written during the past thirty years about the structure and objectives of three experiments with inclined planes. Galileo had carried them out in Padua and recorded them in his working papers. The assessments of the three experiments differ widely in points of detail, but all regard them as sophisticated, ingenious, and remarkable. This article presents a new critical study of these experiments. Its conclusion is that one of the experiments is indeed a success, but that the other two fail and are abandoned because Galileo did not have a firm enough grip on the underlying physical principles and mathematical relationships.