At the beginning of his course of lectures each session, Professor Thomson read, or rather attempted to read, an introductory address on the scope and methods of physical science, which he had prepared for his first session in 1846. It set forth the fact that in science there were two stages of progress--a natural history stage and a natural philosophy stage. In the first the discoverer or teacher is occupied with the collection of facts, and their arrangement in classes according to their nature; in the second he is concerned with the relations of facts already discovered and classified, and endeavours to bring them within the scope of general principles or causes. Once the philosophical stage is reached, its methods and results are connected and enlarged by continued research after facts, controlled and directed by the conclusions of general theory. Thus the method is at first purely inductive, but becomes in the second stage both inductive and deductive; the general theory predicts by its deductions, and the verification of these by experiment and observation give a validity to the theory which no mere induction could afford. These stages of scientific investigation are well illustrated by the laws of Kepler arrived at by mere comparison of the motions of the planets, and the deduction of these laws, with the remarkable correction of the third law, given by the theory of universal gravitation. The prediction of the existence and place of the planet Neptune from the perturbations of Uranus is an excellent example of the predictive quality of a true philosophical theory. The lecture then proceeded to state the province of dynamics, to define its different parts, and to insist on the importance of kinematics, which was described as a purely geometrical subject, the geometry of motion, considerations from which entered into every dynamical problem. This distinction between dynamical and kinematical considerations--between those in which force is concerned and those into which enter only the idea of displacement in space and in time--is emphasised in Thomson and Tait's _Natural Philosophy_, which commences with a long chapter devoted entirely to kinematics.