205. IN the preceding chapter we considered as a subject of pure geometry the motion of points, lines, surfaces, and volumes, whether taking place with or without change of dimensions and form; and the results we there arrived at are of course altogether independent of the idea of matter, and of the forces which matter exerts. We have heretofore assumed the existence merely of motion, distortion, etc.; we now come to the consideration, not of how we might consider such motions, etc., to be produced, but of the actual causes which in the material world do produce them. The axioms of the present chapter must therefore be considered to be due to actual experience, in the shape either of observation or experiment. How this experience is to be obtained will form the subject of a subsequent chapter.

206. We cannot do better, at all events in commencing, than follow Newton somewhat closely. Indeed the introduction to the Principia contains in a most lucid form the general foundations of Dynamics. The Definitiones and Axiomata sive Leges Motûs, there laid down, require only a few amplifications and additional illustrations, suggested by subsequent developments, to suit them to the present state of science, and to make a much better introduction to dynamics than we find in even some of the best modern treatises.

207. We cannot, of course, give a definition of Matter which will satisfy the metaphysician, but the naturalist may be content to know matter as that which can be perceived by the senses, or as that which can be acted upon by, or can exert, force. The latter, and indeed the former also, of these definitions involves the idea of Force, which, in point of fact, is a direct object of sense; probably of all our senses, and certainly of the “muscular sense.” To our chapter on Properties of Matter we must refer for further discussion of the question, What is matter ? And we shall then be in a position to discuss the question of the subjectivity of Force.