machine. If the problems here presenting themselves be treated separately, those of the three former studies being supposed to be solved, they form a province of investigation which can be worked in by means of Applied Mathematics and Mechanics. The systematised study of the solutions of these problems forms the science with which we have to do, Kinematics, the "Science of Pure Mechanism."[1] It is, as follows from what we have said, the study of those arrangements of the machine by which the mutual motions of its parts, considered as changes of position, are determined.
The difference between this definition of Kinematics and that which Ampère indicated rather than gave fully (see Introduction, p. 11) requires to be noticed. It is principally this, that here Kinematics is made to belong essentially not to Mechanics, as with Ampère, but to the Science of Machines, as has been done more or less, but without any distinct admission of it, by most of Ampère's followers. Its objects and methods subordinate themselves therefore to the chief laws which affect the machinal as distinguished from the kosmical, and must at the same time fit in with the methods of treatment received by the machine in the three different studies already described. So far, that is to say, Kinematics is not an absolutely isolated science, as it would be under Ampère's definition, but works in consciousness of the neighbourhood of other systems of investigation having a common object with it. On the other hand we have in our own way arrived at the same conclusion with Ampère, that Kinematics observes changes of position only. Only we do not thereby shut out the actions of forces, as Ampère does; we take the problems connected with them as solved in every case, and consider the conditions imposed by them, which is a real and important difference. The indistinctness remaining with Ampère upon this point has been the cause of the unavoidable introduction by his followers of fragments of three other studies, with which they could not dispense: thus, for example, Haton gives an abstract of the strength of materials, Laboulaye this and the study of friction also, and so on.[2]
