Instead of learning the laws of force with plain instruments which a boy of fifteen can easily make, they learn them from mere drawings, in a purely abstract fashion. Instead of making themselves an Atwood’s machine with a broomstick and the wheel of an old clock, or verifying the laws of falling bodies with a key gliding on an inclined string, they are shown a complicated apparatus, and in most cases the teacher himself does not know how to explain to them the principle of the apparatus, and indulges in irrelevant details. And so it goes on from the beginning to the end, with but a few honourable exceptions.[191] If waste of time is characteristic of our methods of teaching science, it is characteristic as well of the methods used for teaching handicraft. We know how years are wasted when a boy serves his apprenticeship in a workshop; but the same reproach can be addressed, to a great extent, to those technical schools which endeavour at once to teach some special handicraft, instead of resorting to the broader and surer methods of systematical teaching. Just as there are in science some notions and methods which are preparatory to the study of all sciences, so there are also some fundamental notions and methods preparatory to the special study of any handicraft. Reuleaux has shown in that delightful book, the _Theoretische Kinematik_, that there is, so to say, a philosophy of all possible machinery. Each machine, however complicated, can be reduced to a few elements--plates, cylinders, discs, cones, and so on--as well as to a few tools--chisels, saws, rollers, hammers, etc.; and, however complicated its movements, they can be decomposed into a few modifications of motion, such as the transformation of circular motion into a rectilinear, and the like, with a number of intermediate links. So also each handicraft can be decomposed into a number of elements. In each trade one must know how to make a plate with parallel surfaces, a cylinder, a disc, a square, and a round hole; how to manage a limited number of tools, all tools being mere modifications of less than a dozen types; and how to transform one kind of motion into another. This is the foundation of all mechanical handicrafts; so that the knowledge of how to make in wood those primary elements, how to manage the chief tools in wood-work, and how to transform various kinds of motion ought to be considered as the very basis for the subsequent teaching of all possible kinds of mechanical handicraft. The pupil who has acquired that skill already knows one good half of all possible trades.