It must be admitted, too, that the sense of the reality of this separation has been felt not only by Engineers or others actually engaged in machine design, but also by those theoretical writers who have had any practical knowledge of machinery, in spite of the increasing tendency in the treatment of mechanical science to thin away machine-problems into those of pure mechanics.
There are good reasons for this feeling. Such a treatment of machine-problems is first of all greatly to be deprecated because it would place the scientific part of machine-construction upon a base too indefinite and widely extended. The fundamental notions of force and motion themselves are subject to uncertain interpretation. In the attempt to define ideas standing on the boundary line between Physics and Metaphysics an uncertainty which demands the closest mathematical and philosophical investigation makes itself felt. This uncertainty or indistinctness, by holding open a perspective of ideas entirely beyond all purpose of the study concerned, exercises a disturbing influence on it. It affects every definition, every explanation intended to be exhaustive; it compels the teacher who desires to express himself with scientific accuracy either to use generalisations of which he feels the unpractical nature, or to employ illogical limitations such as "common practice," "usual arrangements," and so on. He who knows laws only is fain to content himself with rules where he would far sooner employ strict scientific methods. Not every generalisation, that is to say, is practical, nor from a certain point of view indeed, even correct. This point of view is that from which Geometry separates itself from Mathematics in general, Descriptive Geometry from Geometry in general, still more from which Kosmical Physics, Hydraulics, Aerostatics, branch away from Natural Philosophy,—in other words, the point of view from which special sciences are seen to separate themselves from the more general sciences to which they are subordinate.
Such a separation becomes at once possible and advisable if any complete circle of ideas lie at the base of the region separated. In the case of machine-problems their separation from those of general Mechanics can be demonstrated. A distinct line of demarcation, although in certain examples less distinct than in others, shows itself between them. To find the real nature of this difference let us endeavour to look at the whole question from outside,
