The Laws of Dynamics, and their treatment in Text-Books

Extract

Among the defects to be found in the treatment of the elements of Dynamics in many current text-books, the most obvious is the way in which the “laws of motion” are customarily introduced without any clear explanation as to the base, or axes, relative to which the motion is to be reckoned. Attention is very likely called to the fact that any statement about the motion of a body must, if it is to have any meaning, include the specification of a base; but in the statement of the law of inertia we are apt to find all this thrown to the winds, and the reader left to discover for himself, as best he can, what base is meant to be used. If a straightforward explanation can be given on this point, why is such a mystery made of it? A reader, approaching the subject for the first time, is apt to draw the inference that the choice of a base will somehow or other turn out to be immaterial. Statements may be met with which give encouragement to this view. Thus, in some of the text-books, the law of inertia is said to be merely a definition of force (or of both force and time); and this may be put in such a way that it is difficult to escape the conclusion that we are to recognise as forces simply mass-accelerations relative to an arbitrarily chosen base; although the abandonment of the law of action and reaction, which this would imply, is not really intended. It is more common to find Newton’s laws of motion quoted, and illustrated by examples of motion relative to the earth, the question of a base being left vague. It would be a more intelligible course, and possibly better for some purposes, to begin an elementary treatment of the subject with an approximate theory of motion relative to the earth only. In some books we find a complication produced by preliminary remarks as to none but relative motions being knowable, followed by expositions of the knowableness of absolute rotation and fixedness of direction, without either apology or explanation. In most of the text-books the point of view adopted is rather obscure. An exception must be made in favour of Love’s Theoretical Dynamics, which has the merit of being intelligible; but the procedure employed seems to be unduly ponderous and complicated.