Principles of Dynamics. Ill 



ideas. Absolute Motion is of fundamental importance in 

 theoretical mechanics, Relative Motion is of fundamental 

 importance in experimented science. As a natural conse- 

 quence, a student of applied mathematics, when asked of the 

 nature of " motion/' thinks of Absolute Motion, and replies 

 that " motion is absolute ;" and the physicist when he meets 

 the same question thinks of relative motion, and replies that 

 44 motion is relative/ 3 But there is no difference of opinion 

 between them, only a mutual misunderstanding. An exact 

 analogy can be imagined. The word ** rule " is, for historical 

 reasons, used in two senses, first as a precept, and secondly 

 as an instrument (slide-rule) : and there can be a relation 

 between the two meanings, as in the phrase 4 * the rule for 

 the use of the slide-rule/' Xow suppose two people were 

 asked whether the rule was accurate : one might think that 

 the question concerned the soundness of the instructions 

 given for the use of the instrument, the other might think 

 that it concerned its construction. They might arrive at 

 formally contradictory conclusions, and no amount of argu- 

 ment would settle the controversy, until they began to dispute 

 in Esperanto. 



But another, and much more interesting, question is raised 

 by such a statement as the following (put in very rough and 

 loose language) : — * ; Absolute motion is a mere mathematical 

 abstraction, whereas relative motion is a real thing." Of 

 course, if (as is usually the case) Absolute Motion and Re- 

 lative Motion are meant, the statement is absurd : for both 

 concepts are mathematical quantities, and it' one is "real" 

 so is the other. But I think that anyone who made such a 

 statement would have different, and much more valuable, 

 ideas in his mind: he would mean to point out that, whereas 

 Absolute Motion can be given a meaning only by use of the 

 Fundamental propositions of dynamics, Relative Motion can 

 be given a meaning without employing those propositions 

 and by using only experimental results and relation A. and 

 that the ideas thus involved appear to him much more 

 fundamental and necessary than those of dynamics. . It is, 

 therefore, very interesting to inquire whether, by any means 

 whatsoever, the Absolute Coordinates can be defined inde- 

 pendently of dynamics (t. e. equations (3) and (4)), and by 

 the use of only those concepts which are necessary to define 

 Relative Motion, or of those which are equally necessary*. 



* It would load us much too far to discuss why we regard on« con- 

 ception as more fundamental or necessary than another, or whether 

 there is any justification for the view. But I think almost every 

 physicist would agree in regarding relation A as on a different plane to 

 the relations asserted in equations (•'>) and (4). 



Phil. Mag. S. 6. Vol. 19. No. 109. Jan. 1910. N 



