Hypotheses of Dynamics. 235 



we are told what are the axes by reference to which it does 

 hold*. 



Much may of course be derived from the first and second 

 laws without specification of axes. The whole science of 

 dynamics bears witness to that fact. But, as Streintz has 

 shown in the work referred to above, much practical incon- 

 venience and much unnecessary complication have arisen from 

 the employment of these laws in their vague form ; and I shall 

 have occasion to refer below to one paradox, the absoluteness 

 of rotation notwithstanding the relativity of motion, which 

 receives its solution when the relativity of these laws is 

 recognized. 



The specification of axes by reference to which the first 

 and second laws hold, or of what may be called dynamical 

 reference systems, is thus no mere refinement of the pedantic 

 mathematical mind. On the contrary, it satisfies a felt want. 

 The want is not felt indeed in dealing with the simple 

 problems of the common school. For the rough experiments 

 which are usually cited in elementary text-books as suggesting 

 the laws show that it is by reference to axes fixed in the earth 

 that they are supposed to hold ; and this tacit specification is 

 quite sufficient for the discussion, e. g., of the inclined plane 

 and 'the wheel and axle. But when we come to treat the 

 problems of theoretical Astronomy, it is at once obvious that 

 we cannot assume the laws to hold with respect to these axes; 

 and the question forces itself upon the attention : What are 

 the axes by reference to which they must now be considered 

 to hold ? And the question having been raised must be 

 answered. The critical student who has seen in his study of 

 kinematics that velocity and acceleration are relative con- 

 ceptions, will not be convinced by Prof. Lodge's ''opprobrious 

 or perhaps complimentary epithets " that they lose their 

 relativity when applied to the motion of bodies. 



Turning now to the second criticism, it is obvious that to 

 one who thinks it is proposed to specify axes by means of which 

 the magnitudes and directions of velocities may be described 

 absolutely (p. 8), the difficulties in the way must appear 



* Should Prof. Lodge, therefore, endeavour to crush a doubter of the 

 first law, as he tells us he would, by saying to him : — "If the speed and 

 direction of a freely moving body vary they must vary in some definite 

 manner; very well, tell me in what manner they are varying. You 

 cannot, unless you can show me absolutely fixed lines of reference,"'— the 

 doubter need be at no loss for a reply. He has but to say : — If you will 

 kindly tell me what are the axes by reference to which you hold the 

 velocity of the body to be uniform, I will then tell you how I suppose it 

 to vary. But unless we agree upon axes of reference it is impossible for 

 us to compare our respective axioms. 



I R2 



