Hypotheses of Dynamics. 239 



left free from the action of force, which do not, however, lie 

 in a straight line, describe any three straight lines intersect- 

 ing in a point (the axes of coordinates for example), the path 

 of any fourth particle free from force will be rectilinear. And 

 relatively to any time-scale, by reference to which one 

 particle free from force will, when its motion is referred to 

 the above axes, move with uniform speed, every other particle 

 free from force will move with uniform speed, if its motion 

 be referred to the same axes. 



It was this method also which I employed in my Address, 

 when I had not yet met with Lange's paper, the conclusion 

 reached being, that the 1st and 2nd laws hold relatively to 

 any particle not acted upon by force, as point of reference, 

 and to lines drawn from it to other particles which are unacted 

 on by force and have the same velocity as the first particle, as 

 axes of reference. I showed also that it followed from this, 

 that in dealing with the ordinary problems of the motion of 

 bodies on the earth's surface, axes fixed in the earth might 

 serve practically as a dynamical reference system*. 



With regard to all such modes of specifying axes as those 

 referred to, Prof. Lodge asks, " How can we utilize as axes the 

 trajectories of particles free from force, without tacitly as- 

 suming the first law continually? " A criticism in the form 

 of a vague question is hard to meet, because indefinite. If 

 the first law is assumed in its own enunciation, when such 

 trajectories are employed in the specification of axes, it should 

 be easy to point out exactly where the assumption seems to 

 be made ; and a definite criticism of that kind might be met 

 at once. But, judging from the context, the question is 

 probably suggested by the mistaken notion, that when such 

 trajectories are employed they must be assumed to be straight 

 lines in absolute space, — a notion which springs directly from 

 the belief that the object of specifying axes is the description of 

 velocities absolutely. The object of specifying axes, however, 

 is not fi to attempt the impossible." And when the trajec- 

 tories of particles free from force are employed as axes, or 

 for the specification of axes, no assumption is made as to their 

 form. Indeed it is recognized that they cannot be said to 

 have any definite form except by reference to other axes ; 

 and that they may be made to take an infinite number 

 of forms by varying the axes by reference to which their 

 forms are specified. And no assumption being made as to 



* I need hardly refer to Prof. Lodge's objection to such statements of 

 the first law on the ground, of their complexity. If intelligibility is 

 consistent with simplicity, well and good. But if not, it is of course the 

 simplicity which must be sacrificed. 



