HYPOTHESES OF DYNAMICS. 9 



meaning unless the points of reference are known. It becomes obAÙous also that if the 

 points of reference are given, no such law will be unintelligible merely because the 

 points of reference may have velocities rehitivoly to other points. Accordingly if we 

 introduce into Maxwell's argument a specification of the point of reference, where he 

 speaks of velocity simply, using the same point of reference both for Newton's law and 

 for the hypothetical law, the argument becomes manifestly inconsequent. For the second 

 last sentence becomes in that case : For if it is a relative velocity, its direction as well as 

 its magnitude depends on the velocity of the point of reference relative to the point of re- 

 ference ; — and the only conclusion we can draw from this is that as the velocity of a point 

 relative to itself is invariably zero, the velocity referred to in the hypothetical law satisfies 

 the maxim by which Maxwell is testing it. 



We may put the same criticism otherwise by pointing out that one of the elements 

 of the cause whose effect is the change of velocity of the hypothetical law, is the velocity 

 of the point of reference. As therefore, the maxim which Maxwell is applying assumes 

 the cause to be the same at all times and places, this velocity is thus assumed to be every- 

 where and always the same, and must not be taken to be variable as it is in the second 

 last sentence of the argument under consideration. 



I think, therefore, we may conclude that the first law of motiou has not been shown 

 to be capable of deduction from merely kinematical principles. 



As has often been pointed out, however, the first law may be at once deduced from 

 the second law of motion, being merely a particular case of that law ; ' and this being ad- 

 mitted, its enunciation as a distinct hypothesis, however advantageous in introducing 

 young students to dynamical science, must be pronounced illogical. 



There is one objection, however, which may perhaps be urged against the omission 

 of the first law, viz., that Maxwell " and other authorities, following Newton, hold that 

 this law, " by stating under what circumstances the velocity of a moving body remains 

 constant, supplies us with a method of defining equal intervals " of time. As no such 

 statement is ever made about the second law, it would thus appear that the omission of 

 the first would leave us without a basis for the measurement of time. 



This objection, however, is easily met. For, first, the second law supplies us with 

 more methods of defining equal intervals of time than the first law. In addition to the 

 definition given by the latter, it tells us, for example, that those intervals are equal in 

 which a body acted upon by a constant force undergoes equal changes of velocity. 



Second, both laws assume that ecjual intervals of time have already been defined. 

 So far as power of defining is concerned, therefore, they give us nothing that we did not 

 possess before their enunciation. The only advance in time measurement which we owe 

 them is that they show us how to construct time-pieces which will mark off for us the 

 intervals assumed to be equal in their enunciation. 



Third, the intervals assumed equal in the enunciation of these laws are not known 

 to be equal. What they assume is therefore nothing more than a conventional time 

 scale ; and what they give us is nothing more than certain methods of securing accurate 

 copies of this scale. 



' Maxwell's position with regard to the first law, considered above, would thus make it possible to deduce 



from kinematical principles a particular case of an admittedly dynamical law. 



- Matter and Motion, Art. xliii. 



Sec.III, 1892. 2. 



