236 Prof. J. G. MacGregor on the 



insuperable*. They would be in that case the difficulties 

 attending the solution of an inconceivable problem. That the 

 actual problem has only recently been attacked is due not so 

 much to its difficulty as to the fact that the necessity of its 

 solution has been apparent only since the full recognition of 

 the essential relativity of velocity and acceleration, whether 

 uniform or variable. That there are difficulties, however, is 

 obvious from the fact that only some of the methods employed 

 appear to be sound, and that a number of writers have attacked 

 the problem and left it only half solved f . What the difficulties 

 are may be shown best by a sketch of the efforts made to 

 overcome them. 



There would seem to be two legitimate ways of finding 

 dynamical reference systems: — (1) by re-studying the experi- 

 mental results for the deduction of which the laws of motion 

 were enunciated, and re- formulating these laws ; and (2) by 

 assuming that, since the laws of motion in their vague form 

 have been abundantly tested in the hands of men enabled by 

 a kind of dynamical instinct to use them aright, there must 

 be axes by reference to which they hold, and proceeding to 

 determine these axes by the aid of the laws themselves. 



The former method, the historical-critical, is that employed 

 by Prof. Machj:. He points out that Galilei observed the 

 first law to hold, by reference to points fixed in the earth, for 

 motions on the earth's surface of small duration and extent, 

 and that, when Newton came to apply it to bodies moving in 

 space, he generalized it, showing that, so far as could be 

 determined, it held for the motions of the planets by reference 

 to the distant and to all appearance relatively fixed celestial 

 bodies. And he holds that the first law, when referred, so 

 far as space is concerned, to the fixed stars, and, so far as time 

 is concerned, to the earth's rotation, is to be regarded as a 

 sufficient approximation to accuracy for practical purposes, and 

 as forming as close an approximation as it will be possible to 

 obtain until a considerable widening of our experience occurs. 



It seems to me that the historical- critical method might 

 carry us farther than this. For we now know that the 

 so-called fixed stars are not fixed ; and means have been 

 devised of correcting observations made on this assumption. 

 We also know that the laws of motion do not hold when 

 referred to a time-scale determined by the earth's rotation ; 

 and a rough correction has been determined for application 



* The fact that Prof. Lodge regards motion with respect to the aether 

 as absolute motion (p. 30) perhaps renders this statement doubtful. 

 • t Neumann, J. Thomson, and Muirhead. See works cited above. 

 \ Die MecJianik in Hirer Entiuickehmg ; Leipzig, 1889, pp. 217 & 481. 



