240 Prof. J. G. MacGreffor on the 



ev 



their form, no assumption of the first law is made in utilizing 

 them. 



We are also asked how we can appeal to the experience of 

 the human race with regard to such axes *. It must be ad- 

 mitted that we cannot make any direct appeal. The only- 

 dynamical axioms which can make such an appeal are axioms 

 applicable within, but not beyond, the narrow range of direct 

 experience. When we pass from the discussion of the motion 

 of bodies on the earth's surface to the motion of bodies in 

 space, we enter a region which is outside our direct experience ; 

 and the human race, if it is interested in such things, must 

 learn that the hypotheses made by philosophers to coordinate 

 dynamical phenomena generally, must be judged solely by 

 the accuracy of the deductions which flow from them. 



Possibly Prof. Lodge is not thinking of the human race 

 generally so much as of the race of young students. And 

 it is at once obvious that such an enunciation of the first law 

 as that suggested, for example, by Lange, is not suitable for 

 use in an elementary text- book or before a class of beginners. 

 But no one has proposed to use it in either case. The object 

 of writers who have sought to solve the problem under con- 

 sideration has been logical, not pedagogical. The beginner 

 deals with simple motions of bodies on the earth's surface. 

 He is led to see from his own experience that, relatively to 

 axes fixed in the earth (the north-south, east- west, and up- 

 down lines, say, at his place of observation), the first and 

 second laws hold for such simple motions. All that is necessary 

 at this stage is to make clear that it is relatively to such axes 

 that in such cases these laws are found to hold. When he 

 reaches such problems as those of theoretical Astronomy, he 

 will see at once that the laws of motion, as first enunciated, 

 are insufficient and that they must be generalized. And by 

 that time he will have learned that axioms are not to be 

 accepted or rejected according as they do or do not appeal 

 directly to his experience, but according as the deductions 

 which flow from them do or do not stand the test of 

 observation. 



Mach's objection f to such modes of specifying axes as 

 those just considered is more to the point. While he admits 

 that the first law may be expressed definitely by means of 

 them, he holds that in using them we only apparently avoid 



* This objection ought surely not to be urged by a writer who holds to 

 the third law of motion as an axiom, and yet tells us that he is constantly 

 meeting with engineers (whose dynamical experience is of course wider 

 than that of most members of the human race) who refuse to admit it. 



t Die Mechanik, p. 484. 



