Hypotheses of Dynamics. 243 



curved relatively to a dynamical reference system ; but we 

 have no means of making any assertion as to the absolute 

 motion of the particle. The rotation of a body about an axis 

 may be regarded as the motion of its particles in circles about 

 that axis. If, therefore, we observe any body which from oar 

 point of view seems to rotate about an axis, and if we are able 

 to recognize the non-action of centripetal forces on its particles, 

 we may assert that, relatively to a dynamical reference system, 

 the body is not rotating about this axis ; while if we can 

 recognize and measure the centripetal forces, we may be able 

 to assert that relatively to such a system it is rotating about 

 this axis. But we can make no statement about its absolute 

 rotation*. 



It follows that the experimental tests which Streintz pro- 

 poses to apply to his fundamental body would enable him to 

 select a body which was not rotating relatively to a dynamical 

 reference system, but would not enable him to select one 

 which was absolutely without rotation |. 



(2) The Independence of the First Law of Motion. 



Prof. Lodge agrees with me in holding the first law to be 

 a particular case of the second, but imagines that, for reasons 

 I need not quote, I will not seriously adhere to the view that 

 the first law gives us no more useful definition of time than 

 the second. I do, however, seriously adhere to it, for the 

 obvious reason that, if the first law be a particular case of the 

 second, we must be able to obtain from the second all that we 

 can obtain from the first. I quite admit, of course, that for 

 educational purposes it is desirable to give separate enunciation 



* The application to the old problem of the rotation of the earth is 

 obvious. By reference to axes fixed in the earth, the fixed stars rotate 

 about the earth's polar axis, while by reference to axes fixed relatively to 

 the stars, it is the earth which rotates. Which is the real motion ? Both 

 motions are real, as real as any motions can be. But Foucault's, and 

 other similar experiments, are held to show that it is the earth which 

 is really rotating. According to the above they do not prove this ; but they 

 do prove that relatively to a dynamical reference system it is the earth 

 and not the system of fixed stars which is rotating. Motion when spe- 

 cified relatively to such a system is no more real than when specified other- 

 wise. But when it is specified in this way, we find that we are able to 

 represent our dynamical experience by means of simpler formulas than 

 when we specify it otherwise. And thus we come to regard motion 

 specified in this way as being real. 



t On absolute rotation, see Prof. J. Thomson (Proc. R. S. E. vol. xii. 

 p. 577), Prof. Mach (Die Mechanik, p. 216), L. Lange (Bewegimgs- 

 begriff, p. 64), Muirhead {Joe, cit. p. 475), and Prof. K. Pearson (Grammar 

 of Science, Appendix, note 1). 



