478 Mr. R. F. Muirhead on the Laws of Motion. 



" force acting on that body " the words " rate of change of 

 motion of that body," and for the words " direction of force " 

 the words " direction of change of motion/' And we cannot 

 entertain any other measure of force, for reasons which will 

 be adduced later on. 



Again, Prof. Thomson, by not restricting his statement 

 to infinitesimal particles, has to assume the existence of 

 mass-centres. How is a mass-centre to be defined ? We 

 shall give reasons later for rejecting any but a kinetic defini- 

 tion of mass and mass-centre. But it is impossible to arrive 

 at a kinetic definition when we start by assuming a know- 

 ledge of the measurement of mass in the Fundamental Law 

 of Motion, as is done by Professor Thomson. 



While noting therefore that Professor Thomson has adopted 

 the right method of defining chronometry and " true rest," 

 we cannot accept his Law as a satisfactory statement of the 

 fundamental principle of Dynamical science. 



Let us endeavour to frame, after the manner of Professor 

 Thomson, a statement which shall be satisfactory. Taking 

 the definitions of dial-traveller and reference-frame, as given 

 in the paper referred to, let us proceed thus : — 



Let a material system be conceived divided into an infinite 

 number of particles whose greatest linear dimensions are all 

 infinitesimal. To each particle let us attribute a certain value 

 called its provisional-mass. Let us adopt a reference-frame 

 and dial-traveller. Let the acceleration of any particle multi- 

 plied into its provisional- mass be called the apparent-force on 

 the particle. Then it is possible so to choose the provisional- 

 masses, the dial-traveller, and the reference-frame, so that the 

 provisional-masses and the apparent-forces shall, within the 

 limits of error of observation, have relations expressible by 

 the laws of physical science, i. e. the law of the Indestructi- 

 bility of Matter, the law of Equality of Action and Reac- 

 tion the law of Universal Gravitation, the laws of electric, 

 magnetic, elastic, and capillary action, &c, &c. Such a 

 system being chosen, the provisional-masses in it are masses 

 and the apparent-forces, forces. The dial-traveller indicates 

 " absolute time," and the reference-frame is absolutely without 

 rotation or acceleration. 



We have thus kinetic definitions of force, mass, absolute 

 time-measurement, and of absolute rest so far as that is possible. 



It is evident kinematically that any other reference-frame 

 which has no rotation or acceleration relatively to one chosen 

 as above would lead to exactly the same results ; and that 

 this would not be the case if any reference-frame not fulfilling 

 this condition were chosen. 



