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



is accelerated, it is said to have a force acting upon it in the 

 direction of the acceleration and of magnitude proportional to 

 the acceleration and mass conjointly. 



The system of chronometry is arbitrary, as well as the 

 system of coordinate axes. 



The expressions, mass of a body, centre of mass of a body, 

 force on a body, and force acting on a body at a point, are 

 defined in the same way as before. 



This forms the subject of " Abstract Dynamics/ 5 which deals 

 only with mental conceptions, and which is a sort of Kine- 

 matics, but Kinematics enriched by the conceptions of force 

 and mass. 



This being premised, then, in place of Newton's Definitions 

 and his First and Second Laws of Motion, we have the 

 Physical Law or Theory that we can so choose the masses to be 

 assigned to our material particles, our coordinate axes, and our 

 system of chronometry, that the forces may be resolved by the 

 parallelogram of forces into such as are expressed by our 

 Physical Laws. 



Perhaps we should keep more faithfully to the historical 

 conception of Dynamics were we to state our Law of Experi- 

 mental Dynamics as follows : — 



Lt is possible to choose the masses of the solar system, the 

 axis, and the chronometry, so that the masses shall correspond 

 with those of Astronomy, and the forces shall be resolvable into 

 such as will be expressed by the Law of Universal Gravitation, 

 and conformable to Newton's *6rd Law of Motion and to the 

 Law of the Indestructibility of Matter (Conservation of Mass). 



Then true time, absolute velocity, and mass-measurement 

 being defined from this system, there would be the further Law 

 of Physics, that the forces on the various particles composing 

 the different members of the solar system and others are expres- 

 sible by our various Physical Laws or Theories. 



We have now arrived at the conclusion that the attempt to 

 state the Laws of Motion by means of a set of detached defini- 

 tions and axioms is futile. We have found that Newton's 

 First Law of Motion cannot be stated until we have the con- 

 ception of a certain system of reference, whose definition 

 involves the knowledge of the First Law, as well as the defini- 

 tion of force, &c. We have therefore seen that the Experi- 

 mental Principle of Dynamics should be stated as an organic 

 theory or hypothesis. We have found it convenient to 

 formulate a science of Abstract Dynamics, which is an ex- 

 tended Kinematics, depending only on space and time-measure- 

 ments, but including the ideas of force and mass (abstract). 



By means of this we can state in a succinct form the 



