Mr. R. F. Muirhead on the Laws of Motion. 479 



The above statement includes all in the First and Second 

 Laws of Newton that can conceivably be tested by experiment or 

 observation. 



We observe that Newton's Third Law appears classed 

 along with other laws of physics, and along with that of the 

 Indestructibility of Matter, which must be assumed as a 

 preliminary to the ordinary statement of Dynamical Laws 

 before the measurement of matter has received its definition. 



In our statement of the fundamental principle of Dynamics, 

 neither of these Laws is assumed, and it could be modified so 

 as to be equally definite and intelligible were they untrue. 



By dealing with infinitesimal particles, we have avoided 

 the necessity of assuming a priori the existence of mass- 

 centres ; for on the supposition that the angular motion of no 

 element is infinite (or, more generally, that there is no finite 

 relative acceleration or velocity between the parts of any 

 particle), the motion of any point of a particle might betaken 

 to represent the motion of that particle. 



To define the expression force acting on a body, used in 

 Dynamics, we would require simply to define the centre of 



mass by the usual analytical equations of the type x=-^ — , 



where the summation extends over all the particles of the body, 

 and then to define the mass of the body by 2m, and the force 

 on the body as that acting on its whole mass supposed con- 

 centrated at its centre of mass. 



What would be the meaning of " a force acting on a body 

 at a certain point "" ? This expression is appropriate only to 

 rigid bodies, or at least to such as retain their shape unaltered 

 while under consideration. The meaning would be that this 

 force, acting on the particle at the point referred to, together 

 with the forces between particles determined by the kinema- 

 tical conditions of rigidity, are the actual forces on the body. 



One objection might be raised to the fundamental Law of 

 Dynamics, as above stated by us ; it seems awkward to imply 

 a knowledge of the whole of physical science in stating that 

 fundamental principle. 



This objection leads us to cast aside Prof. James Thomson's 

 type of statement, and to adopt another, which states exactly 

 the same thought in a different form. We shall propound as 

 preliminary a science of Abstract Dynamics, which shall be a 

 pure science to the same extent as Kinematics is a pure science. 



It is as follows : — 



In a dynamical system, each particle is credited with a certain 

 mass, and by coordinates with reference to a system of coordinate 

 axes its position and motion are determined. When a particle 



