83-89] POSTULATES CONCERNING MOTION. 93 



which motion of a body relative to a frame is set up, altered, or 

 stopped. Such actions are mechanical. 



We replace in imagination the natural body whose motion is 

 observed to be changing by a body as conceived in Rational 

 Mechanics, and attribute to that body a certain mass, called the 

 mass of the natural body; then, from the observed changes of 

 motion, we can find expressions for the forces that act on the body. 

 The solution of the equations of motion of the body with the 

 attributed mass, under the action of the deduced forces, gives a 

 rule for determining the position of the body at any time. We 

 state that the mass may be so chosen that the observed position 

 coincides with the determined position. 



87. Postulates of Mechanics. The method indicated may 

 be summed up in the following postulates : 



(1) Every body, and every individual part of a body, has 

 a constant mass, and the mass of the body is the sum of the masses 

 of its parts. 



(2) Every body may be conceived as made up of particles 

 (continuously filling the volume within the surface of the body) 

 which act upon one another so as to produce accelerations. 



(3) All changes of motion arise from the mutual actions of 

 the particles of bodies. 



(4) The component accelerations produced in two particles by 

 their mutual action are localised in the line joining the particles, 

 have opposite senses, and are of magnitudes inversely proportional 

 to the masses of the particles. 



(5) In no circumstances do the surfaces of two bodies intersect 

 so as to contain a finite volume, or two bodies never at the same 

 instant occupy the same space. 



88. Frame of reference. The accelerations mentioned in 

 postulates (2) and (4) are, of course, accelerations relative to a 

 frame. It is possible to choose frames for which the postulates 

 apply to natural bodies and also frames for which they do not. 

 This matter will occupy us again in Chapter XIII. 



89. Field of Force. We can seldom discover what com- 

 ponent accelerations, arising from the mutual actions of particles, 



