92 MASS AND FORCE. [CHAP. V. 



83. Impulsive motion of a body. The motion of a body 

 whose particles are subject to impulses is determined from the 

 motion of a particle at its centre of inertia in the same way as 

 when it is subject to forces. Thus the changes of momentum 

 produced in two bodies by their impulsive mutual action are equal 

 and opposite, or the changes of velocity produced in them are 

 inversely as their masses. 



84. Rational Mechanics. The system of definitions and 

 rules which we have laid down lead to a system of differential 

 equations for determining the motions, relative to a frame, of a 

 system of particles, or of a body or a system of bodies, conceived to 

 be made up of particles. It may be regarded as a purely ideal 

 system, and its validity is unaffected by the question whether it 

 has or has not any relation to the observed motions of natural 

 bodies. The subject, so treated, is known as Rational Mechanics. 

 The objects of which it treats are pure objects of thought. Its 

 development consists in the logical deduction of particular results 

 from the general principles laid down. 



85. Mechanics of Natural Bodies. The application of 

 Rational Mechanics to the formulation of the Laws that govern 

 the motions of natural bodies consists in the statement that it is 

 possible to assign masses to the bodies and to choose a frame of 

 reference determined by parts of natural bodies, such that the 

 observed motions of natural bodies, relative to the frame, obey the 

 Laws of Rational Mechanics within certain limits of exactness ; 

 that in fact the observed motions coincide with the motions 

 described in the phraseology of Rational Mechanics so closely that 

 no discrepancy can be observed. 



There are motions, e.g. the phenomena of diffusion, which 

 cannot easily be brought under the above statement. A mechan- 

 ical theory of such phenomena, like that of any other phenomenon, 

 is a statement concerning bodies, as conceived in Rational 

 Mechanics, which will move as the natural bodies are observed to 

 move. 



86. Mutual Action. Natural bodies act on each other in 

 various ways. The sun warms a stone, rain wets a coat, buffers 

 stop a train. Among these actions many are clearly actions in 



