4 The Kinetic Theory conception of Matter [OH. I 



Of the three states of matter which have just been sketched, the 

 mathematical development of the Kinetic Theory is at present concerned only 

 with the last. A properly developed Kinetic Theory of liquids and solids 

 is still wanting, and throughout the remainder of this book we shall be 

 content to discuss matter in its gaseous state. 



Mechanical Illustration of the Kinetic Theory of Gases. 



6. It is important to form as clear an idea as possible of the conception 

 of a gas which has just been reached. Now very little is known as to the 

 structure or shape of actual molecules, or of the way in which they act upon 

 one another. Since, however, it is advisable to have as concrete a repre- 

 sentation as possible before the mind, we may for the present (following the 

 usual procedure in the development of the Kinetic Theory) agree to 

 associate the idea of a molecule with that of a spherical body of great 

 elasticity and rigidity to make the picture quite definite, let us say a 

 billiard-ball. The justification for this procedure lies in its success : it will 

 be found that the behaviour of a gas in which the molecules are complex 

 structures of the most general kind, can, to a large extent, be predicted 

 from the behaviour of the much simpler ideal gas of which the molecules 

 are of the simple type just described. In fact one of the most striking 

 features of the Kinetic Theory is the way in which we are enabled to 

 predict the behaviour of a gas as a whole while remaining in almost complete 

 ignorance of the behaviour and properties of the molecules of which it is 

 composed. 



7. Before proceeding to exact mathematical analysis, it may be profitable 

 roughly to indicate the questions which are to be- examined, and at the same 

 time to forecast some of the results which will be obtained. This can 

 well be done by taking a mechanical illustration in two dimensions. 



Let us represent the molecules of the gas by billiard-balls, and the vessel 

 in which the gas is enclosed by a large billiard-table. The walls of the 

 vessel are of course represented by the cushions of the table, and if the 

 vessel represented is to be a closed one, there must be no pockets. The 

 materials must be of such good quality that a ball once set in motion will 

 collide thousands of times with the cushions before it is brought to rest 

 by the friction and various other passive forces which tend to destroy 

 its motion. Most of the properties of gases can be illustrated with this 

 imaginary apparatus. 



If we take a very large number of balls and start them at random on 

 the table with random velocities, the resulting state of motion will give a 

 representation of the supposed state of the gas. Every ball will continually 

 be colliding both with the other balls and with the cushions. The velocities 

 of the balls will be of the most varying kinds : at one instant a ball may be 



