THE KINETIC THEORY OF MATTER. 135 



experience of statistics of population dealing with large groups of in- 

 dividuals. Whenever the group as a whole shows constant features, we 

 find that it can be subdivided into, smaller groups, also showing constant 

 features, even though the individuals in these groups change; for example, 

 in a large town where the circumstances remain pretty nearly the same, 

 the percentage of the population whose age lies between given limits 

 will remain constant, though fresh individuals are coming into the 

 group and others are moving out of it. Or, to take another illustration 

 more nearly resembling the case of a gas. With similar external circum- 

 stances as to day, hour, and weather, probably a certain fraction of the 

 people in a town will be in the streets on different days, with so many 

 moving at four miles per hour, so many at three miles per hour, so many 

 in collision, stopping to talk to each other. The individuals forming 

 each of these groups will change, but the number in the group is probably 

 nearly constant. 



Similarly, if we consider a sufficient number of molecules, we may 

 assume that a constant number move with a given velocity in a given 

 direction. 



Let us take, for simplicity, a vessel whose interior is cubical and one 

 centimetre each way, and let ABO be three perpendicular faces meeting 

 at an angle. Consider a molecule impinging with velocity V T in a cer- 

 tain direction against the face A of the vessel, and resolve this velocity 

 into three components u v v v w v perpendicular respectively to A, B, and 0. 



Then V x 2 = u^ + v* + 10* 



We shall suppose that the walls of the vessel are perfectly plane and 

 with coefficient of restitution unity, so that a molecule impinging on a 

 side has its velocity perpendicular to that side exactly reversed, while 

 the other components are unaffected. This, as we have seen, is probably 

 not true for individual impacts in some there may be a gain of energy, in 

 others a loss ; but, so long as the gas and wall are at the same temperature, 

 the average energy is the same before and after impact, and the number 

 of molecules moving away with a given velocity is the same as if in each 

 impact the above supposition were true. That this is the right view is 

 shown by considering the case in which it is no longer true, that in 

 which the temperature of the gas differs from that of the wall. Then 

 the energy of the gas is different after impact, and from this difference, 

 as we shall see later, such motions as that of the radiometer can be 

 explained. 



If we take the mass of the molecule as m, it moves up with the 

 velocity u^ perpendicular to the wall, and has this changed to - u v or 

 there is a total change of momentum, 2mu r This, therefore, is the 

 momentum given to the wall by the impact. 



Through the velocity M X the molecule would move to and fro w x times 



per second if there were no collisions, and impinge against A -^ times. 



2i 



Now, though no actual molecule does this, the effect is the same as if it did, 

 for when it has its velocity altered by a collision, some other molecule at the 

 same distance from A takes its place, and moves on with the same velocity, 

 and no appreciable time is, by our supposition, lost by the collisions. In 

 one second then the total momentum imparted to A by one molecule will 



