Kinttic Theory of Gas. 369 



The importance and value of these results depend : — 



1. On the small volume and the short time, as estimated by 

 what are involved in human experiments, which suffice for 

 the requisite averages — since each cube of a micron (the 

 thousandth part of a millimetre) in the volume of the gas 

 contains about 1000 millions of molecules * if it be under 

 the same pressure and temperature as atmospheric air, and 

 each of these molecules meets with about seven million 

 encounters within the thousandth part of one second. 



2. They also depend on the principle recited above, viz. — 

 that if the data of a dynamical theorem be slightly altered, the 

 conclusions are only disturbed to a small extent, 



3. And they depend on the circumstance that the forces to 

 be taken account of in applying the theorem may be confined 

 to such forces as are concerned in those events which either 

 directly or indirectly influence the motions of molecules in 

 their journeys between their encounters. If, accordingly, 

 there be any events of the kind which we have termed Be 

 events, they and the forces concerned in them may be kept 

 outside the theorem, and may exist and involve any amount 

 of energy ; which energy is, however, additional to that which 

 in the theorem is regarded as the total energy, which is to bo 

 understood as the total of the energy of the events with which 

 the theorem is concerned. 



The following mechanical illustration, which is that usually 

 employed, will enable us better to grasp the meaning and 

 appreciate the value of these remarks. In it I will suppose 

 the gas to be of one kind, with molecules that are all alike, 

 and that the number of molecules and the average duration 

 of a journey are what they are in atmospheric air at the sur- 

 face of the earth. 



The simplest way of fulfilling the condition that the ex- 

 pression for the energy shall be a sum of squares, is to pro- 

 vide a mechanical model in wbich the whole energy is kinetic ; 

 and the simplest way of securing this is to suppose each mole- 

 cule to be a rigid elastic body, with a frictionless surface. 

 The expression for the energy of the molecule will then take 

 the familiar form : 



T=i[M(w 2 + ^ + ^)+Aft) 1 2 + Bft) 2 2 H-Co> 3 2 ], 



where the letters have their usual meanings. Here each term 

 in the expression corresponds to one of the six degrees of 

 freedom of the rigid body, and the theorem states that the 



* See Phil. Mag. for August 1868, p. 141. 

 Phil Mag. S. 5. Vol. 40. No. 245. Oct. 1895. 2 C 



