OF ENEHGY IN A SYSTEM OF MATERIAL POINTS. 727 



and therefore in respect of temperature. Hence by (/3) the temperature of every 

 part of the system must be the same. 



Therefore if equations (45) and (51) are satisfied, the condition of equality 

 of temperature is also satisfied. 



But the condition of equality of temperature does not depend on the 

 configuration of the system, for though we can alter the configuration by external 

 constraint we cannot prevent the temperature from becoming equalized. It does 

 not depend, therefore, on equation (45). We must therefore conclude, that if 

 equation (51) is satisfied, the condition of equality of temperature is also satisfied, 

 or, in other words, that equation (51) is the condition of equality of temperature. 



Hence when two parts of a system have the same temperature, the average 

 kinetic energy corresponding to any one of the variables belonging to these 

 parts must be the same. 



If the system is a gas or a mixture of gases not acted on by external 

 forces, the theorem that the average kinetic energy of a single molecule is the 

 same for molecules of different gases is not sufficient to establish the condition 

 of equilibrium of temperature between gases of different kinds such as oxygen 

 and nitrogen, because when the gases are mixed we have no means of ascer- 

 taining the temperature of the oxygen or of the nitrogen separately. We can 

 only ascertain the temperature of the mixture by putting a thermometer into it. 



We cannot legitimately assert that the temperatures of the oxygen and 

 of the nitrogen must be equal because they are in contact with each other, 

 for the only way in which we can conceive the oxygen or the nitrogen as 

 existing in the mixture is by picturing the medium as a system of molecules, 

 and as soon as we begin to see the molecules distinctly, heat becomes resolved 

 into motion. 



But since our investigation is equally applicable to a system of any kind, 

 provided only it satisfies the equations of dynamics, we may suppose it to 

 consist- of pure oxygen and pure nitrogen separated by a solid diaphragm, 

 the solid diaphragm consisting of molecules capable of motion, but acting on 

 each other with forces which are sufficient to prevent any molecule from getting 

 far apart from its neighbours except under the action of disturbing forces 

 greater than any which would occur in a system at the given temperature. 

 In this system, though the oxygen and the nitrogen cannot mix, each can make 



