BOtmUlW'i tmOHKM ON THE AVKEAOE DISTRIBUTION 



with the surface molecules of the diaphragm, 



MM f 1*~BT can go on within the solid diaphragm itself without 

 wage of tm4r'* between distant parts of the diaphragm. 

 Hence in this system, the average kinetic energy of a molecule of oxygen 

 will become equal to that of a molecule of nitrogen in the final state of the 

 k ^m if to say, when the temperatures of all parts of the system have 

 me equal, and since in that final state we have pure oxygen on one side 

 and pure nitrogen on the other, we can verify the equality of temperature by 

 mqiflt* of a thermometer, and we can now assert that the temperatures, not 

 only of oxygen and nitrogen, but of all bodies, are equal when the average 

 kinetic energy of a single molecule of each of these substances is the same. 



Approximate value of the probability when V is small compared with E. 



To find the number of systems the configuration of which is specified as 

 regards the limits of certain of the variables while the other variables are left 

 undetermined, we should have to integrate the expressions in equations (41), 

 (45), or (47) with respect to each of the undetermined variables in succession, 

 the integrations being extended to all values of these variables which are 

 consistent with the equation of energy. 



These integrations cannot be performed unless the potential energy of the 

 system is a known function of the variables which determine its configuration. 

 We cannot therefore in general continue the integration so as to determine 

 the number of systems in which the limits are specified for some, but not all, 

 of the variables. 



But when the number of variables is very great, and when the potential 

 energy of the specified configuration is very small compared with the total 



energy of the system, we may obtain a useful approximation to the value of 



-i 

 ' K- FJ~ in an exponential form, for if we write, as in equation (53), E nK, 



[J0-F] 

 nearly, provided n is very great and V is small compared with E. The 



- _r 



'"* (56), 



