60 MOLECULAR MOTION AND ITS ENERGY 29 



^ame law as that which was found for the special case of 

 /a simple gas. MaxweJJSj^Jmv of distribution^ is apglic- 

 v able equally to single and mixed gases. There is, therefore, 

 in gaseous mixtures, too, such a~~"clistribution of molecular 

 energy that of all possible values of the kinetic energy a 

 definite value can be assigned which will be found in any 

 given particle more frequently than any other value, 

 whether larger or smaller. The deviations from this most 

 probable value of the molecular energy of motion follow the 

 same law in each kind of molecules that are mixed in the 

 gas.V A definite amount of energy of forward motion occurs, 

 therefore, in a particle of one kind with the same degree of 

 probability as in a particle of another kind. 



From this follows directly a proposition first given by 

 Clausius, that in a mixture of two or more gases the mole- 

 cules of both kinds possess on the average equal kinetic 

 energy ; or, to express this by a formula, if m p m^ are 

 the molecular masses of the two gases, G } , G 2 the mean 

 values of the corresponding speeds as calculated from the 

 values of the energy, then 



2 . 



'2 > 



or, if the arithmetic mean speed O be introduced instead 

 of the magnitude G, 



n 2 



This mathematical proposition possesses an important 

 ^physical meaning, which will be easily understood on re- 

 pealling our former considerations ( 9, 14) regarding the 

 increment of pressure with temperature. We there saw 

 that the kinetic energy of the molecular motion forms 

 the mechanical .measure of temperature. If we further 

 remember that two gases must attain equal temperatures 

 when mixed together, the conclusion follows that the equality 

 of the temperature of two gases consists in equality of the 

 mean energy of the forward motion of their molecules. 



These conclusions cannot be strictly proved without 

 mathematical investigation into molecular mechanics. 

 Still, we can show their probability without mathematical 



