140 JAMES CLERK MAXWELL 



of variables defining the position of the molecule is 

 rti + 3, and it is said to have tit -f X decrees of freedom. 

 Hence, in this case, its total energy is (w + 3) K and 

 its energy of translation is 3 K, thus we find 



Hence y = 1+ ; + 3 = 1+ -j; 



if n bo tho number of degrees of freedom of tho 

 molecule. 



Thus, if this Boltzmann-Maxwell theorem bo true, 

 tho specific heat of a gas will depend solely on tho 

 number of degrees of freedom of each of its molecules. 

 For hard rigid bodies we should have ?* equal to 0, 

 and henco 7=T333. Now tho fact that this is not 

 tho value of 7 for any of the known gases is a 

 fundamental difficulty in the way of accepting tho 

 complete theory. 



Boltzmann has called attention to the fact that if 

 n be equal to five, then 7 has the value 1*40. And this 

 agrees fairly with the value found by experiment for 

 air, oxygen, nitrogen, and various other gases. Wo 

 will, however, return to this point shortly. 



There is, perhaps, no result in the domain of 

 physical science in recent years which has been more 

 discussed than the two fundamental theorems of the 

 molecular theory which we owe to Maxwell and to 

 Boltzmann. 



The two results in question are (l)the expression 

 for the number of molecules which at any moment 

 will have a given velocity, and (2) the proposition 



