60 MOLECULAR AND ATOMIC ENERGY 141 



If now a gas which possesses q degrees of freedom is heated 

 just as much, each of the q degrees of freedom will require 

 a corresponding share of heat, and therefore / 



heat -units are necessary for the heating at constant volume, 

 if we have to consider only translatory kinetic energy. If, 

 besides, there is other energy in question, a further amount 

 of heat 



/ 



is needed, whereja is a constant. The whole heat, therefore, > 

 required for heating at constant volume is 



J(q -f h$W; 

 on the contrary, for heating at constant pressure the heat 



is needed. The specific heats, therefore, must be in the ratio 



C _ q + hq + 2 _ ^ 2 



c " q + &q q(l + h)' 



where h is a constant and q the number of degrees of 

 freedom and therefore an integer, the value of which is the-^ 

 greater the more atoms there are in a molecule. 



Before this formula can be tested by experiment, the , 

 mode of dependence of q on the number of atoms n must f 

 be determined. In most cases, since the degree of movable- \ 

 ness of the atoms is in general unknown, this can only be\ 

 done by the aid of hypotheses; and for several cases suchj 

 necessary hypotheses have been made. 



Of these we shall here pursue those which Boltzmann 

 has investigated. For monatomic molecules q = 3, and, since 



If the molecules consist each of two atoms, Boltzmann 

 puts q = 5, since he assumes that the atoms do not alter 

 their distance apart, but are bound fast together ; the 

 position of a molecule is then completely given by the 



