140 MOLECULAR MOTION AND ITS ENERGY 60 



number of ways in which a system of particles is movable. In 

 this method they have been followed by Boltzmann, 1 and 

 then by Koiti, 2 and later also by Violi. 3 It shall be given 

 here on account of its clearness, although very weighty 

 objections must be raised against its admissibility. 



We can assert with regard to a single massive point that 

 it has a threefold freedom of movability, since its motion is 

 determined by the values of the three components of its 

 velocity. The above-named English physicists ascribe to it, 

 therefore, three degrees of freedom, which Boltzmann ex- 

 presses as three kinds of movability (Beweglichkeitsarten) . A 

 material system consisting of a multitude of particles possesses 

 as many degrees of freedom or kinds of movability as the 

 number of variables which must be given for the complete 

 determination of its state of motion ; if made up of atoms, 

 , therefore, a gaseous molecule has a greater number of degrees 

 of freedom, the number depending upon that of the atoms. 

 This mode of attacking the question is marked by simplicity 

 and clearness, and it therefore leads to very simple results. 



If heat W is added to a gas whose molecules consist 

 each of a single atom, while its volume is kept constant, the 

 energy, which is only kinetic, will increase equally in the 

 ^yfe-ection of each of the three given degrees of freedom, and 

 thus in each by the amount ^W measured in heat-units. If 

 this gas is heated at constant pressure, so as to attain the 

 same temperature as before, there must, in addition to the 

 heat W, be given to it, to overcome the external forces, a 

 further amount of heat W, which bears to W the ratio 2:3; 

 for in this case the ratio of the specific heats is 



C _ W W_ 5 

 c W 3' 



whence 



17 . -8' 



1 Wien. Sitzungsber. Ixxiv. 1877, p. 553 ; Pogg. Ann. clx. 1877, p. 175 ; 

 transl. Phil. Mag. [5] iii. 1877, p. 320. 



2 Atti deir Ace. dei Lincei [3] i. 1877, p. 774 ; Nuovo Cimento [3] ii. 1877, 

 p. 61. 



3 Atti deir Ace. dei Lincei [3] vii. 1883, p. 112 ; Nuovo Cimento, xiv. 1884, 

 p. 183. 



