230 



approaches to 0. The suppositions underlying' the deductions of this 

 paper imply that also for ideal gases Nernst's heat theorem is valid. 

 The results derived in this paper for an ideal gas may also be of 

 value for the theory of free electrons in metals. For this we refer 

 to the next paper. 



§ 2. The energy elements. We may imagine the equilibrium 

 between radiation and molecular translatory motion in an ideal ^) 

 monatomic gas enclosed in a given vessel to be brought about in 

 the following way : let the vessel which contains the gas be sur- 

 rounded totally or partially by a vessel which contains radiation. 

 The walls of the latter vessel are thought to be perfectly reflecting 

 on the inner side. In the wall which is common to the two vessels 

 a cylindrical hole is made, in which moves a piston (reflecting on 

 the side of the radiation). This piston is held, e.g. by a suitable 

 constructed spring, in such a way that under the action of the 

 pressure of those rays which have a frequency v' it is forced to 

 vibrate. We may interpret the newest theory of Planck so that 

 exchange of energy (absorption as well as emission) takes place 

 only by whole quanta at once, if we take care to add the zero 

 point energy to the value of the energy at equilibrium of an 

 oscillator derived on that supposition. So we may suppose that 

 those rays can give their energy to the piston only by quanta ot 

 magnitude liv'. The pressure of radiation, being proportional to the 

 product of electric and magnetic force, has the frequency v = 2v' . 

 The piston is forced to vibrate with the same frequency under the 

 action of the pressure. 



We suppose v' to be chosen in such a way that r is a principal 

 frequency of the gas. The motion of the piston will then excite 

 vibrations in the gas of the same frequency v. We will suppose 

 that the piston can transfer the quanta hv' immediately to the gas 

 in the form of energy of rays with its frequency v (whether the 

 piston transfers all the quanta, which it receives, in- this form, or 

 only part of them, and perhaps remits another part to the radiation, 

 is immaterial). A mode of vibration v of the gas then receives energy 

 by quanta Itv' = 7^ ^^^'• 



The reverse, viz. transfer of energy of a mode of vibration v in 

 the gas by the aid of the above-mentioned piston to the mode of 

 vibration v' in the radiation must also be assumed, in fact in the 

 case of equilibrium to the same amount per unit of time. We could 



^) By this I understand in this paper a gas such, that the volume of the 

 molecules themselves and their mutual attraction need not be considered. 



