tion ol' the corresponding frequency in Ihe surrounding space, suggested Croui 

 analogy wilh tlie ordinary theory of radiation. Einstein c()in[)ares the emission or 

 absorption of radiation of frequency v corresponding to a transition between two 

 stationary states witli the emission or absorption to be expected on ordinary 

 electrodynamics for a system consisting of a particle executing harmonic vibrations 

 of this frequency. In analogy with the fact thai on the latter theory such a system 

 will without external excitation emit a radiation of frequency v, Einstein assumes 

 in the first place that on the quantum theory there will be a certain probability 

 'A'^„dt that the system in the stationary state of greater energy, characterised by 

 the lettern', in the time interval dt will start spontaneously to pass to the stationary 

 state of smaller energy, characterised by the letter n". Moreover, on ordinary 

 electrodynamics the harmonic vibrator will, in addition to the above mentioned 

 independent emission, in the presence of a radiation of frequency v in the sur- 

 rounding space, and dependent on the accidental phase-difference between this 

 radiation and the vibrator, emit or absorb radiation-energy. In analogy with this, 

 Einstein assumes secondly that in the presence of a radiation in the surrounding 

 space, the system will on the quantum theory, in addition to the above men- 

 tioned probability of spontaneous transition from the state n' to the state n", pos- 

 sess a certain probability, depending on this radiation, of passing in the lime dt 

 from the state n' to the state n", as well as from the state n" to the state n'. These 

 latter probabilities are assumed to be proportional to the intensity of the surrounding 

 radiation and are denoted by p,B'^„dt and p.,B'^,dt respectively, where p^di' denotes 

 the amount of radiation in unit volume of the surrounding space distributed on 

 frequencies between v and u + du, while ß"!, and B", are constants which, like A"„, 

 depend only on the stationary states under consideration. Einstein does not introduce 

 any detailed assumption as lo the values of these constants, no more than to the 

 conditions by which the different stationary states of a given system are deter- 

 mined or to the "a-priori probability" of these states on which their relative occur- 

 rence in a distribution of statistical equilibrium depends. He shows, however, 

 how it is possible from the above general assumptions, by means of Boltzmann's 

 principle on the relation between entropy and probability and Wien's well known 

 displacement-law, to deduce a formula for the temperature radiation which apart 

 from an undetermined constant factor coincides with Planck's, if we only assume 

 that the frequency corresponding to the transition between the two states is deter- 

 mined by (1). It will therefore be seen that by reversing the line of argument, 

 Einstein's theorj' may be considered as a very direct support of the latter relation. 

 In the following discussion of the application of the quantum theory to deter- 

 mine the line-spectrum of a given system, it will, just as in the theory of tempera- 

 ture-radiation, not be necessary to introduce detailed assumptions as to the mechanism 

 of transition between two stationary states. We shall show, however, that the 

 conditions which will be used to determine the values of the energy in the station- 

 ary states are of such a type that the frequencies calculated by (1), in the limit 



