Supplement to '' N'atzcre," October ii, 1906 



whole subject before the reader in a connected form. 

 Briefly stated, llie following- is the order of treat- 

 ment : — 



The book opens with an introductory sketch of 

 definitions and first principles, the proof of Kirchhoff's 

 law, and the definition of a black body. In the 

 second section we have an investigation of Maxwell's 

 formula for the radiation-pressure, Boltzmann's proof 

 of Stefan's law, and Wien's law of distribution of the 

 energy over the dilTerent parts of the spectrum, based 

 i>n the well-known application of a modified form of 

 Doppler's principle. In the last chapter of this sec- 

 tion Dr. Planck gives a general discussion of the 

 entropy and temperature of monochromatic radiation. 

 .Although the method of treatment is different from 

 that adopted in the introductory part of this review, 

 the conclusions appear to be identical. In particular. 

 It is pointed out that emission without absorption is 

 irreversible, absorption without emission impossible. 



In the third part emission and absorption are con- 

 sidered from the point of view of the electromagnetic 

 theory. A resonator is under the influence of peri- 

 odical or stationary waves. In these circumstances 

 Dr. Planck investigates the oscillations induced in 

 the resonator, and assigns meanings to the entropy 

 and temperature of the resonator which account satis- 

 factorily for reversible phenomena; but the equations 

 of the electromagnetic field being deducible from 

 those of rational dynamics cannot of themselves 

 account for irreversibility, for, corresponding to the 

 solution representing any given process, another 

 solution representing the reverse process can be 

 obtained by changing the sign of the time-differential 

 dt. Whether the case is stated in this or in some 

 other form, there is no o priori reason for asserting 

 that waves cannot converge to a point as readily as 

 Ihey diverge from it. The convergent wave motion 

 simply represents a second solution of the differential 

 equation of propagation, which is commonly omitted 

 merely on the grounds that the corresponding pheno- 

 menon does not exist. 



The subsequent sections represent an exposition 

 of the valuable work done by Dr. Planck in applying 

 10 radiation phenomena the same probability con- 

 siderations which have led to such fruitful results at 

 the hands of Boltzmann in connection with the kinetic 

 theory of gases. Dr. Planck starts with the assump- 

 tion that the entropy of a system in a given state 

 depends in some way on the probability of that state, 

 whence it follows that if the system consists of two 

 parts which are independent of each other, and we 

 assume that the entropy of the whole is the sum of 

 the entropies of the parts, the entropy must be a 

 logarithmic function of the probability. A short 

 account of Boltzmann's work for the case of mon- 

 atomic gases follows, and Dr. Planck then shows how 

 to determine expressions for the entropy of radiation 

 from analogous considerations. 



Now Boltzmann's work was not independent of an 

 assumed a priori law of probability. He first sup- 

 posed that for an individual molecule all values of 

 the energy were a priori equally probable, and, con- 

 sidering the case of a large assemblage of molecules 

 NO. 1928, VOL. 74] 



the total energy of which was constant, he found 

 that the most probable distribution only agreed with 

 the Boltzmann-Maxwell law in the case in which 

 the molecules were moving in two-dimensional space. 

 To obtain the Boltzmann-Maxwell law in other cases 

 it was necessary to start with the assumption that 

 for an individual molecule all values of the coordinates 

 and momenta were a priori equally probable. If we 

 mistake not. Dr. Planck in § 148 starts with Boltz- 

 mann's first assumption. He supposes he has to 

 deal with a large number N of resonators, that the 

 total energy is divided into a large number P of equal 

 elements, and that these elements are distributed at 

 random among the resonators perfectly independently 

 of each other. This is, of course, an assumption, 

 but it is shown in § 150 to be equivalent to assuming 

 that all values of the electric and magnetic coordinates 

 of the resonator (/ and df/dt) are equally probable. 

 There appears, however, to be an alternative assump- 

 tion in the case of oscillators distributed in space, 

 namely, that all values of the rectangular components 

 of / and dfjdt are equally probable, and this might 

 lead to a different result. Would it? and if so, which 

 is right? 



In any case, the important fact remains that Dr. 

 Planck obtains results consistent with Stefan's law, 

 notwithstanding that this law cannot possibly repre- 

 sent equipartition of energy at all temperatures 

 between ether and matter. Perhaps the other 

 assumption here suggested would result in equi- 

 partition, or the writer of this review has omitted to 

 take account of something in the book. The fifth 

 section is mainly taken up with applications to 

 irreversible processes. In it the consequences of 

 imagining a direct reversal of radiation processes are 

 carefully discussed ; the behaviour of an oscillator in 

 a field of radiation is then investigated ; the next 

 chapter deals with the conservation of energy and 

 increase of entropy, and, finally, we have a detailed 

 discussion of the particular case of an oscillator ex- 

 posed to black-body radiation. 



It will be thus seen that Dr. Planck's work belongs 

 to a class of investigation which has played an all- 

 important part in building up our knowledge of 

 physical phenomena. It deals with the logical con- 

 sequences of certain well-defined hypotheses, and as 

 such brings us measurably nearer obtaining a clear 

 and definite idea regarding the irreversible processes 

 associated with radiation. Moreover, the author is 

 careful to define the limitations of his method. As 

 he points out, an unfilled gap still exists in the theory, 

 as he does not fully discuss the tendency to an 

 equilibrium state between oscillations of different 

 periods. The fact that the oscillators are really in 

 motion shows, in connection with Wien's method, 

 that there is a tendency to an equilibrium distribution, 

 and this process may be capable of association with 

 increase of entropy. All readers must express the 

 hope that Dr. Planck may have an opportunity of 

 pursuing this investigation further. 



Dr. Planck's book has the great merit of being 

 very readable and intelligible. It is quite easy to 

 see everywhere what the author is driving at; many 



