January 24, 1913] 



SCIENCE 



123 



then, nofhing whatever to do, in his judg- 

 ment, except to deny the general validity 

 of the Hamiltonian differential equations, 

 and this is precisely what he has done. 

 Furthermore, the fact that his own equa- 

 tion goes over into Rayleigh's equation 

 when h is made infinitely small, seems to 

 him to show decisively that certain ele- 

 mentary radiation processes, which in 

 Jeans 's theory are assumed to be continu- 

 ous, are in fact discontinuous. 



Now it would be presumptuous in me to 

 attempt to pass upon the cogency of these 

 arguments, especially as they have been 

 made the subject of review by the foremost 

 of the world theorists, among them the late 

 Poineare.^- Nevertheless I shall pause just 

 long enough to express the inevitable point 

 of view of every man who has worked long 

 enough in a laboratory to know from pain- 

 ful experience how large is the entropy, 

 i. e., the probability of the event, that ex- 

 perimental results will come out differently 

 from the way in which, according to the 

 inevitable logic of things, they must come 

 out, and that for the reason that in five 

 cases out of ten, the inevitable logic of the 

 experimentalist, at least, involves some un- 

 discovered or unconsidered element. He is 

 prone to wonder, therefore, whether even 

 the theorist's inevitable logic is absolutely 

 inevitable. 



However, it should be said that Poin- 

 eare,^^ while stating that the assumption 

 that physical phenomena do not obey laws 

 expressible by differential equations would 

 constitute the most profound revolution 

 which physics has undergone since New- 

 ton's day, yet sees no way of escape from 

 Planck's conclusion, unless it be found in 

 the fact that to obtain the relation between 

 his linear oscillator and the density of 

 black-body radiation, Planck assumes the 

 very electrodynamic laws the validity of 



'^Journal de Physique, Se. 5, Vol. 2, p. 5, 1912. 



which he in the end denies. While this is 

 indeed a weakness in his theory, it doesn't 

 in any way affect his argument for the 

 necessity of some such step as that which he 

 has taken. To my own mind, the uncer- 

 tainty in this last argument lies in the fact 

 that the general validity of the law of equi- 

 partition of energy is assumed to be a nec- 

 essary consequence of the Hamiltonian 

 equations. If this be so, then the Hamil- 

 tonian equations certainly must go, for we 

 have known for over thirty years that the 

 law of equi-partition can not have any gen- 

 eral validity. 



Planck has appreciated fully from the 

 beginning the above-mentioned weakness 

 in the method of development of his equa- 

 tion, and within a year^^ he has modified 

 his statement of his theory in the endeavor 

 to meet Poincare's objection. The theory 

 as outlined above implies that, since energy 

 is always contained in the oscillator in ex- 

 act multiples of an energy unit, both the 

 absorption and emission of energy by the 

 oscillator must take place in units — that is 

 discontinuously. Planck now assumes that 

 emission alone takes place discontinuously, 

 while the absorption process is continuous. 

 At the instant at which a quantity of 

 energy hv has been absorbed, an oscillator 

 has a chance of emitting the whole of its 

 unit, a chance which, however, it does not 

 necessarily take. If it in this way misses 

 fire, it has no other chance until the ab- 

 sorbed energy has arisen to 2hv, when it 

 has again the chance of throwing out its 2 

 whole units, but nothing less. If again it 

 misses fire, its energy rises to Shv, 4Jiv, etc. 

 The ratio between the chance of not emit- 

 ting when crossing a multiple of hv, and the 

 chance of emitting, is assumed to be pro- 

 portional to the intensity of the radiation 

 which is falling iipon the oscillator. This, 

 then, is at present the most fundamental 

 and the least revolutionary form of quan- 



" Planck, Ann. der Fhys., 37, p. 642, 1912 



