12 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



ments in mechanics and in thermodynamics and the energy 

 elements in radiation. 



The German word " unkontrollierbar J)1 here used may also 

 with some justice be translated as, unconditioned, undetermined, 

 unmeasurable, unregulated, uncorrelated, ungovernable or hap- 

 hazard. But whichever term is best, PLANCK, mechanically 

 speaking, meant by it, the confused, unregulated and whirring 

 intermingling of very many atoms. 



Either of these two equivalent definitions implies that such 

 elementary disorder or chaos is a condition of sufficiently com- 

 plete haphazard to warrant the application of the Theory of 

 Probabilities to the unique (unambiguous) determination of the 

 measurable physical features of the process viewed as a whole. 



The foregoing ideas more or less tacitly underlie the whole 

 of BOLTZM ANN'S great pioneer work in this vast field. He it was 

 who clearly showed that the Second Law could be derived from 

 mechanical principles: that entropy was a property of every 

 state, turbulent or otherwise; that the entropy idea would be 

 emancipated from all thought of human, experimental, skill, 

 and who thereby raised the Second Law to the position of a real 

 principle. He did all this by a general basing of the idea of entropy 

 on the idea of probability. Consequently we find much attention 

 paid in all his work to haphazard molecular conditions. He 

 first used the terms " molekular-geordnet " (molecularly ordered, 

 or arranged), and " molekular ungeordnet " molecularly dis- 

 ordered or disarranged), which latter phrase we must regard 

 as synonomous with the term " elementar ungeordnet " (elemen- 

 tary disorder or chaos) with which we have already become 

 acquainted in PLANCK'S presentation. We will, therefore, con- 

 fine ourselves here to BOLTZMANN'S illustrations of these terms, 

 for his work does not, in these particulars, contain any sharp 



1 On p. 133 of Warmestrahlung PLANCK says, "only measurable mean values 

 are kontrollierbar, " and this may help us to get the meaning here. 



