viii CONTENTS 



SECTION B 



PAGE 



Simple analytical expression for dependence of entropy on probability 53 



PLANCK'S derivation; illustration, limitations, consequences, features and 



comments 53 



SECTION C 



Determination of a precise, numerical expression for the entropy of 



any physical configuration 56 



BOLTZMANN'S pioneer work, PLANCK'S exposition, and the six main steps. 56 



Step a 



{ probability or number 1 

 Determination of the general expression for the { 



[ of complexions J 



of a given configuration of a known aggregate state 57 



Step b 



Determination of the general expression for the entropy S of a given con- 

 figuration of a known aggregate state 63 



Step c 



Special case of (&), namely, expression for the entropy 5 of the state of 



thermal equilibrium of a monatomic gas 63 



Step d 



Confirmation, by equating this value of S with that found thermodynamic- 



ally and then deriving known results 64 



Step e 



PLANCK'S conversion of the expressions of (b) and (c) into more precise 



ones by finding numerical value of k 66 



Step/ 



Determination of the dimensions of the universal constant k and there- 

 fore also of entropy in general 67 



