14 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



11 molekular-geordnet." But then the locality of one molecule 

 would have some influence on the locality of another molecule 

 and then in the Theory of Probabilities the presence of one mole- 

 cule in one place would not be independent of the presence of 

 some other molecule in some other place. Such dependence 

 is not permissible by the Theory of Probabilities. Before, how- 

 ever, we can further describe what is here perhaps the most impor- 

 tant term (molekular-ungeordnet), we must point out that BOLTZ- 

 MANN considers the number of molecules m of one kind whose 

 component velocities along the co-ordinate axes are confined 

 between the limits, 



and + d, y and 1?+^, and dt . . (i) 



and also the number of molecules mi of another kind whose 

 component velocities similarly lie between the limit 



... (2) 



then, considering the chances that a molecule m shall have 

 velocities between the limits specified in (i) and molecule m\ 

 have velocities between limits (2), BOLTZMANN intimates that these 

 chances are independent of the relative position of the molecules. 

 Where there is such complete independence, or absence of all 

 minute regularities, the distribution, according to BOLTZMANN, 

 is " molekular-ungeordnet " (molecularly-disordered). 



BOLTZMANN furthermore informs us that, as soon as in a gas, 

 the mean length of path is great in comparison with the mean dis- 

 tance between two adjacent molecules, the neighboring molecules 

 will quickly become different from what they formerly were. 

 Therefore it is exceedingly probable that a " molekular-geord- 

 nete " (but molar-ungeordnete) distribution would shortly pass 

 into a " molekular-ungeordnete " distribution. 



Furthermore, from the constitution of a gas results that the 

 place where a molecule collided is entirely independent of the 

 spot where its preceding collision took place. Of course, this 



