THERMODYNAMICAL EQUILIBRIUM 79 



know which way to point. It would not be true to say 

 that such a region is timeless; the atoms vibrate as usual 

 like little clocks; by them we can measure speeds and 

 durations. Time is still there and retains its ordinary 

 properties, but it has lost its arrow; like space it extends, 

 but it does not "go on". 



This raises the important question, Is the random 

 element (measured by the criterion of probability 

 already discussed) the only feature of the physical world 

 which can furnish time with an arrow? Up to the 

 present we have concluded that no arrow can be found 

 from the behaviour of isolated individuals, but there is 

 scope for further search among the properties of crowds 

 beyond the property represented by entropy. To give 

 an illustration which is perhaps not quite so fantastic 

 as it sounds, Might not the assemblage become more 

 and more beautiful (according to some agreed aesthetic 

 standard) as time proceeds?* The question is answered 

 by another important law of Nature which runs — 



Nothing in the statistics of an assemblage can distin- 

 guish a direction of time when entropy fails to distinguish 

 one. 



I think that although this law was only discovered in 

 the last few years there is no serious doubt as to its 

 truth. It is accepted as fundamental in all modern 

 studies of atoms and radiation and has proved to be one 

 of the most powerful weapons of progress in such 

 researches. It is, of course, one of the secondary laws. 

 It does not seem to be rigorously deducible from the 

 second law of thermodynamics, and presumably must 

 be regarded as an additional secondary law.t 



* In a kaleidoscope the shuffling is soon complete and all the patterns 

 are equal as regards random element, but they differ greatly in elegance. 



f The law is so much disguised in the above enunciation that I must 

 explain to the advanced reader that I am referring to "the Principle of 



