RECENT STATISTICAL THEORIES 675 



The model proposed for a cubic centimetre of gas under the ordinary 

 conditions of temperature and pressure consists of something Hke lO^" 

 particles. Merely the mention of so extravagant a figure is sufficient 

 to persuade that it is vain to dream of making any progress by postu- 

 lating a definite position and a definite velocity for each of these. 

 The life of the human race would not be long enough to write down 

 even the postulates, to say nothing of the inferences. 



This seems a fearful handicap; but it is not so at all. Adopting 

 the statistical method, one does not even begin upon the hopeless 

 task of fixing place and motion for every particle. We content our- 

 selves with writing down a function, which states how many among 

 the multitude of particles we assume to be situated in each small 

 (but not too small) element of volume; and how many we assume to 

 have momenta which lie in each small (but not too small) range of 

 momentum. These are specifications much more modest and vague; 

 but they are ample. For the things which we wish to interpret — 

 entropy and temperature, viscosity and conduction and diffusion — 

 the atomic picture need not be made one whit more definite. 



In saying this I am understating the case. If the atomic picture 

 could be made more definite, say by stating the locations and the 

 velocities of all the atoms with absolute precision, the meanings 

 which we shall presently attach to entropy and temperature would 

 be dissolved. Our theory of these entities depends upon the vagueness 

 of the picture. Seemingly they appeal to us as physical realities 

 because our senses and our instruments are too obtuse to perceive 

 the atoms. Our minds must feign a somewhat similar obtuseness, 

 pretending not to fix the particles of the imagined swarm too sharply; 

 therefore it does not matter that they are so numerous that the 

 pretence becomes sincere. Exact knowledge of the individual atoms 

 is unattainable; but it is useless, is not desirable even. One remembers 

 i^sop's tale of the fox and the inaccessible grapes; in this case it is 

 probable that the grapes really are sour. 



For that matter, perhaps they do not even exist. One of the most 

 striking of the very recent ideas in theoretical physics is the thought, 

 that even for atom-models with but a few particles, even in thinking 

 of an isolated particle, it may be altogether pointless to assign exact 

 positions and velocities. In dealing with a swarm of particles by the 

 statistical way, we do in efi'ect fix the position of each corpuscle, 

 but with a certain latitude; we fix the velocity of each, but again 

 with a certain latitude. Perhaps this latitude, this indefiniteness, 

 is something inherent in nature. Insisting as I am upon the contrast 

 between the theory of the structure of the atom and the statistical 



