MATHEMATICS 



Before the Quantum Theory arose, it was well 

 understood that some restrictive principle was 

 necessary in the ultimate unit of matter, and the 

 reason for its necessity is not at all difficult to 

 understand. Let us return to the hydrogen atom. 

 Dynamics tells us that the angular velocity and 

 radius in that atom are connected by Kepler's 

 law, but it is incapable of telling us more. With 

 two unknown quantities and only one equation, 

 we cannot determine both a commonplace of 

 elementary algebra. Thus dynamics allows the 

 atom to have any radius it chooses provided that 

 the electron rotates with the proper corresponding 

 speed. In a planetary system like our own round 

 the Sun, the particular radii selected are determined 

 by the motions which existed when the planets 

 were formed as such or what the mathemati- 

 cian calls initial conditions. But such motions of 

 matter on the large scale involve no resultant 

 transfer of energy to the asther, in the sense that 

 our reception of light from the Sun does. Clas- 

 sical dynamics of the statistical aggregate of 

 immense numbers of atoms is therefore competent 

 to deal with such problems. 



But these ' initial conditions ' are not operative 

 in atoms. They are of course a restrictive principle 

 in themselves, for they serve to pick out the orbits 

 our planets (and the Earth) are adopting, as a 

 choice from the infinite number which the laws 



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