PROBLEMS OF MODERN SCIENCE 



of motion would allow. In an atom, they must 

 be replaced by something quite different, because 

 all hydrogen atoms, wherever found and what- 

 ever their earlier history, behave, spectroscopically 

 for instance, in the same way. This is equivalent 

 to saying that some other universal equation con- 

 nects angular velocity and radius in such cases 

 if we adopt the angular momentum principle, as 

 we find it necessary to do, we obtain the result 

 that r 2 u> has a constant value. The Quantum 

 Theory replaces initial conditions by this form of 

 condition. 



But perhaps I have already said enough on 

 this matter. My aim has not been, as that of a 

 physicist might be, to give any account of such 

 matters as the Theory of Relativity or the Quantum 

 Theory, but only to point out the essential nature 

 of the mathematical questions involved in the roots 

 of the theories, for experience shews that the 

 essential difficulties found in their comprehension 

 are due to a lack of realisation of this essential 

 nature, which is not always difficult even for the 

 non-mathematician to understand. To some ex- 

 tent, in these two problems, I have trespassed 

 on the domain of physics. My excuse must be 

 that by far the most fundamental developments 

 of Applied Mathematics have recently been, and 

 must continue to be for some time, in these two 

 directions. I can only conclude by expressing the 



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