MATHEMATICS 



tained electrons. We can, however, shew that some- 

 thing very like, at least, the Quantum Theory is 

 needed for such explanations. According to this 

 theory, radiation is not being emitted continu- 

 ously in appropriate circumstances from an atom, 

 but in definite jumps of prescribed amounts, these 

 amounts involving a new universal constant of 

 nature, denoted usually by h, to which all are 

 proportional. Many other phenomena of different 

 type involve fi, for example, the kinetic energy 

 of an electron which, by striking an atom, causes 

 it to emit its characteristic X-ray, or the energy 

 with which, when an electron is driven from an 

 excited atom, that electron departs. Now h itself 

 is not an energy, but an action, and we have a 

 universal constant of action. Perhaps I should 

 explain what action means. It is the product of 

 an energy and a time, or we can think of it as 

 an angular momentum of rotation, so that it is 

 not a concept of which the elementary student 

 has no cognisance. One very good method of 

 visualising the significance of h is to suppose that 

 the electrons in every atom can only rotate with 

 speeds corresponding to definite values of their 

 angular momentum determined by h. Then, of 

 course, the expression for the energy or any other 

 property of the atom, which can be determined 

 from a knowledge of these angular momenta and 

 the distribution and number of electrons, will also 



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