544 Prof. J. W. Nicholson on the High-frequency 



is certainly necessary"*, and it will probably remain so when 

 the nucleus is, as is probable in terrestrial elements, of a 

 complex character. Our precise conclusion will be, there- 

 fore, that we cannot retain Bohr's theory of the more complex 

 atoms, and van den Brook's hypothesis in its present form, 

 simultaneously, and one or the other must be changed or 

 abandoned altogether. In the two cases of hydrogen and 

 helium there is no conflict, however. 



It has been assumed universally that an atom can form a 

 Saturnian system with concentric rings of electrons rotating 

 round a positive nucleus, and this assumption is an important 

 part, for example, of the later sections of Bohr's theory 

 which do not deal with spectra, but rather with the chemical 

 properties of atoms. The phenomena of radioactivity have 

 led inevitably to the conclusion that an atom with a simple 

 nucleus, or pure positive charge, at its centre, and a single 

 ring of rotating electrons, is insufficient for their interpre- 

 tation, although the measurements of scattering of a and ft 

 particles have compelled Rutherford to enunciate the view 

 that the atom is Saturnian. We are obliged, therefore, to 

 imagine a more complicated arrangement. For it now seems 

 certain that the B particles in radioactive transformations 

 cannot come from a ring whose radius is comparable with the 

 atomic radius, and accordingly they must come either from an 

 inner ring, or from the nucleus itself. The attempt to pre- 

 serve the simple character of ihe nucleus, and the reluctance 

 to endow it with a structure of its own, have led to the fairly 

 general adoption of the view that the j3 particles come from 

 an inner ring of electrons, which can also give rise to radia- 

 tion of the appropriate wave-length for X-rays, just as an 

 outer ring is believed to give rise to the visible spectrum of 

 an element. 



A mathematical examination does not confirm the possibility 

 of such an arrangement. We shall consider the question, in 

 the main, from a point of view which is common to ordinary 

 dynamical theory and to that of Bohr, which is the first non- 

 mechanistic theory yet given. Bohr has supposed that in 

 the determination of the steady states of rotation of an atomic 

 system, the ordinary mechanics can be used, proceeding 

 according to the law of inverse square for both the repulsion 

 between electrons and the attraction between an electron 

 and the nucleus. The formula so obtained for circular 

 motion may be written, for a single ring of n electrons 

 rotating round a nucleus Ne with angular velocity co, 



<J = -^(N-|S n ), 



ma 6K * y 



* Monthly Notices of R. A. S. July 1912 and later. 



