RECENT ADVANCES IN SCIENCE 379 



hard or K-series of characteristic rays, and also for the a and 

 j3 lines of the softer series, the L-series. It is this progression 

 which justifies us in assigning a series of " atomic numbers " 

 to the various atoms, differing from and more fundamental than 

 the atomic weights. Our present series of atomic numbers is 

 simply this Moseley series of steps based on square roots of 

 frequencies, although such a series had been suggested, but 

 not with such definiteness, by other workers, notably van der 

 Broek, who based his suggestion on the changes in radio-active 

 substances accompanying the loss of alpha and beta particles. 

 Millikan proceeds in this paper to draw some important con- 

 clusions as to atomic structure which are rendered extremely 

 probable by Moseley 's law. 



The first is this. We assume (1) that the ordinary law of 

 inverse squares holds for the forces exerted by the atomic 

 nucleus on negative electrons near it ; (2) that the electrons 

 in the atom rotate in circular orbits ; (3) that the observed 

 highest frequencies of radiation are proportional to the highest 

 orbital frequencies of the electrons. The first assumption, whose 

 truth is so well known in celestial regions, has been amply 

 verified in the subatomic world by the work of Rutherford 

 and his pupils on the scattering of alpha rays ; the second 

 assumption is justified by the demands of stability, the existence 

 of the Zeeman effect, the phenomena of magnetism, especially 

 the recent work of Barnett (Phys. Rev. 6, 239 (191 5) and July 

 (19 1 7)) and" Einstein and de Haas {Verh. d. Deut. Phys. 

 Gesell. xvii. (191 3)), which well-nigh demonstrates the existence 

 of permanent, and therefore non-radiating, electronic orbits ; 

 the third assumption is probable from a priori considerations, 

 and, as will be seen presently, necessary from certain theoretical 

 considerations. From Moseley's law and these assumptions, 

 one deduces, without any appeal to the quantum theory, that 

 the distances from the nucleus of each type of atom to the 

 orbit of the inmost electron is inversely proportional to the 

 positive charge on the nucleus, i.e. to the atomic number. 

 For let E be the intensity of force due to a nucleus at unit 

 distance, then the force on an electron e in an orbit of radius 

 a is eE/a? ; if this electron has a mass m and an orbital 

 frequency n, then 



eE/a 2 — (27rw) 2 m.a 



