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SCIENCE 



[N. S. Vol. XLV. No. 1162 



h—Ei 



when there results at once from (1) and 

 (2) 



(3) 



It may be objected that in the setting up of 

 these relations I have made two assump- 

 tions, the one that the electrons rotate in 

 circular orbits, and the other that the ob- 

 served highest frequencies are proportional 

 to the highest orbital frequencies. The 

 first assumption is justified (a) by the fact 

 that the recognized and tested principles 

 of physics give us no other known way of 

 providing a stable system, (&) by the ex- 

 perimental facts of light (Zeeman effect) 

 and (c) by the phenomena of magnetism, 

 especially the recent ones brought to light 

 by Einstein and de Haas,^ and by Bar- 

 nett,^" which well-nigh demonstrate the 

 existence of permanent and therefore non- 

 radiating electronic orbits. The exact 

 circular form for the orbit is a secondary 

 matter upon which, as will appear later, 

 it is not necessary to insist. The second 

 assumption, that the frequencies of the cor- 

 responding emission lines in the spectrum 

 of the various atoms are proportional to 

 the orbital frequencies, is from a priori 

 considerations probable and from certain 

 theoretical considerations to be presented 

 later, necessary. 



A second conclusion may be drawn from 

 Moseley's discovery that the L lines pro- 

 gress in frequency from element to element 

 just as do the K lines, the frequency being 

 in each case between 1/7 and 1/8 as great. 

 It is that, if there is a first or inmost elec- 

 tronic orbit, there must also be a second 

 one in all elements the radius of which is 



to straiglitness and as to intercept may well be at- 

 tributed to secondary causes. (See below.) 



VerJi. d. Phys. Ges., XVII., p. 152, 1913. 



10 Phys. Eev., 6, 239, 1915. 



given by (1) to be about 8% or 4 times as 

 great as that of the first. 



Guided then by the newly discovered 

 facts of X-radiations and the unquestioned 

 laws of force between electric charges, we 

 get our first information as to the probable 

 positions and conditions of some at least of 

 the negative electrons within the atom. 



Again, having found the highest natural 

 frequency which can come from any ele- 

 ment, viz., that from uranium, it is of ex- 

 traordinary interest to inquire where, ac- 

 cording to Moseley's law (2), the highest 

 frequency line of the K series would fall 

 for the lightest known element, hydrogen, 

 whose nucleus should consist of but a single 

 positive electron. This is obtained, as 

 shown in (2), by dividing the observed 

 highest frequency of any element by the 

 square of the atomic number. The shortest 

 wave-length given out by tungsten, atomic 

 number 74, and the only heavy element 

 whose X-ray constants have been accurately 

 determined, is .167 X 10"^ cm. according to 

 Hull's measurements. This gives for the 

 shortest wave-length which could be pro- 

 duced by hydrogen .167 X 10"^ X 74^ = 91.4 

 fi/x. This is as close as could be expected, in 

 view of the uncertainties in the measure- 

 ments 'and the further fact that Moseley's 

 steps are not quite exact, to the head of the 

 ultra-violet series of hydrogen lines recently 

 discovered by Lyman and located exactly at 

 91.2 fi/x. There is every reason to believe, 

 too, from the form of Balmer's series, of 

 which this is the convergence wave-length, 

 that this wave-length corresponds to the 

 highest frequency of which the hydrogen 

 atom is capable. It is practically certain, 

 then, that this Lyman ultra-violet series of 

 hydrogen lines is nothing hut the K X-ray 

 series of hydrogen. Similarly, it is equally 

 certain that the L X-ray series of hydrogen 

 is the ordinary Balmer series in the visible 

 region, the head of which is at 365 /*/*. In 



