34 



KNOWLEDGE. 



February, 1915. 



represented by five 

 point. For example, the 

 hydrogen-vacuum tube are 

 Wave- 

 lens;th. 



Ha 6563-042 



H/i 4861-49 



H-y 4340-66 



Hd 4101-89 



figures before 



the decimal 



four lines seen in a 

 given thus : — 

 Oscillation- 

 frequencv. 



15236-84 



20569-82 



23038-0 



24379-0 



Professor Johnstone Stoney, guided by musical 

 Table 7. 



analogy, endeavoured to explain the rhythmical 

 arrangement of lines on the theory that they were 

 overtones of a very low fundamental vibration, 

 since Ha, H^, and Ho might be the twentieth, 

 twenty-seventh, and thirty-second harmonics of 

 a fundamental vibration of oscillation-frequency 

 761 -845. But there was no place for H-y in this 

 arrangement, and no reason why these harmonics 

 only should be observed ; nor does the theory account 

 for the extensive series of lines observed in stellar 

 spectra by Sir William Huggins and others. It is 

 now generally admitted that such theories will not 

 account for the facts. 



The first striking success in the attempt to explain 

 these regularities was obtained in 1885 by Pro- 

 fessor Balmer, who found that the hydrogen lines 

 were connected in a simple manner with the suc- 

 cession of natural numbers from 3 onwards, the 

 wave-lengths of Ha, H^, Hy, Ho, and so on, being 

 f' i' If' S' ^^"^ so on, of the wave-length 3646-1 

 of a " head " in the violet, to which the lines crowd 

 continually closer and closer. Otherwise expressed, 



X = 3646-14 



m' 



where m 



is put equal to 

 or, if we use 



w — 4 ' 

 3, 4, 5, and so on, in succession 

 oscillation-frequencies, O.F. = 27418-75 (1 - Altn^). 

 We may obtain an interesting representation of the 

 law which holds in this spectrum by measuring 

 the distance of the lines from the " convergence- 

 frequency " at 27418-75, which we may write C.F. 



4C.F. 



We have C.F. — O.F. = 



V = — . then y^ = .^ .^ 

 ■^ m -^ 4C.F. 



m' 



or, if we put 



(C.F. - O.F.) , which is the 



equation of a parabola. 



Figure 27 illustrates this, in which the upper part 

 shows the series of hydrogen lines which have been 



observed, and the lower shows the parabolic curve 

 which connects the stars, plotted with a scale of 

 1 jm along the left margin, and a scale of oscillation- 

 frequencies along the bottom of the diagram. 

 Along the right-hand margin is shown a scale of 

 1 jni^ ; and, when the lines are plotted with this 

 and the bottom scale, it is seen that all the points 

 lie accurately along a straight line. 

 The formula given above, namely, 

 1 



r 



may be written 



.,2 ■ 



4C.F. 



1 



m^ 109675 



(C.F. -O.F.) 



(C.F.-O.F.), 



or 



O.F. =27418-75 - 



109675 



nr 



The researches of Kayser and Runge, of Rydberg 

 and others, have shown that in most spectra, 

 though the lines may appear to be distributed at 

 random, yet in very many cases series of lines. 



* Ames, Phil. Mag., 1890, XXX. 33. 

 t Dyson, Phil. Trans., 1906, CCVI, 403. 



+ Evershed, Phil. Trans., 1903, CCI, 457. 



§ Mitchell, Astrophys. Joiirn., 1913, XXXVHI, 407. 



