18 Mr. H. Eamage. Relat ions of Spectra, Densities, pfov. 7, 



and triad metals. The constant B is approximately equal to 

 Eydberg's constant N , but a different value is used in different 

 series. 



Modifications of these formulse have been proposed by Ames,* by 

 Balmer,f and by Thiele.]: 



The formula of Rydberg is of wide application, its form is simple, 

 and the values of the constants are easily calculated. It has every 

 appearance of being a more natural formula than that of Kayser and 

 Runge. This is an important consideration, for there is doubtless 

 some common cause acting to produce series of this type. The view 

 has been expressed by Rydberg that : " The equation of Kayser and 

 Runge is a formula of interpolation, which has no other object than to 

 represent with the greatest accuracy possible the given observations." 

 For these reasons we shall proceed to discuss it in detail, with special 

 regard to its application to the principal series of lines. 



The Constant N . — This constant was calculated from the lines in the 

 hydrogen series — N = 4.10 s /^- Rydberg has given two values : (1) In 

 1890, the value 109721-6; and (2) in 1900, 109675*00. 



Using the figures given by Ames for the hydrogen lines,§ we have 

 obtained the number 109706. Dyson || used the number 109705, and 

 we have calculated the same number from the strongest hydrogen 

 lines in Rowland's ' Solar Spectrum Wave-lengths.' By reducing the 

 wave-lengths of Rowland to their corresponding values in a vacuum, we 

 calculated the value of N as 109674. It would appear that Rydberg's 

 later value must have been obtained in this manner. 



In my earlier work, the value of N was taken as 109706, and in the 

 later as 109675. The oscillation frequencies were in like manner 

 reduced to their value in a vacuum. 



The lines in the plates which accompany this paper are those 

 given by the lower values of m in Rydberg's formula, and it is in 

 these, especially in the strongest lines, where m = 1, that the formula, 

 as used by its author, gives the greatest differences from the observed 

 numbers. Rydberg only claims that his formula is approximately 

 true, but the fact that it is of such general application is strong evi- 

 dence for thinking it may be made more accurate. Certain facts 

 revealed by a study of the diagrams, referred to above, and of the 

 calculations made by Rydberg's method, indicate a modification of the 

 formula, which will give much greater accuracy. 



The Principal Series of the Metals of the Alkalies. — Each metal, except 

 lithium, gives two principal series, the corresponding members of 



* ' Wied. Ann.,' vol. 25, pp. 80-87, 1885. 



f ' Verhandl. d. Naturf . Gtes. in Basel,' vol. 11, pp. 418-462. 



X 1 Astrophys. Jour.,' vol. 6, p. 65. 



§ ' Phil. Mag.,' vol. 30, 1890, p. 33. 



|| 'Roy. Soc. Proc.,' toI. 68, p. 33, 1901. 



