536 SCIENCE PROGRESS 



i cm. of a train of such waves ; it is, in fact, io 8 /X where X is 

 the wave-length in Angstrom units (io -8 cm.). N is a uni- 

 versal constant, known as Rydberg's constant, and has the 

 value 109675 according to the most recent measurements. 

 (Bohr has recently shown that this constant is very closely 

 dependent on and calculable from the fundamental electronic 

 charge and Planck's constant.) If now the integral series of 

 values 3, 4, 5, 6, etc., be given to n in turn we obtain a set of 

 numbers approximating with remarkable closeness to the 

 wave-numbers of the lines of the hydrogen spectrum, the 

 value n = 3 giving the well-known H a line in the red (6563 

 A.U.), n = 4 giving Hp (4861-5 A.U.), and so on. It will be 

 seen that as n gets greater the wave-number steadily in- 

 creases, and one progresses by steps up into the ultra-violet 

 region towards the limit N/4 or 27419, corresponding to a 

 wave-length 3646 A.U. Such a limit is referred to as the 

 " convergence wave-number " of the series of lines. In the 

 cases of other elements whose line spectra have been investi- 

 gated the facts and formulae are not so simple and much work 

 is still required, not only to determine perfectly satisfactory 

 formulae, but also to give a theoretical basis for them. Bohr's 

 theory of the atom does indeed give a very complete explana- 

 tion of the Balmer formula for hydrogen and similar formulae 

 for some of the lighter atoms such as helium and lithium. 

 The elements which have been most thoroughly investigated 

 and for which some order has been evolved from the apparent 

 chaos of their line spectra are the alkalis, the alkaline earths, 

 and some of the metals, such as zinc, cadmium, magnesium. 

 These elements are individually found to possess several series 

 of lines (not merely one, as in the case of hydrogen) and in 

 most cases also lines which have not yet been brought under 

 any series law. There are, as might be expected, certain 

 simple relations found to hold between the formulae which 

 express the different series for one element. The whole matter 

 is somewhat involved, and a fairly complete account is given 

 in Baly's Spectroscopy, 2nd edition, Chap. xvii. For our 

 purpose at the moment suffice it to say that for any of these 

 elements very good agreement is obtained by the use of the 

 Rydberg formula 



N N 



V = 



(m + a) 2 (n + /3) 2 



