794 Dr. L. Silberstein on Radiation from 



If the dispersion-curve , as (43) may conveniently be called, 

 has (anywhere but at the origin) an asymptote \ 2 = <y 2 , as in 

 fig. 2, then there will be an infinity of lines which will crowd 

 towards the asymptote from the red to the violet end o£ the 

 spectrum (in the case of fig. 2, a) or in the opposite sense (in 

 the case of fig. 2, b). The experimentally known line-series, 

 properly so-called, correspond to the former case, but in 

 band spectra both cases occur. In either case we shall have 

 what is called a " head " or a convergence-point, of wave- 

 length X = 7- If the asymptocy is of such a nature that k 

 is, in the neighbourhood of 7, proportional to any positive 



power of — g gs then — especially if behind 7 there is 



another similar convergence-point — the dispersion curve may 

 well emerge again from the lower into the upper part of the 

 plane giving rise to fresh lines beyond the convergence- 

 point 7, the first of these lines being, in the case represented 

 by fig. 2, a, of wave-length L. But what seems interesting 

 to remark is that a certain region behind the convergence- 

 point (from A to B) will be entirely dark, i. e. free from lines. 

 If there is a certain number of such asymptotes, then we 

 shall have a succession of such gaps,'following upon crowded 

 lines. Multiple lines could be accounted for by narrow 

 protuberances of the dispersion curve, and so on. But let 

 us leave these generalities. 



It will be understood that it is only in some cases that we 

 might expect to be able to guess the precise form of the 

 dispersion curve belonging to the atom of a substance, and 

 deduce from it, by means of equation (43), the lines of its 

 characteristic spectrum. But as a rule, what is given by 

 experience are the lines themselves, and the dispersion curve 

 has to be constructed from these data. The former is 

 certainly the more fascinating task of the mathematical 

 physicist, but even the latter does not seem useless. The 

 knowledge of atomic dispersion curves thus defined and 

 constructed by means of spectroscopic material may well 

 throw some new light on the intrinsic properties of atoms. 

 It is not my purpose, however, to enter into investigations 

 of the latter kind just now. I shall limit myself, therefore, 

 to give here only one such "experimental'"' curve (fig. 3), 

 which corresponds to hydrogen, as far only as its diffuse or 

 Balmer series is taken into account. The abscissae of the 

 centres of the small circles are the squares of the observed 

 wave-lengths of H^Ha, H 2 = H j8 , &c, and their ordinates 

 the squares of the successive roots of tanzt = w, beginning 

 with Ui, that is 20*1906. The vertical bar represents 



