426 



BELL SYSTEM TECIISICAL JOVRSAL 



accepted hy the theorist without Cjuestion and without suggestion, 

 for he is not competent to analyze the data for himself. 



Having grouped a certain number of lines into a series, ha\ing 

 guessed as well as possible the convergence-frequency vum of this 

 series, the spectroscopist has still the task of finding the numerical 



a 



10 



I"'ig. 3 — I'riiiripal scrlc- 



)f soiliiim (two photonraphsl. ((i. K. Harrison, Physical 

 Kniiiv I 



l.iw to which the consecutive frequencies conform. As a matter of 

 course, all the fre(|uencies can be e\|)ressed by a formula j^eiurali/cd 

 from (1) and (2): 



vi = viim -f(i) (o) 



in which / is the oriler-number distinguishing each line, and /(/) is a 

 different quantity for each of the lines, which approaches zero as we 

 pass along the series to the limit. This means nothing by itself; the 

 (juestion is, does the function /(/) ha\'e a simplicity comparable wiili 

 the simplicity of the subtrahenda in (1) and (2) which suggested that 

 the>' are the symbols of something deeply important? In general, 

 the function /(/) is not so simple as the function which occurs in the 

 series of the spectra of hydrogen and ionized helium. In many cases, 

 howe\er, it is almost as sim|)le, in others a little more complicated, 

 in others a little more complicated yet, and so forth; so that the 

 eventual result is this, that the formula (8) appears to be the proper 

 way of de.scribing the lines of series spectra, even in cases where the 

 '^cric'; i>; so irregular and the form of the function /(») .so intricate 



