RECENT ADVANCES IN SCIENCE 537 



where N is the universal Rydberg constant referred to above, 

 m and n take integral values (or occasionally integral values 

 + -5, such as 1*5, 2-5, etc., and a and /3 are two constants 

 (between zero and unity) which are definite for a given series 

 of a given element, but which differ for different series even 

 of the same element. In particular, for each of these elements 

 there exist what are called " principal " series and what are 

 called " sharp " series, which are related as follows : writing 

 m equal to 1 (or perhaps 1*5) and then giving successive in- 

 tegral values to n we obtain the principal series ; writing 

 n= 1 (or i*s) and giving successive integral values to m we 

 get the sharp series (the minus signs which make their appear- 

 ance in some cases are to be disregarded). Obviously the 

 convergence wave-number of the principal series is N/(i -f a) 2 

 or N/(i'$ + a) 2 as the case may be, and of the sharp series 

 A/(i+/3) 2 or Ay ( 1 • 5 + /3) 2 . For convenience such an ex- 

 pression as N/(m + a) 2 is devoted by the symbol (m, a) f so 

 that the general Rydberg formula for series of lines can be 

 written 



v = (m, a) — (n, /3) 



Thus the Balmer series for hydrogen can be written 



v = N/{\ + i) 2 -N/(n+ i) 2 

 = (i| — (»j l> = 2, 3, 4, etc.] 



As another example there are series of lines in the arc spec- 

 trum of sodium which can be included in the formula by put 

 ting a = -152 and /3= '146 ; i.e. 



v = (m, -152) — (n, -146) 



Thus putting m= 1-5 and n = 2, 3, 4, etc., we get a principal 

 series (the first principal series of sodium), the first line of 

 which (n = 2) is, in fact, the well-known D 2 line (the more 

 refrangible of the well-known doublet in the yellow). The 

 D\ line corresponds to m= 1*5 and n = 2 in the second prin- 

 cipal series of sodium which is 



v = (m, -152) — (», -145) [m= i'S \ n = 2, 3, 4, etc.] 



This indicates (what is, as a matter of fact, the most usual 

 occurrence) that series may be doubled or even trebled, the 

 series being really series of doublets or triplets. It should be 



