Rigli-Frequeney Spectra of the Elements. 711 



proportion o£ Sm. The Sm, Eu, and Grd appeared to be 

 pure. I hope soon to complete the examination of the 

 spectra of this group. 



Conclusions. 



In fig. 3 the spectra of the elements are arranged on 

 horizontal lines spaced at equal distances. The order chosen 

 for the elements is the order of the atomic weights, except in 

 the cases of A, Co, and Te, where this clashes with the order 

 of the chemical properties. Vacant lines have been left for 

 an element between Mo and B,u, an element between Nd 

 and Sa, and an element between W and Os, none of which 

 are yet known, while Tm, which Welsbach has separated 

 into two constituents, is given two lines. This is equivalent 

 to assigning to successive elements a series of successive 

 characteristic integers. On this principle the integer N for 

 Al, the thirteenth element, has been taken to be 13, and the 

 values of N then assumed by the other elements are given 

 on the left-hand side of fig. 3. This proceeding is justified 

 by the fact that it introduces perfect regularity into the 

 X-ray spectra. Examination of fig. 3 shows that the values 

 of v* for all the lines examined both in the K and the L series 

 now fall on regular curves which approximate to straight 

 lines. The same thing is shown more clearly by comparing 

 the values of N in Table I. with those of 



Qk=v/^, 



v being the frequency of the a line and v the fundamental 

 Ry dberg frequency. It is here plain that Q K = N — 1 very 

 approximately, except for the radiations of very short wave- 

 length which gradually diverge from this relation. Again,. 

 in Table II. a comparison of N with 



Ql =\ / -« — > 



V 3°gZ>o 



31 



where v is the frequency of the L a line, shows that 

 Ql = N — 7*4 approximately, although a systematic deviation 

 clearly shows that the relation is not accurately linear in this 

 case. 



Now if either the elements were not characterized by these 

 integers, or any mistake had been made in the order chosen 

 or in the number of places left for unknown elements, these 



* Welsbach, Monatsh. xxxii. p. 373 (1911). 



