34 Mr. J. S. Ames on Relations between 



cule of the element, the more were these lines shifted towards 

 the red end of the spectrum. The main objection to all this is 

 that until recently the selection of homologous lines has been a 

 purely personal matter : any observer has had the privilege of 

 calling " homologous " any lines he saw fit ; and even now, 

 as I shall show, it is mainly in the ultra-violet part of the 

 spectrum that homologous lines and series can be definitely 

 determined. To verify his law, M. de Boisbaudran takes the 

 average of wave-lengths lying often far apart. This process 

 can be justified only when each line separately obeys the law. 

 But far more important than this relation is one which M. de 

 Boisbaudran deduced some years later *. He states it as 

 follows : — 



" In the natural families (of elements), the variation in the 

 increment of atomic weights is proportional to the variation 

 in the increment of the wave-lengths of homologous rays (or 

 groups of rays) in the l third harmonic ' of the spectra.'"' 



I cannot better explain the meaning of his terms than by 

 giving in detail the application of the law to the determination 

 of the atomic weight of germanium |. 



Aluminium, gallium, and indium belong to the same " natural 

 family ; ' ' and their atomic weights and spectra are known, so 

 the ratio of the " variations in the increments " can be deter- 

 mined once for all. The average of the wave-lengths of a 

 prominent pair of aluminium lines is, according to him, 3952; 

 and homologous pairs in the spectra of gallium and indium 

 give similarly 4101 and 4306. He takes as the atomic 

 weights of the three metals 27*5, 69'9,and 113*5 respectively. 



Hence we have: — 



A 2 X. Variation in Increment. 



56 ^ = -37584 



149 





X. 



AX. 



Al. 



3952 



149 



Ga. 



4101 



205 



In. 



4306 





Atomic weight. 



AL 



27-5 



42*4 



Ga. 

 In. 



69-9 

 113-5 



43-6 



1-2 sl= -° 283 



* Comptes Rendus, cii. p. 1291 (1886). f Ibid. 



