264 Mr. W. Sutherland on the 



sible, on account of certain factors being unknown, to compare 

 directly the period of the Li atom in a compound with its 

 period in the metal, although we could say that its relation 

 to the period of the Na atom was the same in both cases. 

 But by means of facts communicated in " Further Studies 

 on Molecular Force" (Phil. Mag. [5"| xxxix. pp. 19-21) the 

 missing factors can be introduced ; so that if mz/fjzT? is taken 

 to give relative periods of the uncombined metallic atoms as 

 in my previous papers, then for compounds of the type NaCl 

 we have only to introduce the factor a/ 2, and for the type 

 SrBr 2 the factor ^3, to get their relative periods on the 

 same basis as the periods for the pure metals. Thus, then, 

 the periods given for the combined Li metals and the 

 combined halogens in "A New Periodic Property " are to be 

 multiplied by v 2, and those for the Be family of atoms in 

 combination and for F 2 , 01 2 , and so on, by i/4"5, when we- 

 get :— 



Li. Na. K. Rb. Cs. F. CI. Br. I. 



•106 -212 -318 -530 -207 -414 -621 -828 : 



Be. Mg. Oa. Sr. Ba. F 2 . Cl 2 . Br.,. I . 

 -212 -318 -424 '530 -331 -662 -993 1-324 



Now it is very noteworthy that these periods for the Li 

 family of atoms in combination are very nearly one-half of 

 the periods for the pure metals, namely, '205, *43, and so on ; 

 while in the Be family the periods for the combined atoms are 

 nearly the same as for the free. Thus it appears that the 

 periods of the metallic atoms in compounds are harmonically 

 related to their free periods, and we see now why the spectra 

 for the pure metals in vacuo are the same essentially as the 

 spectra of their vaporized compounds ; for though the mecha- 

 nical period of vibration of an atom may change with its 

 change of chemical state, the change being an harmonic one,, 

 the combined atom and the free atom have still periods in 

 common, just as we saw that the different metals have. 



To look more closely into the compound molecule's having 

 a period which is the sum of periods belonging to its atoms, 

 let us consider two pieces of the same iron rod whose periods 

 of longitudinal vibration arejo T and p 2 . Then, if they were- 

 welded together, the whole rod would have a period Pi+p 2 - 

 But if the one bit of rod were iron and the other copper, and 

 they were brazed together, we should expect the discon- 

 tinuity at the joint to divert some of the energy into other 

 modes of motion ; but still there would be a fundamental 

 period of vibration Pi+p 2 . If jt?i and p 2 were to one another 

 as two whole numbers, then the two parts would have a 



