642 Mr. W. Sutherland on the 



equivalent of metal, the latter having the values 

 Be. Mg. Ca. Sr. Ba. 



2-1 2-7 3-2 3-7 4-2 



which can be written 0*53 (4, 5, 6, 7, 8). 



These simple laws for s lead to the folk) wing statement in 

 regard to the Periodic Classification of the elements : — In 

 successive columns the valency charges form the arithmetical 

 progression e, 2*, 'Se and so on, while in the successive rows 

 the values contributed by atoms to s, which is the other com- 

 ponent factor of electric moment, form arithmetical pro- 

 gressions such as are exemplified above. In conjunction 

 with these simple numerical relationships amongst the 

 elements we must take the corresponding ones demonstrated 

 in " A New Periodic Property of the Elements'" and "The 

 Cause of the Structure of Spectra" (Phil. Mag. [5] xxx. 

 and [6] ii.). The volumes of the gramme-atom B of the 

 alkali metals as given in " Further Studies " are subject to a 

 simple numerical law, being given by 



2 + (n-l)n2'7 = 2'7{(n-±) 2 + ±} nearly; 



where n has the values 1, 2, 3 and so on, as the following 



comparison shows 



Li. Na. K Kb. Cs. 



B found... 2-0 7-4 18*6 34-4 



Bcalc. ... 2-0 7-4 18'2 34*4 56*0 



The volumes of the gramme-atom of the halogens in com- 

 pounds run as 1, 2, 3, 4. But in the Be family there is no 

 such simple relation discoverable. But in "Further Studies'" 

 it was shown that the following relations hold approximately 

 between F and B, namely in the Li family F 2 = 09B + 4-4, 

 and in the Be family F 2 /4 = (r9B + 3-0. From formulae 

 just given we see that for the Li family a more accurate 

 relation is 



B = 2 + 2-7(F/P2-l)(F/P2-2). 



For the uncombined metals the following results are 

 established by Tables XXIX. and XXX, of "Further 

 Studies/' First that (M/p)/W 2 l or B/M 2 / is the same for 

 the members of one chemical family, and second that for 

 families of different valency n the values of /*B/M 2 Z are 

 nearly 2*8, except in the case of the Be family, for which it 

 is 2*0. Thus, then, for the metals we have the relation that 

 e*s* is proportional to the volume of the atom with which the 

 doublet is associated. To assign a simple meaning to this 

 for inula let us assume a doublet in a metallic atom, and use 



