A New Periodic Property of the Elements. 319 



All the quantities in this expression are known for a large 

 number of substances ; but it so happens that a has not been 

 determined for several of the bodies in Mendelejeff s most inter- 

 esting families — those of Li and Be. To get over the want of 

 these data it might seem advisable to use R. Pictet's empirical 

 formula aT(M./d)$= constant (Comptes Rendus, lxxxviii., and 

 Meyer's ' Modern Theories of Chemistry/ translated by Bedson 

 and Williams, p. 135). But this formula applies with accu- 

 racy only to the harder and heavier metals, for which the 

 mean value of the constant is '045 ; instead of which for Mg 

 we get *066, and for Al *057, while for Ka the discrepancy 

 is greater : this formula fails, then, just where we need it at 

 present. But I have found an empirical equation which will 

 suit our purpose, namely aTMj= constant, the constant lying 

 between '04 and *05 for all the metals for which data are 

 available except Sb, Bi, and Sn (Ir also falls to *037). This 

 formula includes Mg, Al, and Na, and may therefore be hope- 

 fully applied to the other metals of the same families, as will 

 appear in the result. Taking -045 as the mean value of the 

 constant and substituting for aT, we get p proportional to 

 (M/d)i M^/a/T, dropping the constants -045 and MC. Using 

 the values for d and T obtainable from Meyer's i Modern 

 Theories of Chemistry,' and in our uncertainty as to the true 

 molecular weight of the solid elements, taking M as atomic 

 weight, we get the following relative values of the periods of 

 vibration of the members of the lithium family at the melting- 

 point : — 



Li. Na. K. Kb. Cs. 



•21 -43 -m -96 1-23 



At a glance these numbers are seen to run as 1, 2, 3, 4*5, 6. 

 For the next family we get 



Be. Mg Ca. Sr. Ba. 



•35 -70 1-04 1-62 1-88 



These numbers run as 1, 2, 3, 4*5, and 5*3, not 6 exactly, 



Considering the nature of the assumptions we have been 

 forced to make, we must allow that these numbers show 

 beautifully simple harmonic relations to exist between the 

 periodic times of the molecules of solid metals at their 

 melting-points. Taking now Cu and Ag, which are sub- 

 sidiary relatives of the Li family, we get periods *21 and 

 •30, which are nearly as 2 to 3, and involve the same funda- 

 mental constant as the main family. Again, Zn and Cd, 

 which stand in the same relation to the second main family 



Z 2 



