Bayley — On the Development of Chemical Elements. 795 



niobium respectively, as shown by Brauner, by tbe study of their oxides 

 and other compounds and the sequence of their atomic weights. 



The space between didymium and the platinum group, occupied 

 with certainty according to our present knowledge only by tantalum 

 and tungsten, is still a terra incognita requiring exploration. Erbium 

 may be a member of a second series in the cycle, and tantalum and 

 tungsten higher members of the same period. The determination of 

 the specific heat of erbium and its associates, or, failing this, of the 

 densities of some of their most volatile compounds, would be, at the 

 present time, an important increment of chemical knowledge, as throw- 

 ing light upon the constitution of the fifth and, by analogy, the sixth 

 cycles. 



If this second period exists, and fills up the gap between the cerite 

 and platinum groups, the fifth and sixth cycles probably contain three 

 primary septenary series, and the comparison of dimensions between 

 the various successive cycles is as follows : — 



Terms of the geometric series a, a x h, a xlP' . . . ay. h^ — 



1 A 10 i 0.^ O. 1 1 

 ^^1 6J 36; 216> 1296- 



The progression between successive alkali metals — 



16, 16, 3 X 16, 3 X 16, 6 x 16, (6 x 16). 



The number of primary septenary series in the cycle — 



1, 1, 2, 2, (3), (3). 



The diagram on Plate XXI. shows the dimensions of the fifth and 

 sixth cycles in accordance with the suggestions made in this Paper. 

 The curves of the lower series are the curves of atomic volume, and 

 the curves of the upper series show the melting points of the elements. 



Note added in Press. — This rule is only an approximation. Strictly speak- 

 ing, the increments of atomic weight which give the positions of lowest atomic 

 volume are alternately equal to the lateral dimensions of a pair of equal cycles 

 and to the mean lateral dimensions of a pair of adjacent unequal cycles. 



