IN THE LAST HALF-CENTURY. 57 



in the physical and chemical characters of 

 its several terms, but breaks np into a 

 number of sections, in each of which the 

 several terms present analogies with the 

 corresponding terms of the other series. 

 Thus the whole series does not run 



a, 6, c, d, e,f, g, 7i, i, k, &c, 

 but 



a, o, c, d, a, b, c, d, a, /3, 7, 8, &c. : 



so that it is said to express aperiodic law 

 of recurrent similarities. Or the relation 

 may be expressed in another way. In 

 each section of the series, the atomic 

 weight is greater than in the preceding 

 section, so that if w is the atomic weight 

 of any element in the first segment, w + x 

 will represent the atomic weight of any 

 element in the next, and w + x + y the 

 atomic weight of any element in the next, 

 and so on. Therefore the sections may 

 be represented as parallel series, the cor- 

 responding terms of which have analo- 



