164 PROCEEDINGS OP THE AMERICAN ACADEMY 



XIV. 



CLASSIFICATION OF THE ATOMIC WEIGHTS IN TWO 



ASCENDING SERIES, CORRESPONDING TO THE 



GROUPS OF ARTIADS AND PERISSADS. 



By W. R. Livermore, Major of Engineers, U. S. Army. 

 Presented by the Corresponding Secretary, April 10, 1889. 



If the atomic weights of all chemical elements are arranged in a 

 single ascending series, it will take the following form if expressed in 

 whole numbers : 



1,-7, 9, 11, 12, 14, 16, 19,-23, 24, 27, 28, 31, 32, 35,-39, 

 40, 44, 48, 51, 52, 55, 56, 59, etc.; 



corresponding to the elements, 



H, — Li, Be, B, C, N, O, F, — Na, Mg, Al, Si, P, S, CI, — K, 

 Ca, Sc, Ti, V, Cr, Mn, Fe, Co, etc. 



The well known " Law of Octaves" calls attention to the fact that 

 each element bears a strong resemblance to that seven places from it 

 in this series, and the " Periodic Law " states that the properties of 

 elements stand in periodic relation to their atomic weights. These 

 laws have been enunciated and illustrated by Newlands, Mendeleeff, 

 Lothar Meyer, and others, and are now familiar to all students of 

 chemistry. 



Referring to these laws, Wurtz in his "Atomic Theory " says : 

 " Though it may be generally true that the properties of bodies are 

 subject to periodic modifications with the increase of their atomic 

 weights, the law of these modifications escapes our observation, and 

 seems to be of a complicated nature ; for, on the one hand, the atomic 

 weights of successive elements vary within considerable limits without 

 displaying any regularity in these variations ; on the other hand, we 

 must confess that the gradations of properties, in other words the 

 greater or less divergencies between properties of successive elements, 

 do not appear to depend upon the degree of the differences between 

 the atomic weights. These are real difficulties." * 



* Tlie Atomic Theory, 1881, p. 1C2. 



