100 KAXSAS ACADEMY OF HCIEXVE. 



HARMONIC SERIES. 



HARMONIES OF THE CHEMICAL ELEMENTS. 

 By B. B. SMYTH. 



The development of harmonic forms from arithmetical and figurate series; 

 and the study of harmouical series in the phyllotactic arrangement of leaves, 

 scales, etc., of plants and their fruits; in the waves, tones, and velocities of 

 music, light, and electricity; in the distances, weights, and movements of 

 the planets and their satellites; in organic chemistry; and the finding of 

 harmony everywhere in nature has led to researches to determine what har- 

 mony there should be in the constitution of the primary elements and in their 

 respective properties. 



Earliest researches were happily made in wrong directions, resulting m 

 negative knowledge, which serves as a lamp to positive knowledge. The 

 atomic weights of all the elements were first resolved into their prime factors, 

 Avith a view to determining a relation between their weights and valences. 

 The result was generally negative. 



One difficulty lies in the fact that a slight error in the determination of 

 the atomic weight of an element would lead to a conclusion entirely erroneous. 



For instance, the atomic weight of gold is often given as 197. It is also 

 sometimes given as 199. Each of these is a prime number; and if either 

 were correct, and the atomic weights were in exact multiple proportion, gold 

 could have only one valency, namely monovalency. But gold is also trivalent. 

 Yet the factor 3 does not enter into either of these numbers. If the atomic 

 weight were shown to be 198, then the metal might be divalent or even hexa- 

 valeut as well as trivalent. 



In a few cases (as, for instance, Ca 40, Cd 112, and Hg 200, which are diva- 

 lent; Al 27, Ga 69, and Sm 150, which are trivalent; C 12, and Ti 48, which are 

 tetravalent; As 75, and Sb 120, which are pentavalent; Mo. 96, and U 240, 

 which are hexavalent), the atomic weight appears to be in multiple propor- 

 tion to the valency; but in most cases there is no such concordance. If this 

 Avere true, N 14, Fe 56, and Sn 119, should be heptavalent; and Ca 40, Mn 55, 

 Br SO, Te 125, Sm 150, Tb 160, Pt 195 and Hg 200 should be pentavalent. Sim- 

 ilarly, O 16, Ca 40, Br 80, Sb 120, Tb 160 and Hg 200 should be tetravalent if 

 not pentavalent. 



This is a field that has been worked over thoroughly by many eminent 

 chemists in the last forty years; yet at this late day there are golden grains 

 to be garnered even by a mathematician; and, whether new or old, these 

 ideas are presented to show the harmonies that exist in the constituent 

 properties of the several chemical elements. 



On these charts I have arranged the elements in octaves as done thirty 

 years ago by Newlands, and much better done four years later by the Rus- 

 sian chemist Mendeleeff , that being the most rational method yet devised for 

 a classification of the chemical elements. The arrangement of Dr. Charles 

 Skeele Palmer, of the University of Colorado, is an admirable one, and a vast 

 improvement over that of Mendeleeff. I have, however, modified that ar- 

 rangement to some extent to accord with recent discoveries in inorganic chem- 

 istry. 



