642 



SCIENCE 



[N. S. Vol. XXXIV. No. 880 



There remains only the origin of the curve 

 where I have placed the letter E for the ether, 

 electron, protyle or Urstoff, which must have 

 a valence and density equal to zero,^ and we 

 may also almost say with an atomic weight 

 of zero, since IE is the x of Mendeleeli for 

 which he calculated a hypothetical atomic 

 weight equal to one-millionth that of the 

 hydrogen atom. The numerical relations of 

 the helix are summarized in the following 

 table. The positions and the number of the 

 elements on the different circles may be ob- 

 tained by drawing a regularly increasing 

 number of diameters to each succeeding type 

 or circle. One vertical diameter is drawn in 

 the quarter-octant, giving place at its ends 

 for two elements. Two diameters are drawn 

 at right angles in the half-octant for four 

 elements. The angles are bisected by two 

 other diameters, giving place for eight ele- 

 ments in the octants; and then again bisected, 

 giving sixteen for the double, and a final bi- 



TABLE or THE STMMETKIES OF THE HELIX 



* G-. T. Stoney, ' ' The Non-existence of Density 

 in the Elemental Ether," Fhil. Mag. (5), Vol. 29, 

 p. 467. 



section gives thirty-two for the quadruple oc- 

 tants. 



The helix is placed horizontally, so that the 

 nullivalent elements shall form its axis — they 

 being the lightest elements — from which each 

 group is continued downward with sym- 

 metrical increase in valence and density on 

 either side to a maximum in the triads at the 

 bottom. The alkalis on the one side are the 

 antitheses of the halogens on the other, and 

 this maximum of dissimilarity decreases 

 downward symmetrically on either side. In 

 the double octants it reaches a valence of 8 

 and a corresponding specific gravity. In the 

 octants the circle closes with a valence of 4. 

 It is interesting that carbon, the element of 

 life, and silicon, the element of the rocks, form 

 the center of the figure and are both tri- 

 morphic like the triads at the bottom of the 

 double octants. If the helix be cut along its 

 axis and the curves opened out on a flat sur- 

 face the table of the elements given below re- 

 sults. This shows that the newcomers inter- 

 calated between the homologues of the pre- 

 ceding group are three for the octave, nine 

 for the double-octave and seventeen for the 

 quadruple octave if there be a triad at the 

 bottom of the large curve. Symmetry would 

 demand a group of twelve at that place. 



If the helix be cut along the lower line of 

 densest elements and flattened out we have 

 the following table, where, as the lowest ele- 

 ments have an equal right to be placed at 

 either side, they are placed on both sides. 

 This suggests the possibility that the second 

 element beyond uranium would be the first 

 member of a triad. 



Doubtless a better suggestion would come 

 from the preceding table, that there would be 

 a triad or larger group at the bottom of the 

 larger circle. 



I. Longitudinal Relations. Fig. 1. 

 At the bottom of Fig. 1 is placed the atomic 

 volume graph of Meyer: (1/sp. gr.) the 

 specific volume graph of A. J. Hopkins,' 



'Jour. Am. Chem. Sac, July, 1911. 



