648 



SCIENCE 



[N. S. Vol. XXXIV. No. I 



ranged along a narrow rising band tte sul- 

 phur and halogen series rise along different 

 and much steeper lines and drop to the com- 

 mon band when divided as suggested above. 



The transverse relations may be diametral 

 or symmetrical to a vertical diameter (Fig. 3) 

 equatorial or symmetrical to a horizontal 

 diameter (Fig. 4), and ecliptic or symmetrical 

 to an oblique diameter (Fig. 5). 



n. Diametral Relations. Fig. S 

 A vertical diameter representing a vertical 

 plane bisecting the helix divides the elements 

 into two groups, which are for many relations 

 the counterparts of each other, some exactly 

 and some approximately. Each of these rela- 

 tions is placed on a separate ring — an arrow 

 indicating the direction of increase, and a 

 cross the points of change. It is curious that 

 some of these relations are symmetrical to a 

 line a little to the right of the diameter and 

 passing between C and Si, and others to a 

 line passing to the left of the diameter and 

 to the right of C and Si. The only complex 

 relations are those of the Mendeleeff series 

 and the magnetic relations, which would seem 

 more simple if the two octants were drawn as 

 a single double octant. The most inexplicable 

 of all these relations is expressed in the outer 

 circle. As we pass down the right-hand curves 

 an addition of 1, 2, 3 and 4 units (= H atoms) 

 successively produces the same unit increase 

 in valence and density and thus there is great 

 condensation; going up on the left with the 

 same increasing addition and thus with still 

 increasing mass, there is lessening valence 

 and density, and this contrast is repeated seven 

 times. 



m. Equatorial Relations. Fig. k 

 The horizontal diameter makes very simple 

 relationships, most of which are combined with 

 the diametral relations in quadrantal arrange- 

 ment. The valence may be a simple dia- 

 metral relation or may increase to 4 and then 

 decrease as an equatorial relation. The elec- 

 tro-potential relations are equatorial in so far 

 as they are all strong above the horizontal line 



and weak below; quadrantal as far as the sign 

 is concerned. 



IV. T/ie Ecliptic Relations. Fig. 6 

 The most important ecliptic relation is fusi- 

 bility. On the one side are the high fusing 

 elements, reaching a maximum fusing point 

 at the end of an axis at right angles to the 

 ecliptic. On the other side are the low fusing 

 or volatile elements, reaching the maximum 

 volatility at the end of the vertical axis. At 

 one end of the ecliptic is the liquid mercury 

 and at the other the luminous radium, while 

 all the elements of the central most volatile 

 quadrant, cut out of the volitile semi-circle 

 by the equator and meridian, are absent from 

 the sun, except these at the center, oxygen and 

 nitrogen, the elements of the air. 



Relations of Partial and Complex Sym- 

 metry. Fig. 6 



The gas and rock areas show an antithesis 

 which is only approximately an ecliptic rela- 

 tion. The gas area points upward and for- 

 ward with the motion of the helix like a 

 flame, and the rock area points downward and 

 backward toward the center of the earth. The 

 way the rocks and meteorites find orderly ar- 

 rangement on this area from the light alka- 

 line to the heavy ferric groups is very sug- 

 gestive. The rock area typifies the increasing 

 stability of the downward curves of increas- 

 ing valence, density, and condensation. The 

 gas area is its striking antithesis. 



Attention may be called to the quadrilateral 

 of life, CHOlSr, in the center of the figure, 

 surrounded by the elements on which life sub- 

 ordinately depends. These last are almost the 

 only unsymnietrical relations. 



A remarkable result is reached (in figures 

 not reproduced here) by placing the elements 

 on the helix in their true positions as deter- 

 mined by the real differences between succes- 

 sive elements rather than by the average dif- 

 ferences for each type of circle. It is found 

 that the agreement with the ideal position is 

 much less perfect than might have been ex- 

 pected, and curious and unexpected sym- 

 metries come to light. It is further found that 



