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Some of our readers may be glad to have a drawing of the Platonic solids, since they play so large a part in the building up of elements. The regular solids are five, and five only; in each:
(1) The lines are equal.
(2) The angles are equal.
(3) The surfaces are equal.
It will be seen that the tetrahedron is the fundamental form, the three-sided pyramid on a triangular base, i.e., a solid figure formed from four triangles. Two of these generate the cube and the octahedron; five of these generate the dodecahedron and the icosahedron.
The rhombic dodecahedron is not regular, for though the lines and surfaces are equal, the angles are not.
NOTES.
Mr. C. Jinarâjadâsa[1] writes:
The asterisk put before metargon in the list of elements should be omitted, for metargon had been discovered by Sir William Ramsey and Mr. Travers at the same time as neon (see Proceedings of the Royal Society, vol. lxiii, p. 411), and therefore before it was observed clairvoyantly. It is not, however, given in the latest list of elements in the Report of November 13, 1907, of the International Atomic Weights Commission, so it would seem as though it were not yet fully recognised.
Neon was discovered in 1898 by Ramsey and Travers, and the weight given to it was 22. This almost corresponds with our weight for meta-neon, 22.33; the latest weight given to neon is 20, and that corresponds within one-tenth to our weight, 19.9. From this it would seem that neon was examined in the later investigations and meta-neon in the earlier.
He says further on a probable fourth Interperiodic Group:
Thinking over the diagrams, it seemed to me likely that a fourth group exists, coming on the paramagnetic side, directly under iron, cobalt, nickel, just one complete swing of the pendulum after rhodium, ruthenium, palladium. This would make four interperiodic groups, and they would come also periodically in the table too.
I took the diagram for Osmium, and in a bar postulated only three columns for the first element of the new groups, i.e., one column less than in Osmium. This would make 183 atoms in a bar; the new group then would follow in a bar, 183, 185, 187. Here I found to my surprise that the third postulated group would have a remarkable relation to Os, Ir, Pt.
Thus
Os.--245 (in a bar); less 60 = 185
Ir. 247 less 60 = 187
Pt. 249 less 60 = 189
But strange to say also
Ruthenium (bar) 132 less 60--72
Rhodium 134 less 60--74
Palladium 136 less 60--76
But 72, 74, 76, are Iron, Cobalt and Nickel.
So there does probably exist a new group with bars (183), 185, 187, 189, with atomic weights.
X=bar 185; atoms 2590, wt. 143.3
Y= 187, 2618, wt. 145.4
Z= 189, 2646, wt. 147.0.
They come probably among the rare earths. Probably also Neodymium and Praseodymium are two of them, for their weights are 143.6, 140.5.
CHAPTER III.
THE LATER RESEARCHES.
The first difficulty that faced us was the identification of the forms seen on focusing the sight on gases.[2] We could only proceed tentatively. Thus, a very common form in the air had a sort of dumb-bell shape (see Plate I); we examined this, comparing our rough sketches, and counted its atoms; these, divided by 18—the number of ultimate atoms in hydrogen—gave us 23.22 as atomic weight, and this offered the presumption that it was sodium. We then took various substances—common salt, etc.—in which we knew sodium was present, and found the dumb-bell form in all. In other cases, we took small fragments of metals, as iron, tin, zinc, silver, gold; in others, again, pieces of ore, mineral waters, etc., etc., and, for the rarest substances, Mr. Leadbeater visited a mineralogical museum. In all, 57 chemical elements were examined, out of the 78 recognized by modern chemistry.
In addition to these, we found 3 chemical waifs: an unrecognized stranger between hydrogen and helium which we named occultum, for purposes of reference, and 2 varieties of one element, which we named kalon and meta-kalon, between xenon and osmium; we also found 4 varieties of 4 recognized elements and prefixed meta to the name of each, and a second form of platinum, that we named Pt. B. Thus we have tabulated in all 65 chemical elements, or chemical atoms, completing three of Sir William Crookes' lemniscates, sufficient for some amount of generalization.
In counting the number of ultimate atoms in a chemical elemental atom, we did not count them throughout, one by one; when, for instance, we counted up the ultimate atoms in sodium, we dictated the number in each convenient group to Mr. Jinarâjadâsa, and he multiplied out the total, divided by 18, and announced the result. Thus: sodium (see Plate I) is composed of an upper part, divisible into a globe and 12 funnels; a lower part, similarly divided; and a connecting rod. We counted the number in the upper part: globe—10; the number in two or three of the funnels—each 16; the number of funnels—12; the same for the lower part; in the connecting rod—14. Mr. Jinarâjadâsa reckoned: 10 + (16 x 12) = 202; hence: 202 + 202 + 14 = 418: divided by 18 = 23.22 recurring. By this method we guarded our counting from any prepossession, as it was impossible for us to know how the various numbers would result on addition, multiplication and division, and the exciting moment came when we waited to see if our results endorsed or approached any accepted weight. In the heavier elements, such as gold, with 3546 atoms, it would have been impossible to count each atom without quite unnecessary waste of time, when making a preliminary investigation. Later, it may be worth while to count each division separately, as in some we noticed that two groups, at first sight alike, differed by 1 or 2 atoms, and some very slight errors may, in this way, have crept into our calculations.
In the following table is a list of the chemical elements examined; the first column gives the names, the asterisk affixed to some indicating that they have not yet been discovered by orthodox chemistry. The second column gives the number of ultimate physical atoms contained in one chemical atom of the element concerned. The third column gives the
