548 HEPOET— 1889. 



might be built up out of these ; and, finally, forms representing the chemical ele- 

 ments themselves. The conditions are, doubtless, thus made more difficult, but 

 if satisfactory results are nevertheless arrived at, the presumption of their correct- 

 ness "vvill be greater. 



Such secondary forms would be : — 



1. Two triangles united along their bases, with a linear element, or bar, con- 

 necting their vertices. 



2. The open cube, consisting of four squares apposed along pairs of edges, or 16 

 bars. 



3. The closed cube, consisting of six apposed squares, or 24 bars. 



4. A solid equilateral triangle, consisting of three squares apposed by pairs of 

 their edges. 



5. A system of 10 bars, consisting of two squares apposed by a pair of edges aa 

 before, but having their opposite edges separated by single bars. 



6. A system of 10 bars, consisting of two triangles apposed by their bases to 

 opposite sides of a square, and joined together at their vertices. 



The models suggested as representing elemental forms are exhibited ; that for 

 lithium being constructed of two squares apposed by a pair of their linear edges, 

 and separated at their edges opposite to these by the bases of two triangles placed 

 at right angles thereto, the vertices of the triangles coming into apposition again 

 80 as to complete a solid figure. 14 bars representing the linear dimidium element 

 are thus employed in constructing the lithium model ; the monad valency of the 

 element is represented by the apposed pair of edges of the squares, these being the 

 analogues of the bi-linear form suggested for solid hydrogen. 



The salient angle formed by the two squares is suggested as the representa- 

 tion of tbe electro-positive condition ; a corresponding re-entiant angle being found 

 in the models representing electro-negative elements. 



The models being constructed for the most part out of equilateral triangles and 

 squares, with single bars occasionally interposed, present angles of 60°, 90°, and 120°, 

 and are very frequently hexagonal in shnpe. The carbon model is formed by placing 

 two pyramids base to base, each pyramid being formed of four equilateral triangles, 

 in all 24 pieces, its combining number being 12. The crystalline forms, both of the 

 diamond and of graphite, will be seen to correspond with this, the former being 

 made by placing a number of the carbon atoms together by their edges, and the 

 latter by placing them in apposition by their triangular facets. 



Silicon is formed by replacing each of these triangles by a group of seven, 

 formed of two triangles united at their bases and separated at their -vertices by a 

 sino-le bar component. This will be seen to correspond with both the crystalline 

 forms of silicon; tlie three-sided terminal pyramids of the silicon crystal being 

 brought out in the model. 



Sodium and potassium are so constructed as to correspond with the form 

 adopted for lithium, these being all members of the same series. Similarly, mag- 

 nesium and calcium are so constructed as to correspond with beryllium ; phos- 

 phorus and vanadium with nitrogen ; sulphur with oxygen ; chlorine with 

 fluorine, &c. Sulphur is brought out by replacing the triangles used for oxygen 

 by corresponding groups of seven (No. 1.) This corresponds with both the crystal- 

 line forms of sulphur. 



Iron, and the group of Tetrad elements analogous with it, are constructed out 

 of a common base form consisting of 88 components, to which two secondary forms 

 in each case, consisting of 20, 22, and 24 components respectively, are added to 

 represent chromium, manganese, and iron respectivel3^ The forms adopted for all 

 these elements correspond with that representing aluminium, so that the replac- 

 incr of an atom of this latter element by one of any of the former in the alum com- 

 pounds will be seen to be in accordance with the theoretical forms assigned to these 

 elements. 



It seems probable that metals may combine with non-metals by lateral inter- 

 penetration, a salient angle of the former corresponding with a re-entrant angle 

 of the latter ; but that two non-metals combine by superposition, corresponding 

 ingles being applied one to the other. The union of boron with nitrogen at a 



