260 



Dr. A. C. Crehore on the Construction of the 



and coincides with it in position. Plane +4 is at a short 

 interval and is a repetition of plane -—1 directly over it, and 

 this completes the cycle. 



In brief, there are but three situations of similar planes, 

 Nos. -12, —11, -6, -5, 0, 4-1, +6, +7 being like the 

 plane bounded by dashes ; Nos. —10, —9,-4,-3, +2, 

 4-3, 4-8, 4-9 like planes bounded by dots; Nos. —8, — 7, 

 — 2, — 1, 4-4, 4-5, +10, 4-11 like planes bounded by the 

 full lines. 



A study of the model made from these directions shows 

 perfect symmetry in each of the four directions corre- 

 sponding to the elementary tetrahedron, and the model may 

 be turned so as to make any one of the four faces of a tetra- 

 hedron horizontal, when each becomes a duplicate of the 

 others. We will select the atom in plane zero with its 

 axis pointing downward and calculate the forces of every 

 other atom upon it. The directions of the axes have been 

 chosen after many trials so as to make the turning moments 

 of all other atoms upon any given one zero and to produce 



Ffr. 3. 



stable equilibrium for these moments. This may easily be 



shown to be true for this arrangement o£ axes as follows : — 



Referring to fig. 3, let be the atom selected in plane zero 



with axis pointing downward perpendicular to the zero plane. 



