264 Dr. A. C. Crelrore on the Construction oftlie 



seen from symmetry that the sum of all x and y forces in the 

 plane of the hexagon, the zero plane, due to all other atoms 

 in the structure upon atom vanish, and it is then only 

 required to figure the z component forces ; for upon substi- 

 tuting the values of the quantities given in Table I. in the 

 equations, we must obtain the same x and y component 

 forces for atoms 20, 22, and 24, because the values are 

 identical. The x components are therefore equal and their 

 directions are along — 28, — 26, and — 27 respectively, 



Table I. 



Plane 

 No. 



Atom 

 No. 



X 



y 



z 



r 



X 



Y 



z 



cL 



cosa 



sina 



■^Direction of Axes 



X 



y 



z 



+ 1 



J 











4 L 



\/6 , 











-1 



o° 



+1 







- 



- 



0-I9 



+ 1 



20 



•' 



-L 



•■ 



V&8. 

 II L 



» 



2V22 

 II 



J/33 



109° 



1 

 3 



+§& 



0-28 



O-IO 



'• 



+ 1 



21 



" 



-hi 



•• 



» 



» 



Z\T2Z 



+ II 





" 



•' 



» 



0-27 



0-8 



» 



-hi 



22 



" 



-L 



•■• 



" 



•• 



2V22 

 II 





» 



•• 



" 



0-26 



0-/2 



» 



■hi 



23 



" 



+ 1 



- 



" 



•• 



.2V22 

 + It 





•• 



•• 



" 



0-28 



0-10 



■> 



-hi 



24 



» 



-I 



'• 





» 



2\/22 

 ~ II 





- 



•• 



•• 



0-27 



0-8 



" 



tl 



25 



•• 



+ L 



" 







.2V22 





" 



» 



•• 



0-26 



0-/2 



„ 



-1 



29 



3 L 



o 



+ ,2 1 



4 l 



2V2 

 3 



O 



♦i 



" 



« 



V 



0-29 



O-IO 



- 



-1 



30 



■> 



» 





- 





• 



- 





- 



» 



0-26 



0-12 



tt. 



-/ 



31 



- 



» 



>> 



" 



- 



" 



1 



•• 



" 



„ 



0-27 



0-6 



" 



-/ 



32 



+fl 



•> 



T, 2 l 



\Tbq, 



8 L 



+ 33 



" 



j/33 

 + 33 



0° 



+1 







11 



a 



" 



-/ 



33 



» 



•• 



- 



- 



" 





» 



« 



•> 



•• 



0-28 



O-IO 



'• 



-/ 



34 



" 



- 





" 



- 



• 



>t 



" 



a 



'■' 



0-26 



0-12 



'• 



-3 



35 



+% 





h 5 -^L 





,2^6 

 +33 





.51/33 

 + 33 



109 



1 

 -3 



iffi 



0-27 



0-8 



" 



-3 



36 



'-> 



<• 



« 



« 



■> 



» 



" 



■> 



•■> 



" 



0-28 



0-10 



» 



-3 



37 



" 



" 



" 



" 



- 



» 



•■• 



» 



» 



1 



0-26 



0-12 



" 



making 120° with each other, and therefore evidently vanish, 

 without making any further calculation. The y components 

 lie along — 10, — 12, and — 8, and also vanish for a similar 

 reason. The x and y components of atom J, which is on the 

 axis of 0, both vanish. The three atoms, 29, 30, and 31, 

 fig. 4, in the base of the tetrahedron of which is the 

 centre, similarly make the sum of the x and y components 

 vanish, and, lastly, the lower triangle of atoms 35, 36, and 

 37 in plane —3 makes the x and y components vanish. 



