494 Mr. FoRSTER on the Molecular Formation of Crystals. 



a plane where the cohesion is least, or, in otlier words, for a direction of least 

 resistance. In Dana's formation (Fig. 7), it is evident that any division 

 parallel to a face will separate each molecule from one other only, or, in other 

 words, will overcome the cohesion of one pole in each molecule, while a divi- 

 sion in a plane replacing an edge would separate each molecule from two 

 others; and in a plane replacing a corner, from three others. The plane 

 parallel to a face is evidently, then, the direction of least resistance, and will 

 be the direction of cleavage. But there are two other cleavages — the very two 

 to which we have been alluding — namely, tangential to the edges of the cube, 

 and truncating the corners, which we shall for the future call the dodecahedral 

 and octahedral cleavages, and which we shall now endeavour to explain. 



If the molecules be spheres, each having twelve poles, or centres of force, 

 on its surface, the form which they will assume is the tetrahedron. Such a 

 molecule is shown in Fig. 8. The intersection of the great circles shows the 

 positions of the poles : these poles evidently lie six and six on great circles : 

 these circles are four in number, inclined to each other at the same angle as 

 the faces of the tetrahedron (70° 31' 44"), and are evidently divided each by 

 the others into segments of 60°. The arrangement of the poles is perfectly 

 symmetrical. For if any two of these spheres become united by two of their 

 poles, they will assume such a position as shown in Fig. 9, that is, the relative 

 positions of all the poles will be the same in consequence of their mutual 

 attraction : if they become attached in any other position, they will rotate round 

 a common axis till they occupy that position : a third will unite itself, as 

 shown in Fig. 9, for the very same reasons ; while a fourth would attach itself 

 by its three poles. A', B', C, (Fig. 10) to the three poles A, B, C ; for, since 

 all the arcs joining these poles are 60°, these poles are the very points at 

 which the spheres touch each other. We have now a tetrahedron formed, and 

 by precisely analogous reasoning we can continue the process of formation. 



It will be observed that a fifth molecule, if attached, will be in a plane with 

 three others, and will only touch two, a result to the necessity of which I have 

 already adverted when speaking of Dr. Wollaston's hypothesis. 



We have seen how a tetrahedron may be formed : we will now investigate 

 how it may be modified. 



If a row of molecules along each edge is deficient in each consecutive layer. 



