6 AKT. 1. — Y. S1II13ATA : ÏIIE ACTION OF 



tliat formula II proposed by Sachse, which is constructed in such 

 a way that tlie six tctrahedra are all rigidly combined with one 

 another and in which the distance between the two free solid 

 angles of any two adjacent tetrahedra is too great for a third 

 tetrahedron of the same size to fit in, can not account for the 

 formation of double ring (A), and still less for the formation 

 of (B) or (C). 



In Graebe's model, on the other hand, any one of the three 

 pairs of tetrahedra, connected together through two of their solid 

 angles, can be rotated about the points, through which it is con- 

 nected with the two other pairs and, in this way, any two ad- 

 jacent free solid angles can be brought closer together until the 

 distance between them is equal to the length of an edge of the 

 tetrahedron, so that the fitting in of the third tetrahedron and, 

 with it, the completion of double ring (A) offers no difficulty. 



If, as the limiting case, three pairs of tetrahedra are supposed 

 to be rotated in the manner above described, model I would 

 coincide with model IV and the distance between the tAvo meta- 

 positions would become equal to the length of an edge of the 

 tetrahedron, which would render the completion of double ring 

 (B) possible. But, as already explained, formula IV can not be 

 reconciled with certain facts, and the formation of double ring 

 (B) must, therefore, be regarded as improbable. 



Again, even in the limiting case above supposed, the distance 

 between the tw^o free solid angles in the joara-position is too great 

 for the third tetrahedron to fit in between them, so that the 

 formation of double ring (C) is likewise rendered improbable. 



It thus appears that of all the space formulae hitherto pro- 

 posed, that of Graebe, which is nothing but a representation in 

 space of Kekule's well known formula, is in best agreement with 



