500 Mr. FoESTER on the Molecular Formation of Crystals. 



we have mentioned are clearly the most likely to happen, and they are those 

 which have been found in nature. 



Cases in which hemitropism has occurred, and where the crystal has cubi- 

 cal cleavage, have been already explained by Dana. As, however, his theory 

 could not account for the octahedral or dodecahedral formation, it could not 

 possibly show how such crystals might be subject to hemitropism. I trust that 

 I have shown that the theory which I have put forward is not wanting as 

 regards this test. 



In Fig. 19 is given a representation of a crystal of spinel in which compo- 

 sition has taken place parallel to two octahedral faces. Fig. 20 represents a 

 dodecahedron in which composition has taken place parallel to an octahedral 

 face. These may be taken as instances of twin formation, where the parts 

 together make up only one crystal. There is, however, another descrip- 

 tion of crystals which have been generally placed in the same category, namely, 

 those in which the complete parts of two crystals appear. There does not 

 seem to be any reason why these should be classed as twin crystals at all, 

 except to preserve the rule that simple crystals are never foimd with re-entrant 

 angles. In Figs. 21, 22,* instances of this sort of formation are shown ; 

 they can evidently be explained on the very same principle of decrements as 

 all other secondary forms. These hemitrope forms are known to be very 

 numerous : to enumerate all of them would be both tedious and unnecessary. 

 I shall content myself with one example illustrative of the cases in which 

 Dana's hypothesis fails, and where it is necessary to suppose the existence of 

 twelve poles. In Fig. 23 is shown a crystal of copper pyrites, which evidently 

 consists of six octahedra united by their extremities. It is not possible to 

 conceive how six of Dana's molecules could unite in this manner ; but it will 

 readily take place when the poles are disposed as shown in Fig. 16, the four 

 poles at the extremities of the molecule uniting in this position. It is also to 

 be remarked, that the cleavage in this case is octahedral. 



On a subject so vast much must remain unsaid ; but I trust that, although I 

 may not have reviewed every case, there is no important class of phenomena 

 which cannot be brought under the hypotheses which I have advanced. 



* These figures have been taken from the first volume of Brewster'8 "Edinburgh Journal," 

 where they are appended to a most able Paper on Twiu Formation, by Haidinger. 



