VOL. LXXXVIII.] PHILOSOPHICAL TRANSACTIONS. 371 



time, and in the same proportion, it is easy to conceive that the height of the 

 hexaedral prism must be the same as that of the rhomboidal parallelopiped, on 

 which it has been formed. The height bc (fig. 1,) must therefore bear the same 

 proportion to the line ab, drawn through the middle of the 2 opposite sides of the 

 planes on the extremities, as the whole height ep, of the rhomboidal parallelopiped, 

 (fig. 2,) bears to the small diagonal gh, from one of the rhombs; that is, nearly 

 as 6.45 to 5. 



But though this exact proportion appears in a very great number of corundum 

 crystals, yet we meet with some whose lengths are more or less considerable; and 

 this is owing to different circumstances which have existed at the time of their 

 crystallization. We may conceive, for instance, that if, before the progressive 

 decrease of the crystalline laminae, in the manner above-mentioned, the increase 

 of the rhomboidal parallelopiped had taken place by a superposition of laminae, in 

 which the rows of crystalline molecules experienced a progressive decrease along the 

 edges of the acute angle of the base only, (fig. 6,) and that, the sides of the 

 prism having already acquired a certain length, the succeeding crystalline laminae 

 had experienced a decrease at the acute angle of the summit, the same regular 

 hexaedral prism would have resulted from this process; but the proportion between 

 the height and the line drawn from 2 of the opposite sides of the planes on the 

 extremities, would have been much greater than that of 6.45 to 5 ; and conse- 

 quently this prism would have been longer than that of the rhomboidal parallelo- 

 piped which served as its nucleus. 



On the other hand, if the increase of the rhomboidal parallelopiped had taken 

 place by a superposition of crystalline laminae, decreasing at the acute angle of the 

 summit, and some time after decreasing also along the sides of the acute angle of 

 the base, (fig. 7,) the regular hexaedral prism resulting from this process would 

 have been shorter, in proportion to the duration of the mode of decrease in the 

 crystalline laminae which were first deposited. There are some of the hexaedral 

 prisms, in corundum crystals, which are so short, that they appear no more than 

 segments. Calcareous spar offers the same phenomenon ; as do likewise all the 

 substances in which the hexaedral prism has any analogy of formation with that 

 which we have here described. 



It happens frequently, when the superposition of the crystalline laminae does 

 not go on equally on all the faces of the rhomboidal parallelopiped, that 1 or 2 

 only of the solid angles of the hexaedral prism, taken alternately, still show, by 

 small isosceles triangular planes, some remains of the faces of the parallelopiped, 

 while the others do not show any at all. Mr. Greville, in his collection of this 

 substance, has a crystal of corundum on one side of which, only 2 of the planes 

 of the rhomb have experienced an equal and perfect superposition, while there has 

 been but a very small number of crystalline laminae deposited on the 3d plane. 

 Consequently, this crystal presents a regular hexaedral prism, one of whose solid 

 angles is so much truncated, that the half of the plane of the end of the hexaedral 



3b 2 



