363 PHILOSOPHICAL TRANSACTIONS. [ANNO 17Q8. 



culation and measurement, we may admit the laws of crystallization ; for whenever 

 the superposition, or subtraction, of simple or compound molecules on a nucleus, 

 shall by calculation give a series of planes and angles, which corresponds exactly to 

 the angles and planes measured on natural crystals, it will amount to no more nor 

 less than a demonstration of the rule or arrangement of elective attraction by 

 figures. These laws may be reduced to simple practice; for instance, the Abbe 

 Hauy, by measuring the rhombic plane of corundum, found its 2 diagonals to be 

 as 2 to 3; which gives to its acute angle 81° 47' 10", and to its obtuse angle 

 98 12' 50 // ; the same as martial vitriol*. The forms of fragments in corundum are 

 all acute rhomboids. The cosine of the little angle in corundum is -f of the radius; 

 but in calcareous spar the cosine is -l of the radius; in short -f- of the radius; in 

 the garnet \ ; and in rock crystal -fr 



Thus the application of general laws, to ascertain constant character, after they 

 shall have been fully verified, may be very simple and general. It will not require 

 perfect crystals; for when crystals separate into laminae, which subdivide into frag- 

 ments, and show the form or arrangement of their molecules, it is easy, from such 

 fragments, to connect them with primitive crystal, and consequently with their 

 class. It will be a great step, to obtain one regular and permanent external cha- 

 racter. Attention to other characters will be necessary to ascertain the nature of 

 the substance ; and other external characters, such as irregular fracture, colour, &c. 

 must be resorted to, where no permanent characters exist; but from their nature 

 they are fallible, and in fact are seldom conclusive. 



The progress of crystallography appearing to me of consequence to the progress 

 of mineralogy, induced me to desire the Count de Bourbon, above-mentioned, one 

 of the honourable victims to his allegiance to his King, to describe such crystals, 

 in my collection, as showed the different known modifications of corundum; 

 which will develope the theory of crystallization, so far as is consistent with the 

 avowed object of this paper. The subject, I believe, has not hitherto been sub- 

 mitted to the consideration of the r. s. The translation of the Count de Bour- 

 bon's description has been carefully made to preserve its clearness, and I hope it 

 will be favourably received by the Society, and make some amends for my tedious 

 introduction. After it, I have added a table, connecting in one view the specific 

 gravities of corundum, &c. herein mentioned, with those given by other authors. 

 An Analytical Description of the Crystalline Forms of Corundum, from the East 

 Indies, and from China. By the Count de Bourbon. 



The most usual form of corundum is a regular hexaedral prism, (pi. 6, fig. I ;) 

 in general, the surface of the crystal is rough, with little lustre, owing to unfavour- 

 able circumstances under which it crystallized. The crystals of corundum hitherto 

 found were not formed in cavities, where each crystal being insulated, its surface 



* This result is extracted from the Joum. de Phys. j but it appears, from the Joum. des Mines, N° 28, 

 that the Abbe Hauy has since rectified this measure, and given 86° 26 v for the acute angle, and 93° 34' 

 for the obtuse angle. — Orig. 



