456 On Crystallography. 



in a word, to seize as if at one glance the diversity of the 

 details and the unity of the wliole. 



Let us suppose that fig. 48 represents an oblique-angled 

 parallelopipedon, the angles of which have different mea- 

 surements, and which is the primitive form of a particular 

 species of mineral, such as feldspar*. 



Having adopted the vowels to designate solid angles in 

 general, place the first four A, E, I, O, to the four angles 

 of the upper base, following the order of the alphabet, and 

 at the same time that of common writing, which is to be- 

 gin at top and go from left to right. Vide fig. 49, in which 

 the arrangement of the letters is rendered perceptible to 

 the eye. 



Having adopted the consonants to distinguish the ridges 

 in general, place, according to tlie same rule, the first six 

 B, C, D, F, G, H, on the middle of the sides of the upper 

 base (fig. 48), and on the two longitudinal ridges of the 

 lateral face which is first presented from right to left. 



Finally, place on the middle of the superior base, and of 

 the lateral faces situated in front, the three letters P, M, T, 

 which are the initials of the syllables composing the word 

 primitive. 



Each of the four solid angles, or of the six edges de- 

 signated by letters, is susceptible in the present case, on 

 account of the irregular form of the parallelopipedon, of un- 

 dergoing particular laws of decrements: letAp (fig. 50) 

 be the same parallelopipedon. If we compare the two solid 

 angles diametrically opposite to 0,?', it is easy to see that 

 there is an equality between the plane angles which com- 

 pose them, taken by pairs, \*iz, : 1st, between E 01 and 

 s r u ; 2d, between EOp and ur A; 3d, between I Op and 

 s r A. It results, that among the plane angles which are 

 joined by threes round solid angles A, O, there are only 

 two w)>ich are equal, viz. EOT, I AE, as being opposite 

 on one and the same parallelogram j but the angle E Op is 

 the supplement of the angle I A r, and the angle I Op is 

 that :,f EAr, In the same way the solid angles I, s are 

 composed of equal plane angles two and two ; but 

 among the plane angles formed by the solid angles 

 E, I, there are only A 10 and AEO which are equal. 

 Hence it follows, that the solid angle O being in a situa- 

 tion different from that in which the solid angle A is, and 

 the same difference taking place with respect to the solid 



• The parallelopipedon is considered as beinj; represented in such a man- 

 ner that the angle BAG which is the furthest from the observer, is one of 

 the obtuse angles of the upper base. 



angles 



