226 MR HAIDINGER on the Forms of Crystallisation 



It will now be easy to determine the relation of the simple 

 forms which enter into the combination Fig. 3. ; those under 

 which it is principally contained, being known from the pre- 

 ceding varieties. 



The face i is determined, by immediate measurement, to be- 

 long to the horizontal prism, which truncates the terminal edge 

 of the pyramid P 1 (g) ; and those faces which appear in the 



II 



combination, will therefore be designated by Fr ~ 1 . The incli- 



IB 



nation of i to a is 147 52'. For the development of the pyra- 

 mid k, we have two data in the situation of the edges produced in 

 intersecting the faces of other forms. From the parallelism of the 

 edges between P and k, k and h, h and f, &c. it follows, that the 

 terminal edge of k, corresponding to the long diagonal of P, has 

 exactly the same inclination to the axis as the analogous edge of 

 that form. From the parallelism between k and g, and g and m, 

 it appears, that the other terminal edge of k, which corresponds 

 to the short diagonal of P, has the same inclination to the axis as 

 the analogous edge of P 1 ; and the result of both these obser- 

 vations is, that the ratio between the lines a' : b' : c' in the pyra- 

 mid k, expressed by functions of the analogous lines in the funda- 

 mental form, will be a : b : 2c ; or ^ : b : 2c, which corresponds to 



the crystallographic sign ^ Fr ~ 1 ^ The edge in which two faces 



k and k intersect each other, is = 111 32'. Of the three hori- 

 zontal prisms /, m, and n, contiguous to the short diagonal of P, 

 only m can be determined from the situation of the edges of com- 

 bination between m and g ; it is Pr 1 = 84 30'. Immediate 

 measurement was resorted to, for ascertaining the dimensions of 

 the other prisms, which were found to be / = Pf 2 = 122 20', 

 and n = f Pr = 62 24'. The inclination of / to a is = 151 10'; 

 of m to a = 132 15'; of n to a 121 12'. The scalene four- 

 sided pyramid, to which belong the faces o, o, is perfectly deter- 



