. 144. OF COMBINATIONS. 159 



required the knowledge of the angles at which the 

 faces of different forms intersect each other, or of 

 the edges of combination. 



In every particular case, the magnitude of the edges of 

 combination may easily be calculated from the dimensions 

 of the simple forms. There is, however, also a general so- 

 lution of this problem, effected in every system by the same 

 number and kind of equations as those for the Line of 

 Combination.* Those parts by which the simple forms 

 are determined, enter into these equations as variable quan- 

 tities, whose real value is found by the developement 

 (. 143.). These values being substituted instead of the 

 variable quantities, we obtain trigonometrical functions for 

 the Edge of Combination. 



The application of these equations pre-supposes the di- 

 mensions of one of the forms to be known. These dimen- 

 sions must be found by immediate measurement, whenever 

 the form belongs to one of the systems whose dimensions are 

 variable. If in a species one of the forms, for instance, the 

 fundamental one, is known in respect to its dimensions, no 

 new measurement is required for the combinations of this 

 species, provided the situation of the edges contain suffi- 

 cient data for their developement. Hence it appears that 

 we must endeavour to ascertain the dimensions of the fun- 

 damental form, with the utmost accuracy, but at the same 

 time also that the measurement of different forms of the 

 same series may be useful in correcting each other. This 

 subject, however, will be treated of more at large in the 

 Elementary Treatise on Crystallography. 



The designation of compound forms must be founded 

 upon the relations of the simple forms among each other. 

 It will therefore be sufficient to indicate, by their peculiar 

 signs, the simple forms, in order to express the combinations 



* Gilbert' s Annalcn, 1. c. 



