278 



NOTES TO BOOK XV. 



(L.) p. 242. MY Memoir of 1825 depended on the 

 views of Haiiy in so far as that I started from his " primi- 

 tive forms ;" but, being a general method of expressing all 

 forms by co-ordinates, it was very little governed by those 

 views. The mode of representing crystalline forms which 

 I proposed seemed to contain its own evidence of being 

 more true to nature than Hatty's theory of decrements, 

 inasmuch as my method expressed the faces by much lower 

 numbers. I determine a face by means of the dimensions 

 of the primary form divided by certain numbers ; Haiiy 

 had expressed the face virtually by the same dimensions 

 multiplied by numbers. In cases where my notation gives 

 such numbers as (3, 4, 1), (1, 3, 7), (5, 1, 19), his method 

 involves the higher numbers (4, 3, 12), (21, 7, 3), (19, 

 95, 5). My method however has, I believe, little value as 

 a method of " calculating the angles of crystals." 



M. Neumann, of Konigsberg, introduced a very con- 

 venient and elegant method of representing the position of 

 faces of crystals by corresponding points on the surface of 

 a circumscribing sphere. He gave (in 1823) the laws of 

 the derivation of crystalline faces, expressed geometrically 

 by the intersection of zones, (Beitrage zur Krystallonomie.) 

 The same method of indicating the position of faces of 

 crystals was afterwards, together with the notation, re- 

 invented by M. Grassmann (Zur Krystattonomie und Geome- 

 trischen Combinationslehre, 1829.) Aiding himself by the 

 suggestions of these writers, and partly adopting my 



