222 MB HAIDINGER on the Forms of Crystallisation 



If we designate AP by a, MB by b, MC by c, MP by d, and, 

 moreover, call y and y the terminal edges AB and AB' conti- 

 guous to b, x the terminal edge AC, contiguous to c, and z the 

 lateral edge BC, which joins the two diagonals of the base, b and 

 c with each other, we obtain the following formula; : 



COS / = 



cos y = 



COS X = 



COS Z = 



tang MAP = 

 tang BAP = 

 tang B'AP = 

 cos CAC' = 



a 2 (6 2 + c 2 ) + c 2 (6 



^^^ + (& + d)*O(*(&* + c s ) + (& < 



v'L (* (6 2 -f c 2 ) + (6 + d)* c 2 ) (a 2 (6 2 + c 2 ) + (6 



d - 



a ? 



6 + rf 

 ~^~~ ; 



S d 



cos CBC' - 



A* + 



The ratio of the lines a:b:c:d, which gave a result agree- 

 ing nearest with observation, was that of 120 : 95 : 54.5 : 1. The 

 values of a = 120, b =. 95, c = 54.5, and d= 1, being substituted 

 in the above-mentioned formulae, give the dimensions of the fun- 

 damental form as follows : 



p = 



QR> \ 



10 } ; 



7 ; 137 



72 10 



Moreover, we have the angle of inclination MAP 29' ; 

 BAP = 38 40' ; B'AP = 38 4' ; CAC' = 49 51' ; CBC ; = 

 59 40'. 



