52 NEW YORK STATE MUSEUM 
which are the supplements of the true interfacial angles between the faces 
measured. The general formula for the normal angle between any two 
faces P==(h kil) and P’==(h’ k’ i’ l) expressed in terms of the Bravais-Miller 
indexes is: 
Oe Pw lla (ae ap bela ap 2a ln ae 2 Ie Ik) 
VBE 44e (he +e +hk)] [Ie + 4c? (A? +k? +h k)] 
in which c==0.8543 
This general formula becomes much simplified for the special cases 
involving the angles between faces of the same form or between the faces of 
any given form and those of the basal pinacoid. prism of the first and second 
order and unit rhombohedron. ‘These modified formulas are as follows: 
1 Dihexagonal prisms (h k i 0) 
; h? + k?+ 4hk 
Cos X (axial) = 57h 4124 hk) 
Zh? + Qhk—k? 
2 (ae eal) 
3(h + k) 
VW (a(he Fie? +e ink) 
27 (hia ke) 
V (4c? (h? + ke + hk)]X 5.9193 
2 Pyramids of the second order (h. h. 2h. 1) 
Cos Y (diagonal) = 
“ Cos @u20 ani <te)— 
Cos lOMaain ato) p= 
P+ 2¢?h? 
Cos ive Gerinatial) Seas 
os Y (terminal) P+ deh 
_ 4¢?h’—P 
Cos Z (basal) = 4 4ck 
Bls= ine”) 
V 3(2 + 4h?) X 5.9193 
Cos (1011: h.h.2h.1) = 
3 Rhombohedrons (h 0 h 1) 
2829 h??? 
: Cos X (terminal) = ee 
Oe aaa 
Tan (0001:ho hl) = 5X .986447 
