CALCITES OF NEW YORK 53 
4 Scalenohedrons (h k i 1) 
ae Sle 26 ier 2ink 
Cos X, (h kil: hikl) =~gay de (ht le + hk) 
A (inte Pistols BP + 2c°(2h' + 2hk—k') 
Cos Y, (hkil:ik hl) = 32+ de (h?+ ke + hk) 
De (ae se eae 4M) Ie 
ale ar aioe (la ar ecae lalkc)) 
h?) 
Cos Z, (hn kil:khil) = 
Goce (an ele MONG ye eee ee =o be Weal, 
(S20) 
3 (a 1 ale lO a |, (Se ee 
Fhe eee aD 
Cosn(nnicals000 1) ey ee 
Wrdlecis AC (a2 kee hike) 
The relation between X, Y and Z is expressed in the following equation: 
sin ; X +sin4 Y—cos 4 Z 
To find the Naumann symbol of any scalenohedron from measure- 
ments of any two of the angles X, Y and Z 
Fyaecos TLS On Oia COS >, (ISO YO) 
COSMOS Oe SO COs nS 0) ne) 
toe De Sinn S0 = Z) pie 
2 cos = (180 — X) Sim = (SO — Z) 
sec Si USO pam) 
Sia 2 80 =D) = Orcas PAS 
__ gaily (USO = ®) 
nV 3 
—cos— m=—cot — + 2.0274 
For the calculation of the coordinate angles employed in measurement 
with the two circle goniometer, as well as in the construction of the various 
spherical projections, the following formulas, adopted from Moses and 
Rogers! give the values of g and ¢ 
‘Moses, A. J. & Rogers, A. F. Formulae and Graphic Methods for Determining 
Crystals in Terms of Coordinate Angles and Miller Indices. Sch. of Mines Quar. 1902. 
290A 
