54 NEW YORK STATE MUSEUM 
1 Dihexagonal prisms (h k i 0) 
il = la 
CATO allege arn ars 90 
2 Pyramids of the second order (h. h. 2h. 1) 
9 —— 30% 
h 
raneon—— be 
3 Rhombohedrons (h o h 1) 
ae tan 9 = 1.1547 re 
4 Scalenohedrons (k k i 1) 
a es tan peo 
ae la 1 “cos (30 — ¢) 
In many instances it will be found that the above formulas do not lend 
themselves to logarithmic solution. For such cases the following multi- 
plication table of constants will be found useful. 
Caine =i—elevaoe, 
Cc 2c 2c? 4c? V3 |1.1547Xe} 2.0274 5.9193 
1 . 8543 1.7086 1.4597 2.9193 1.7321 . 9865 2.0274 5.9193 
2 | 1.7086 3.4172 2.9193 0.8386 3.4641 1.9730 4.0548 | 11.8386 
3 | 2.5629 59.1258 4.3790 8.7580 | 5.1962 2.9594 6.0822 | 17.7579 
4 | 3.4172 6.8344 5.8386 | 11.6773 6.9282 3.9459 8.1096 | 23.6772 
5 | 4.2715 | 8.5430 7.2983 | 14.5966 | 8.6603 4.9323 | 10.1370 | 29.5965 
6/5) 12589| 10" 25116 8.7580 | 17.5159 | 10.3923 5.9188 | 12.1644 | 35.5158 
7 | 5.9801 | 11.9602 | 10.2176 | 20.4352 | 12.1244 6.9053 | 14.1918 | 41.4351 
8 | 6.8344 | 13.6688 | 11.6773 | 23.3546 | 13.8564 7.8917 | 16.2192 | 47.3544 
9 | 7.6887 | 15.3774 | 13.1369 | 26.2739 | 15.5885 8.8781 | 18.2466 | 53.2737 
log.| 1.93161 . 23264 . 16426 46528 . 23856) 1.99408 . 30694 11227 
METHODS OF REPRESENTATION 
The various methods employed for presenting to the eye the relations 
between the faces developed on a given crystal may be included under 
three heads: 
t Spherical projections, which are purely diagrammatic and which 
represent by means of groups of points projected upon a plane the relative 
