CALIFORNIA ACADEMY OF SCIENCES. 11 



just visible with a hand lens, and was recognized by the two 

 zones c (P a) : c ( ? oo) and s (oo P) : od (— 3 P 3). The faces 

 of a are almost invariably among the most largely developed of 

 the terminal planes. 



y (P) is never absent and varies greatly in size under the cir- 

 cumstances explained on p. 7. It is sometimes strongly stria- 

 ted parallel to the edge y : d, resulting from an oscillatory com- 

 bination with r (| P §). In one instance this striation is quite 

 coarse, so that its cause is easily determined. At other times it 

 is so extremely delicate as to be nearly invisible even with a lens, 

 and again is absent altogether. 



v (2 P), the only other positive hemi-pyramid determined*, is 

 constantly present and large. 



Of the negative hemi-pyramids of the vertical series, b ( — P) is 

 nearly always present either as a narrow face on the edge g 

 (0 P) : s (oo P) (Fig. 1, PI. I.) when g (0 P) is large, or as a 

 more triangular face when g is small or absent, (Fig. 3, PI. I.) 



a ( — 3 P) (Fig. 4, PI. II.) was found on four crystals, in three 

 very small on the edge s (co P) : b (— P) and on the fourth with 

 one of its faces considerably developed and the other absent. It 

 is determined by the two zones s (oo P) : b ( — P) and I (oo P 2) : 

 y (P). For s : <r, the angles 161° 21' ca. and 161° 38' ca. (cal- 

 culated 161° 29i') and for b : a, 158° 12' ca. 158° 31', 158° 22' 

 ca. (calculated 158° 24f) were obtained. 



^ ( — _Y- p) (Fig. 9, PI. Ill ) was found on but a single crys- 

 tal. The adjacent face of s (oo P) was broken into several sub- 

 individual parts, but it was easy to identify the reflection from 

 that portion of s immediately adjacent to /\\ it was quite sharp, 

 and admitted good adjustment. The reflection from [\ was sin- 

 gle, and somewhat blurred at the contact of the two discs which 

 formed the signal. Three readings from it agreed to within 15", 

 so that the angle s : /\ = 162° 19' must be regarded as correct. 

 It is practically identical with the calculated value 162° 19' 5" for 

 A = — -V- P. One would be inclined to favor the simpler symbol 

 — 3 P, and regard A as identical with ff ( — 3 P). But the angle 

 s (oo P) : a ( — 3 P) = 161° 29|' is too far from the observed angle 



*See Appendix II. 



