OF ARTS AND SCIENCES. 57 



sented in Fig. 1. Tliese I consider twins, for the following reasons : — 

 Faces of the form {001} w'cre striated parallel to the combination 

 edge (111) A (TTl), although but very faintly. The striation was 

 shown best by a spectrum which appeared when a crystal was ad- 

 justed for measuring the angle between the poles (001) and (111), 

 and this spectrum did not appear when the crystal occupied any other 

 position. Furthermore, if we assume for the moment that the draw- 

 ing. Fig. 2, is that of a simple crystal, the angle between the poles of 

 (OTO) and (001) will be 90° 4' 30", or the supplement of that between 

 (010) and (001). In fact, however, the following are the actual 

 measurements : — 



(100) A (001) = 89° 44' 30" ) (100) A (TOO) 



(001) A (TOO) = 90° 3' i" 179° 47' 30" 



(010) A (001) = 89° 51' 30" | (010) a (OTO) 



(001) A (OTO) = 89° 46' j 179° 37' 30" 



If, then, we consider the twinning-plane parallel to the form {110} 

 (not present on the crystals), by turning one half of the crystal 

 through 180°, the angle (OTO) A (001) =89° 46' will correspond to 

 (100) A (001) = 89° 44' 30". Again, the angle (THl) A (TTl) is 

 the same as that found for (311) A (^l^* Tn other words, the plane, 

 which appears in Fig. 2 as (T31), is the other member of the form 

 |311|, and lies opposite (311). 



The form (22) of Dana corresponds to what I call {311}. In no 

 instance were four similar planes of the form {311} to be seen on any 

 termination. 



In our projection of the poles of the faces. Fig. 3, the great circles 

 [001, 100] and [010, 100] sensibly coincide with the diameters of the 

 circle of the primitive. 



The drawing. Fig. 2, was made on the assumption that such crystals 

 were simple, and not twinned, as I have above described them. 



WHITE TOURMALINE. 



Specimens of White Tourmaline, from Dekalb, St. Lawrence Co., 

 N. Y., have been recently put on exhibition in the Mineral Cabinet of 

 Harvard College, and, being interested to know what planes were 

 represented on the crystals, I undertook the study of them. The 

 rhombohedral forms which were observed on the several crystals 

 are shown in Fig. 4, and also the table. 



