378 Prof. Miller on a new Locality of Phenakite. 



then taking i any integer number not exceeding /u,, the (m + t)th 

 evectant of the discriminant will contain the factor (ax + by)^ 1 . 

 So that, for instance, if there be but a single group of equal 

 roots, and they be 1 +//, in number, every evectant up to the 

 (/a— l)th inclusive will vanish, and from the /xth to the (2/a— t)th 

 will contain a power of (ax + by)". 



LV. On a new Locality of Phenakite. 

 By Professor Miller of Cambridge*. 



IN the Supplement to the sixth volume of the Bibliotheque 

 Universelle de Geneve, page 299, M. Marignac describes a 

 supposed crystal of tourmaline exhibiting new forms in the fol- 

 lowing words : — 



" Les cristaux de tourmaline dont je vais decrire les formes 

 ont ete observes sur un echantillon provenant probablement du 

 Dauphin e, et portant des cristaux de quartz et cPanatase. lis 

 offrent de petits prismes a douze pans stries longitudinalement, 

 parfaitement hyalins et incolores, rayant facilement le verre, 

 mais non le quartz," et inalterables an chalumeau. Un seul 

 sommet est visible, P autre etant engage dans la gangue; ce 

 sommet presente au moms trois systeines de facettes dont aucun 

 ne correspond aux modifications qui ont ete decrites, a ma con- 

 naissance du moins, dans la tourmaline, bien qu'ils derivent par 

 des lois simples du rhomboedre primitif de cette substance." 



The angles of tbe forms described by M. Marignac approach 

 closely to those of phenakite. For e, e', e" being three faces of a 

 rhombohedron of phenakite truncating the edges formed by the 

 intersections of the faces r, r', r" of another rhombohedron of 

 the same mineral, the angle between normals to ee 1 , according 

 to Beirich's measurements of good crystals from Framont, is 

 35° 56', and between normals to r? J , 63° 20', the corresponding 

 angles in Marignac's crystal being 36° 0' and 63° 30'. The 

 third form described by Marignac is the regular six-sided pyramid, 

 the faces of which truncate the edges in which the faces of the 

 rhombohedrons e, e', e" ; r, r', r" intersect each other. The lim- 

 pidity and absence of colour are favourable to the supposition 

 that the crystal is phenakite, though in hardness it appears to 

 be a very little inferior. Should it on further examination prove 

 to be phenakite, it may possibly lead to the discovery of a new 

 locality of that mineral, and will increase the probability of find- 

 ing it in existing collections formed prior to the discovery of the 

 mineral in Siberia and Alsace. It will also show the name 

 phenakite, from its deceptive appearance, to have been very hap- 

 pily chosen by Von Nordenskiold. 



* Communicated by the Author. 



