Prof. Miller on the Form of Rut He. 269 



of the two crystals, the observed values of p' p m were 65° 

 34'24"-36"— 51" -27"; those ofpp" were 65° 34' 27" --53" 

 -25"— 35". The values of p 1 f l 9 pp" given by the second 

 crystal, agree very well with each other, and with the larger 

 of the two values of pp" given by the first. The mean of 

 these three, 65° 34' 32", will probably be very near the truth. 



The sphere of projection (fig. 2.) exhibits the poles of all 

 the faces observed by Mohs and Levy, as well as by myself. 

 The symbols of the simple forms are 



g {110}, h {210}, I {100}, 

 r {320}, x {410}, c (001 }> 

 p {101}, s {III}, e { 310 }, ■ 

 M {321}, t {313}, u {710}. 

 The calculated angles between normals to the faces are 



IV 90° r lr 33°41' p p' 45° 2' 



Ig 45 cl 90 ss 1 56 52 



lu 8 7*8 cp 32 47*3 pt 10 14 



7# 14 2 cs 42 20 W 20 46 



7 e 18 26 c7 34 10*6 2? z" 61 14'8 



7 7* 26 33*9 cz 66 42*3 p^ 41 43*3 



& is the intersection of the zone circles £>p"', sp' f 9 cr; t is the 

 intersection of the zone circles p V 9 c e. 



Of the crystals above-mentioned, one is a combination of 

 the simple forms having the faces 7, g, //, e, p, s : the other of 

 those having the faces g 9 h 9 <?, u 9 p, s ; t was observed by 

 Levy {Description dHune Collection de Miner aux). 



In the collection of minerals presented to the University 

 by Professor Whewell, a crystal occurs which is a combina- 

 tion of the forms having the faces 7z, c, r, p, z 9 and also others 

 which are combinations of the forms having the faces x 9 p 9 

 and occasionally c, 7, g 9 h 9 e. Among the latter are several 

 twins (fig. 3.), in which the faces c p 9 c t p i9 are all in one zone, 

 and the angle between normals to c c p rather more than 55°. 

 On account of the unevenness of the faces, this angle could 

 not be accurately measured ; if the twin plane were parallel to 

 a plane v 9 the pole of which is the intersection of the zone 

 circles zz" 9 cl 9 the symbol of v would be (301), cv = 62° 

 38 /# 4, cc { — 54° 43'*2. Hence probably the twin plane is 

 parallel to a face of the form {301}. The twins of most usual 

 occurrence are those described by Haidinger (Edinburgh 

 Journal of Science, vol. hi. p. 62.). Mr. Brooke measured the 

 angle between the faces ll i (fig. 4.) of one of these twins in 

 his collection, and found that it agreed perfectly with the sup- 

 position that the twin plane was parallel to one of the faces p. 



