18 jr. E. Ford — Remarkable Tioins of Atacamite. 



indiflferent quality of the faces could easily account for. The 

 relations existing between the two individuals is shown in the 

 stereograpliic projection, figure 4. 



In order to bring the two individuals into their respective 

 positions, i. e., e' of No. II into the prism zone of No. I, we 

 have to conceive of individual No. II as being turned about 

 the pole of e(Oll) as an axis through an arc of 112° 40'. This 

 is the fact that makes these twins unusual and difficult to ex- 

 plain. The arc of revolution of a twin crystal about a twinning 

 axis is usually 180° or sometimes 120°. On account of this 

 peculiarity we cannot consider, at least in the usual sense, either 

 the plane e, although it is common to the two individuals, as a 

 twinning plane nor its pole as a twinning axis. The plane 

 whose pole is lettered P on the stereographic projection, and 

 which is shown as the plane of junction of the two individuals 

 in figure 3, would answer to the ordinary definition for a twin- 

 ning plane. The twinned half of the crystal could be obtained 

 from the normal half by reflection over this plane, as is shown 

 in the stereographic projection, for upon a great circle drawn 

 from any face of individual No I through the pole P will be 

 found at an equal angular distance on the other side of P, the cor- 

 responding face of the twinned individual. No. II. But this 

 plane P does not correspond in its position to any crystal face 

 on atacamite, falling nearest to the possible pyramid (i75). 

 The proof of the law of twinning as stated lies in the follow- 

 ing tables of measured and calculated angles. The crystals 

 were measured on both the two-circle and one-circle goniom- 

 eters, the angles obtained on each being given. 



1. Angles measu.i'ed on the two-circle goniometer giving the 

 position of the faces of the twin individual. 



Faces 



of 

 No. II 



Measured 



Calculated 



m 



<p 





Avei 



age 





P 



Aveiage 



<!> 



P 











36° 



58'* ^ 



















36 



50 



















37 



16 



> 36° 



50' 



0° 0' 



36° 55i' 











36 



45 



















36 



24 











62° 29'* 



•^1 







90° 



1'* 1 











63 1 

 62 12 



'• 



62° 



46' 



90 

 90 



38 

 21 



> 90° 



6' 



02° 25' 



90° 0' 



63 22 



^ 







89 



24 











8° 59'* 



^ 







34° 



31'* ^ 











8 44 

 11 38 



1 



10° 



20' 



31 

 34 



44 

 1 



. 33° 



24' 



8° 47' 



33° 57' 



12 1 



J 







33 



21 J 











