and Laboratory Methods. 



1225 



Both metals also yielded spherolitic aggregates with polyhedral facettes ; and 

 when the cooling was rapid showed confused, interlaced aggregates, with the 

 free surfaces of the globules remaining spheroidal. 



The " slipping figures " obtained with a needle point upon these facettes, 

 were also discussed, their hexagonal nature being undoubtedly proved. 



L. MCI. L. 



Goldschtnidt, V. Ueber Erkennung eines Zwil 

 lings. Zeit. f. Kryst. 30:346-351,1898. 



In previous numbers* reference has 

 been made to the two circle method of 

 measuring crystals and the gnomonic projection used in conjunction therewith. 

 It may therefore be of interest to see how these can be applied to the recogni- 

 tion of twinned crystals. 



The crystal is measured with 

 one individual in normal position, 

 with its prism zone normal to the 

 vertical circle. Symbols are ob- 

 tained for this individual in the 

 usual manner, and then for the 

 other either by comparison with the 

 first or by separate setting up and 

 measurement. The gnomonic pro- 

 jection is then made and the cor- 

 responding faces distinguished for 

 instance by a a, b b, c £, etc. If 

 the grouping is a twinning there 

 will be found a symmetry point j 

 at the intersection of the zones 

 connecting corresponding faces of 

 the two individuals, and this point 

 s will bisect the angle between any 

 two corresponding faces. Furthermore it will be the pole of an important face 

 or zone or, rarely, at 90° to such a face or zone. 



If the poles of two corresponding faces are superposed, then s is either coin- 

 cident with these or at 90° thereto. 



If the two poles, a />, of one individual coincide with two, a' b' , of the other, 

 then s is the pole of the zone a b. 



When it is not known ivhich points are eqiiivaletit several poles of the one are 

 connected by straight lines with one pole of the other, then all of the first to a second 

 point of second, then to a third point, and so on. If several lines go through a 

 common point, especially if it is the pole of an important face or zone, then the 

 test is made whether this point bisects the angle between the two poles on any 

 line. 



The graphic determitiation of this equality in angle, and indeed the graphic 

 measurement of the angle between any two faces in gnomonic projection, consists 

 in finding the stereographic projection of the pole of the zone of the two faces 



Vol. 3, Nos. 2 and 7. 



