350 GEOLOGY OF THE EUREKA DISTRICT. 



nearly rectaugular in outline, or extinguished symmetrically with respect to the trace 

 of the brachypinacoid, gave from more than fifty measurements the following results 

 in sections where the basal cleavage varied not more than 5 from being at right 

 angles to the trace of the brachypinacoid; and in sections without cleavage, almost 

 rectangular, the angle of extinction varied from 30 to 43, in most cases being about 

 40. In sections with symmetrical extinction it was 25, 34, 36, 38, 40 that is, 

 in the zone perpendicular to the brachypinacoid the angles of extinction measured 

 from the trace of the latter plane reached 43 and were mostly greater than 31, 

 showing a part of the feldspar to be anorthite. 



The frequent occurrence in this andesite of nearly rectangular sections of twinned 

 crystals yielding both very high and widely varying angles of extinction led to 

 an investigation of the position of the axes of elasticity in the two halves of sec- 

 tions cut from Carlsbad twins of plagioclase in a zone at right angles to the brachy- 

 pinacoid (aoP*). From the nature of a Carlsbad' twin it is evident that the plane of 

 the optic axes in the two parts, being oblique with respect to the vertical crystallo 

 graphic axis in plagioclase feldspars, would be symmetrically disposed only with 

 respect to the vertical axis, considered as its axis of revolution; hence the extinction 

 angles for the two parts of the twin, that is, the angles on a cutting plane included 

 between the trace of its intersection with the brachypinacoid or composition plane 

 and the traces of its intersection with the planes of the optic axes, respectively, 

 would be symmetrical only for sections in the zone parallel to the vertical axis, that is 

 in the zone a>P<x, ooPdo; consequently in the zone at right angles to the brachy- 

 pinacoid there will be only one position where the extinction angles are symmetrical, 

 and that is in the section parallel to the vertical axis, while in a plane perpendicular 

 to it the extinction angles will be complementary, or equal when measured in the same 

 direction: that is, the axes of elasticity in the two parts will be respectively parallel, 

 but in all other sections of this zone they will be unequal. These relations, together 

 with the degree of variation in the extinction angles throughout the zone may be 

 graphically represented by the following diagram (Fig. 8), derived from the curves of 

 extinction angles of feldspars in the zone at right angles to the brachypinacoid pub- 

 lished by MM. Fouque et Levy. 1 The case of labradorite will serve as an illustra- 

 tion. Fig. 7 represents the projection of a Carlsbad twin of that species on the plane 

 of the brachypinacoid; let (a) be the half in the normal crystallogaphic position, and 

 (b) that in the twinned position, then it is evident that in considering a series of sec- 

 tions perpendicular to the plane of the brachypinacoid, if we pass from the position of 

 a normal to the edge OP, <xP* of the first half (a) in the direction of the obtuse angle 

 of that half, we at the same time pass from a position 52 from the normal to the edge 

 OP, ccPdo of the second half (b) in the direction of the acute angle of that half. In 

 Fig. 8 the heavy line is the curve of the extinction angles for sections of the first half 



1 Min^ralogie Micrographique, etc. 



