54 A. C. Lane— Estimation of the Optical Angle 



Then if we let ^±1 . U -*--° =1 (see Mallard, p. 116) which 



a e -\-u ac x 



will make less than 1 per cent error we have from 1 and 2, 



o — ez=S(y — a) sin 0sin 0' (3) 



§ 2. In the rhombic system we must search for pinacoidal 

 sections. The brightest of these is parallel to y and a. Which 

 of the other two is | to a and /5 the determination of axial plane 

 and sign will settle. Then we may derive from (3), 



(o-e) ya =d(y-a) (4) tan'V=(o- g ) fl/? 



(o-e) a(3 =d(y-a) sin'V (5) (o-e) py (1) 



(o-e)^ = S(y-a) cos a V(6) ( - e ) a/j+ (o-«)^ .. = (o-c) ya (8) 



Equation (7) is the best to find Y, but if the observations 

 are adjusted to satisfy (8), which serves as a check upon our 

 accuracy, either (5) or (6) may be used. 



For example we may pick out the required sections in 

 hypers thene by some of the following marks : 1) \ya oue 

 cieavage direction, ext. +o, brightest polarization colors, ple- 

 ochroism green to red brown, prismatic form with flat dome, 

 no axial image. 2) \yft only one cleavage direction, ext. +0, 

 lowest polarization colors of any such section, pleochroism yel- 

 lowish-brown to green, direct emergence of bisectrix. 3) | a/3, 

 two cleavages nearly at right angles, diagonal ext., quadratic 

 forms, pleochroism .yellowish-brown to reddish-brown. If we 

 meet, in a mineral of any cry stall ographic system, sections 

 which prove by use of convergent light to be principal sections, 

 we may of course use them. This often happens in mica. 



§ 3. In monoclinic minerals we handle but two cases : (a) the 

 elongation is parallel to ft\b. Then if a large enough number 

 of cases be taken, 



No. of cases in which the elongation is -f- — 2 V 



No. of cases in which the elongation is — -J-2V 



But practically in applying this to the commonest case, 

 epidote, we find that in many rocks the elongation is almost 

 always—. This is because the crystals are really tabular 

 through large sized (100). I note in passing, that contrary to 

 Rosenbusch's experience, I find the orthopinacoid (100) the 

 most important face of epidote, one easily recognized too, by 

 the yellow color of c nearly perpendicular 'to it, and frequently 

 by the twinning. 



b). The elongation lies in the axial plane ay (hornblende 

 augite, etc.) In this case sections directly across or parallel 

 to the elongation must be used. 



