56 A. G. Lane — Estimation of the Optical Angle 



one cleavage direction, with maximum extinction of the prism 

 zone, with highest polarization colors, and often with charac- 

 teristic pleochroism. (These give d(y—a)). 2) Prismatic, with 

 one cleavage direction, extinction o with lowest colors of the 

 prism zone, and characteristic pleochroism (gives d(f—ft). 3) 

 Across the prism, with two equally developed cleavages at an 

 angle of about 56°, -f extinction bisecting the acute angle, and 

 characteristic pleochroism. These give d(a'—j3). When twin- 

 ning exists it also helps in selection. 



In estimating the order of an interference color between X 

 nicols, if the natural color interferes, it often is better to raise 

 and lower the color a wave length or so and take the mean of 

 the orders thus obtained. This may be done with a mica or 

 gypsum plate, for it is hardly worth while to use the com- 

 pensator. 



To illustrate the application of equation 12. In 11670,* a 

 hornblende schist, we have a hornblende with pleochroism, c 

 sea-green, b brownish-green, a yellow and sections whose colors 

 indicate the following double refractions : 



6{a'-& y-p, 



-300 

 300 

 350" 

 300 

 260 



-303 

 mean 



+ 125 

 175 

 150 

 175 



155 



-303 



458 



y—a) 

 + 400 



350 



420 ) 



to 520 i" 

 420 [ 

 680 \ 



c: c 



+ 420 + 

 maximum 



I 



16- 

 13 



13 

 16 



19 

 15 

 15 



19 



tr 



170 



Remarks. 



Twin, 6(y—a) for epidote runs up to 1400 

 " " orthoclase " 275 



Twin, 



apatite 



125 



Twin, varying shades, the lighter color the 



greater y—a 

 Twin, " " 



applying eq. 13. 



420(cos 34°=0-829)=348 < 458 



By eq. 12 

 cos 2v=- — 155 



458 



•829=-0'28=cos 106 c 

 .-2V=74° 



Of course the required sections are never exactly found ; we 

 use the nearest approach to them we have. In the example 

 above the un symmetrical extinction shows that there is an 

 error in y—a. Now while any error in the «'/9 and y'fi 

 sections is about as likely to give us higher colors as lower, 

 so that the mean of different observations should be taken (if 

 d is constant), errors in determining y—a will make it' too 

 small. Thus the largest value should be chosen and even 

 then it will be too small. Eq. 13 will show the discrepancy, 

 which serves to measure our error. , As we have the equa- 

 tion of condition (13), a connection between y—a and 2^>, 

 different degrees of liability to error in finding the given 



* The numbers refer to sections of rocks belonging to the collection of the 

 Michigan Geological Survey. 



