Petrographic Microscope Work. 81 



Similarly for the direction OC (NC = NB) in the plane of 

 the obtuse bisectrix we find 



A c 1 — sin 2 r sin 2 V 

 A N cos r 



(8) 



From the last two equations it is evident that for Y = 45°, 

 the path difference in the two quadrants at B and C is the 

 same. For the small angles r (< 20°) which enter into the 

 problem we may write without appreciable error 



A^ 1 - r 2 sin 2 Y 

 A N " 1 -J^ 



9 



an expression which becomes, for Y = 45° 



r 

 Ab_ = 2_ = 1 



An I _ r » 



2 



For the direction OB the path difference is identical with 

 that for ON when the optic axial angle is exactly 90°. The 

 same relation obviously holds true for the direction OC. In 

 other words, the interference color remains unchanged and 

 covers the entire field. If now Y decreases, equation (7) obvi- 

 ously becomes less than unity while equation (8) increases in 

 value and is greater than unity. The interference color falls, 

 therefore, in the direction of the acute bisectrix and rises in the 

 direction of the obtuse bisectrix except for the case 2Y= 90°, 

 where the interference color remains unchanged and the entire 

 field appears isochromatically illuminated. — Both experiment 

 and theory thus disprove Schneiderhohn's statement. His 

 rule,* furthermore, for distinguishing sections perpendicular 

 to the optic normal from sections perpendicular to the obtuse 

 bisectrix by noting that, in the first case, the interference colors 

 fall in all directions, while in the second they fall in one quad- 

 rant and rise in the adjacent quadrant, is likewise invalid. 

 Equally incorrect is the assertion that the eye circle stop 

 (Schieberblende) furnishes results which cannot be obtained 

 from the interference figure. 



Recapitulation. — The study of interference phenomena 

 resulting from oblique illumination between crossed nicols 

 enables the observer to determine many optical features in a 

 given mineral plate. These phenomena are identical, so far 

 as interference colors go, with the phenomena obtained in 



*Zeitsclir. Kryst., 1, 240, 1912. 



Am. Jour. Sci.— Fourth Series, Vol. XXXV, No. 205.— January, 1913. 

 6 



