-Estimation of the Optical Angle, etc, '>'■> 



A in - . XL — On tfu Estimation of the Optical Angle by 

 Observations in Parallel Light;* l>v Alfred C. Lank. 



§ 1. Whenever in a rock section we are lucky enough to 

 find a mineral showinga bisectrix squarely in convergent tight, 

 and large enough to give a definite image with Bertrand's 

 lens, we can employ his method as given by Rosenbusch, Levy 

 et Lacroix, etc.+ ( fccasionally the method developed by Michel- 

 Levy,J — of noting tlie angle that must be turned to bring the 

 image from that of a cross to that of two hyperbolas tangent to 

 a given circle, — may be used here. Supplemental to these 

 methods or in sections in which they cannot he used, nearly or 

 quite as good values of 2Y (not 2E or II) may be obtained with- 

 out finding /9, by comparing the order of colors in different 

 Bections between X nicols. These colors are dependent on the 

 different retardations of the wave fronts in passing through 

 the crystal, and in petrographical textbooks (Rosenbusch-ld- 

 dings, Michel-Levy et Lacroix) are tables giving the relative 

 retardation of one wave front, corresponding to different New- 

 ton's colors, for a unit thickness. This difference is propor- 

 tional to the double refraction. 



l. e. 



(the order of color) ^> o — e ~~ 8 I- ) (1) 



"Where o and e are the thickness of air that would be traversed 

 by the wave fronts in the time that they actually take to 

 traverse the crystal plate, u and u e are the two wave fronts (or 



beam) velocities, and - and - the indices of refraction for 



the given section, o is the section thickness. 

 But for the optical angle we have§ 



■u^-uj—ff-c 1 sin 6 sin & (2) 



"Where a b c are proportional to the three principal velocities 

 and inversely to «, t i and y, least, middle and greatest, indices 

 of refraction, (by a slip of the pen in Dana's Textbook, p. 147, 

 both a and a are called maximum,) and 6' are the angles to the 

 principal optical axes from the normal to the wave fronts. 

 Hence they involve 2V. 



* From the unpublished report of the Michigan Geological Survey, published 

 by permission of M. E. Wadsworth. State Geologist. 



\ See also E. Mallard. Cristallographie Physique, vol. ii, p. M<;. 



\ Levy et Lacroix, p. 94. 



§ Lloyd. Wave theory of Light. §§ 231, 2:32, 216. 



