F. E. Wright — Measurement of Extinction Angles. 367 



In several of the other methods cited below for the exact 

 location of the ellipsoidal axes of a given plate, use is made of 

 quartz plates or wedges, cut normally to the principal axis, 

 which rotate the planes of vibration of normally incident, plane 

 polarized light. For the purposes of this paper it is not neces- 

 sary to enter into the mathematical discussion and theory of 

 the rotatory power of quartz, but simply to apply the known 

 laws of rotatory polarization as they were first proved experi- 

 mentally by Arago and Biot on this mineral. A quartz plate 

 perpendicular to the principal axis rotates the plane of normally 

 incident, plane polarized waves, through an angle which is pro- 

 portional to the thickness of the quartz plate and also approx- 

 imately proportional to the inverse square of the wave length 

 used. The rotation effected by two superimposed plates is 

 moreover the algebraic sum of the rotations produced by each 

 separately. 



By using, therefore, a properly constructed quartz wedge, 

 it is possible to counteract exactly the effect, in plane polarized 

 monochromatic light, of any crystal plate in any given position 

 with respect to the nicols, by rotating the new planes of vibra- 

 tion, determined by the crystal plate back to the original plane 

 of the nicols. 



In the intensity formula (5), 



\ x = cos 2 </> - sin 20 sin 2(0 - <£) sin 2 ""-el (y 1 - a 1 ) 



A 



this rotation affects the angle 6 only, and if the nicols be 

 crossed, then 



I x = —sin 2 20sin 2 - -d(y l — a) Equation (II, page 359) 

 A 



In all measurements of extinction angles, however, 6 is a 

 small quantity and in place of the sine we may use the angle 

 itself without sensible error ; accordingly, 



1, = 4K0 2 . (13) 



This formula, which for small angles 6 states that the light 

 intensity is proportioned to the square of the angle #, will be 

 employed later in the description of a new combination quartz 

 wedge for use in determining extinction angles. 



In certain other methods, convergent polarized light is em- 

 ployed and the disturbing effects of an intervening crystal plate 

 observed whose optic ellipsoidal axes are not precisely jjarallel 

 with the planes of the nicols. The intensity formulae applying 

 to such conditions are similar to those for plane polarized and the 

 general deductions from the latter may be considered to apply 

 to the phenomena in convergent polarized light. The methods 

 involving convergent polarized light, however, have several 



