Double Refraction of Quartz. 97 



denly becomes = 90°: when sin 2./3 + changes its sign, B changes 

 its sign, and is = -90°; its magnitude then diminishes till sin 

 2.p + <p=-l: and it then goes through the same changes. The 

 circle is therefore changed into the form represented in fig. 17. 

 But the rings at the parts where sin 2./3 + c/> = being very faint, 

 the bends of the curve scarcely attract the attention, and the 

 figure appears elliptical. But when /3 increases, the intensity of 

 the rings where sin 2./3+^=o is not small, (it is represented by 

 A), and the change of form is easily seen*. All these conclu- 

 sions correspond perfectly with observation. 



IV. To investigate in a similar manner the appearances pre- 

 sented by plates of quartz, on the suppositions made in the begin- 

 ning of this paper, we must resolve a plane-polarized f ray into 

 two elliptically polarized rays. In fig. 18. let AP, be the plane 

 of primitive polarization : AC the principal plane of the crystal ; 

 the ordinary ray being elliptically polarized, will consist of one 

 vibration in the direction Oo l} and another in the direction o, o, 

 following it one quarter of an interval of undulations: the coeffi- 

 cient of the latter vibration being = k x that of the former, where 

 k is a fraction depending by some unknown law on the incli- 

 nation to the axis, but becoming = 1 when the inclination = 0, and 

 = when the inclination is considerable. And the extraordinary 

 ray will consist of one vibration in the direction Ee,, and another 

 in e& preceding it one quarter of an interval : the coefficient of 



* I have investigated (in nearly the same manner) the form of the curves, supposing 

 the crystal placed between the polarizing plate and the rhomb. The calculated pheno- 

 mena are nearly the same as those described, and agree perfectly with observations. 



t I use this term instead of recli&iearly-polarized, the natural derivative from Fresncl's 

 substantive, only because it is shorter. 



Vol. IV. Part I. n 



