Double Refraction of Quartz. 121 



10. The peculiar vividness of the colours appears to be explained 

 by this consideration. The dark curves are denned by making the expres- 

 sion for the brightness to vanish totally: whereas in some other cases (as 

 in investigation VII.) the dark curves are defined by making the expres- 

 sion for the brightness a minimum. Here then the colours are much less 

 diluted with undestroyed white light than in investigation VII. And in 

 the lines parallel and perpendicular to the plane of reflexion, x = 0, and 



the expression for the brightness is c 5 .||— ^L \Qk\ sin 4 — . Here then 



is no sensible light for a considerable distance nearer to and farther from 



the center than the point corresponding to ~= n*: the colours are less 

 mixed, and are therefore more vivid than perhaps in any other phenomenon 

 of polarization. And the greatest brightness in these lines, if k be not 

 very small, is four times as great as the greatest brightness in the lines 

 making angles of 45" with them (as will be seen on making «£ = 45" in 

 the expression for the brightness). Experimentally the colours are brightest 

 in the lines parallel and perpendicular to the plane of reflexion. 



It is almost unnecessary to point out to the reader that none 

 of the peculiarities of these appearances would exist if k were 

 either or 1, that is, if the light were either plane-polarized or 

 ocularly-polarized. None of the expressions however would be 

 altered, if instead of * we put \. that is, it is indifferent which 



ray we suppose to have the major axis of its ellipse parallel to 

 the principal plane. 



From the agreement between the observed and the calculated 

 appearances, I think there is little doubt that the nature of the 



Vol. IV. Part I. q 



