BY REFLEXION FROM METALLIC SURFACES. 273 



as well as with changes given to | ; or a and h are also functions of the incidence, or 

 of f. When f=2 if a=|3 the light is circular ; this is never the case in any metal at 



the maximum, though in some the ratio approaches it. For some other value off we 

 may have a=|3, but this does not give circular polarization. When f =0 the same 

 formulas give the inclination of the plane of the rectilinear vibrations*. 



(4.) On interposing a plate of crystal cut perpendicular to its axis, for any plane Q 

 in the crystal passing through the axis, inclined to R by an angle <p, and to which Q' 

 is perpendicular, we have the vibrations 



R resolved into l^^'"*"'"^' 

 L R cos (p in Q. 



R' resolved into < . ' ^ 



I R' sin (b in Q. 



<p in Q. 



(5.) And on the general principle of resolution (observing that the resolved parts 

 in one of the planes will be opposed), we have 



R'sin^-|-Rcos<p=Q 

 R' cos (p— R sin ^=Q'. 



The vibrations in Q' form the ordinary ray O, and those in Q the extraordinary E. 

 But after emergence the vibrations in Q are all further accelerated by &, or become 



(6.) Thus we have 



=0 . . . in Q'. 



^=E, . .inQ. 



o(,^in(—{vt^x)-\-&\ 



-^{vt—x)-\-g) cos^ 

 — as'm(—(vt'-x) ) sin 9 J 



+asin( y(*^^"""^) + ^ jcos^ 



(7.) Now if the analyzer be applied with the plane of analyzation A, inclined to R 

 by an angle %, we shall have the angle AQ=-4/=% — (p, and AP=r;^+|. 



The vibrations being again resolved in A and A' perpendicular to it, we find 



O resolved into < ^ . 



L Ocos 4 in A. 



^ : \ . rEcos-vLinA' 

 , E resolved mto < ^ . , . a^ 

 (. E sm -^ m A. 



After analyzation the parts transmitted are those only in A, or 



Ocos-^/— Esin-v}/. 



* See uiy Treatise on the Undulatory Theory, &c., p. 12. 



