226 



Mr. A. W. Flux on the 



Using the values obtained in (ii.), (iii.), (iv.), (v.)> (vit) in 

 evaluating A in (vi.) we obtain 



= kn- 



u 2 + t> 2 



¥ 



fon 



-k(k-l) 



m* + « s 



(Zw + mv), 



► (viii.) 



, 2 /lu + mv\ 2 /y J,. /7 , .w 2 + v 2 ~| 



Section III. Determination of the Equations of the Rings. 



If we now determine the axes of x and y so that the plane 

 xz is parallel to the incident light, and if 6 be the angle of 

 incidence, 



I =sin 6, 0i=O, n = cos 0. 

 Also 



1 L A 6 cos Ox J L ft cos d 0J ' 



where 



sin 6 = /j, sin 1? w = f + tan (f — ^J, v = ^. 



And with this simplification 



7 /] ?< 2 + ^ 2 PcOS# ro/ 2 . «,„ ^ v 



A* = £cos# — =— [2(u 2 + v'){% — Si) 



r v* 



+ 2 ?z 2 tan 2 0(f-8 s )- M tan (9 (w 2 +w 2 )]. (i.) 



We shall find it convenient to refer the system to a new 

 origin and new axis of z, keeping the axis of x and y parallel 

 to the directions just chosen. 



The new axis of z is inclined at an angle 6 to its old 

 direction, i. e. is parallel to the emergent light which has 

 been but once reflected at the surface of the plate. The new 

 origin is the point (f f ), where 



f 0= -^-l)tan^ 6 =rf[l_J!E5Jy. . (i ,) 



The formulae of transformation are : — 

 %=% o + x—zsm0, 



f=? + ecos<9. (See fig. 3.) 



