230 



Mr. A. W. Flux on the 



These lie on the surface (x.), where it is intersected by the 

 series of coaxial elliptic cylinders (oblique cylinders on cir- 

 cular bases) (xii.). 



Section IV. The Surface of Interference. 



We have now to examine the surface whose equation is 

 given in (x.) of the last section. 

 We shall use the form 



x (^+2/ 2 ) sin 6-2A-2f cos 2 6 (z + z x ) =0 



(i.) 



The points of the surface which we have to consider are its 

 intersections with 



x*+y 



2_„2. 



(ii.) 



,2_ 



hr\ 



or 



2/i + l r\ 



where 



cos 6 2 cos 6 



according as we are considering dark or bright rings. 

 Where (i.) is intersected by y = 0, 



x sin 0—2.2=0 (iii.) 



The intersection is therefore a straight line through the 

 origin. 



If co be the angle made by this line with the axis of x, 



2z 2 sin co 



sin 6= 



tan co 



x cos (6 — co)' 

 sin 6 cos 6 



IT 



We may notice that when 6=0 and when 6 = -x , tan co vanishes. 

 It attains a maximum value when tan 0= V% 



