554 Mr. J. Walker on the Orientation of 



view; but it may perhaps not be out of place to. deduce the 

 results from a general expression of the visibility of the fringes 

 for the case of any orientation and any width of the slit. 



In my former paper I showed that at a point x, y of the 

 screen the relative retardation of the interfering streams from 

 a point distant £ from the central line of a properly orientated 

 slit is (measured in length) 



<x + fix + y£, 



the values of «, j3, 7 in the three cases of mirrors, biprism, and 

 divided lens (neglecting the thickness of the two latter) being 

 given by the following schedule : — 



Mirrors. Biprism. Divided Lens. 



1 (/-t— l^tan 2 ^— tan 2 a 2 )a& ~ 



2~ ~^+b~ 



0. 



P 2a sin 2&) (/x— l)(tan« 1 + tan a 2 )a 9 a 



acos2o> + &* a + b ~ 6 ab — F(a + b)' 



2b sin 2o> (fi — l)(tan a. x 4- tan a 2 )b _ ^ b 



7 * a cos 2w + 6* a + b * ab^-F(a + b)' 



Where a, b are the distances of the interference apparatus 

 from the slit and the screen respectively; 



2oo is the acute angle between the mirrors; 



a 1} a 2 are the acute angles of the prism ; 



2e is the separation of the halves of the lens ; 



F is the absolute value of the focal length of the lens. 

 Suppose now that the slit is turned first round the line 

 bisecting its length through an angle cj>, and then about its 

 centre round a normal to its new plane through an angle 0; 

 then if u, v be the distances of a point of the slit from lines 

 bisecting its breadth and its length, we have to write 



a — sin cj)(u sin + v cos 0) for a 7 



u cos 0— v sin for £; 



and the intensity due to an element du . dv at this point is 

 proportional to 



r 27r 



1 + cos — { a + $ x + (7 cos 0— £'# sin sin cj))u 



1 



— (7 sin + fix cos sin (/>) v }\ du dv *, 



* This neglects small terms arising from ot in the case of the biprism, 

 and —7' sin 6 sin <£ should be added to the coefficient of u and y cos 6 sin (p 



1 Q— l) 2 (tan 2 » l — tan 2 ct 2 )¥ 

 to that of v, where y'= 2 (a+b) 2 



