214 Mr. C. V. Raman : The Experimental 



the effect of an element of the aperture is zero. On the other 

 side, the z component of the electric or (as the case may be) 

 magnetic vector is given by the integral (/) taken over the 

 aperture and with its sign reversed. 



From the integral (/) it can be seen that the obliquity- 

 factor, for the z component of the light-vector in the secondary 

 waves, is simply the cosine of the obliquity and is independent 

 of the angle of incidence of the waves on the reflecting 

 screen or aperture. Differentiating and realizing the inte- 

 gral (/), it can be seen that for moderate incidences it is 

 equivalent to the expression (1), for at such incidences, the 

 diffraction-pattern is formed in a direction in which cos 

 does not vary rapidly with 6 and may therefore be put equal 

 to the mean value cos i. At oblique incidences this is no 

 longer true. The integral of (/) in the case of a rectangular 

 aperture (sides I, m) held obliquely in a parallel beam of 

 light, in front of a telescope, gives for the illumination in 

 the diffraction-pattern 



IV sm " "x ( sm l ~~ sm ^ s L~xT sm ^ J 



A2 w 2 cos2 e >*,. • ■ *v T*™ • ,r ' * {9) 



Y ( sm ?~ sm 6) ■— sm y 



6 and yjr being the angles of diffraction, in other words, the 

 angles made by the diffracted 'ray' with the two planes 

 normal to the plane of the aperture. The expression deduced 

 from the non-analytical theory is 



iw \ ( sm l " sm ) Lx" sm ^J 



J — (sin i — sm V) — — sm yr 



These two expressions give, for moderate incidences, 

 practically identical results. At all incidences, they give the 

 same positions for the minima of illumination in the diffraction- 

 pattern. But as regards the distribution of illumination in 

 the pattern, and as a minor point, as regards the positions of 

 the maxima of illumination, they give at oblique incidences 

 very different results. The expression (li), as has already 

 been mentioned, makes it out that the illuminations at corre- 

 sponding points on either side of the central band should be 



equal, and that at the limiting plane = ~ the curve of 



illumination should drop discontinuously from a finite to zero 



