232 Prof. D. N. Mallik on the 



13. Now, according to Rowland electric and magnetic 

 displacements being perpendicular to each other, and the 

 mean energies being equal, the total illumination must vary 

 as 1+ cos#. 



He further argues that Stokes's solution is based on dis- 

 placement and rate of displacement of his elastic medium, 

 but in an elastic medium there is not only displacement bu f 

 rotation also, and the components of this rotation must also 

 satisfy the equation of continuity. But when a wave is 

 broken up at an orifice, the rotation is left discontinuous by 

 Stokes's solution. Now, the equation of propagation of a 

 rotation is the same as that of a displacement, and the two 

 are at right-angles to each other : both are important. 



Hence, according to Rowland, on the elastic solid theory 

 as well as on the electromagnetic theory, the true solution 

 of diffraction will depend on the sum of two similar terms; 

 and it will follow, therefore, that diffraction cannot supply 

 the criterion whereby we may determine the relation between 

 displacement and polarization. 



Glazebrook has, however, pointed out that the magnetic 

 displacement is in consequence of the electric, and if we 

 take account of the latter, we have done all that is necessary. 

 Rowland's results, moreover, contradict the results experi- 

 mentally verified and theoretically obtained by Lord Rayleigh 

 on the blue of the sky. 



14. In any case, for the production of diffraction effect 



7T 



we must have sin</> = ~- nearly. On this understanding we 



can work out the case of oblique incidence at a narrow slit 

 as follows : — 



Let x be the distance of a small element dx from the 

 centre of the slit. The disturbance reaching any point will 

 be [since the difference of phase due to disturbance from 

 the central element and that at a distance x is equal to 



— (sin i — sin #)], 



A 



cosi + cos(i — 0) C 2 . ft 8 X , . . . ax\ 



= 2^ /*.sm2,r(^----(sm*-sm0)J 



1 cos i -fees (i — 0) . 

 . -. — = - a sm 



47r sini-smp 



(- (sin z — sin 0)j. sin 2ir(^—-\ 



where 277-1™—-) is the incident disturbance, and I is 

 breadth of the slit. 



