the Colours of Mixed Plates. 871 



We have not, so far, discussed the relative intensity of the 

 interfering pencils scattered in any given direction- The 

 mathematical treatment of this question may be deferred 

 till a later stage. For the present, it may suffice to remark 

 that experimental observation as already detailed shows the 

 interferences to be remarkably perfect, and hence the inter- 

 fering pencils must be of comparable or equal intensity 

 throughout the region in which we have maxima and minima 

 in the scattered light. There is no difficulty in understand- 

 ing, at least in a general way, why this is the case. In 

 directions nearly normal to the film, light is diffracted 

 chiefly from the wave-fronts regularly transmitted through 

 the film, and the contributions to the scattered radiation 

 from the part of the wave-front lying on either side of each 

 boundary should obviously be equal. In more oblique 

 directions the scattering occurs chiefly at the curved inter- 

 face between the two media, and a calculation on the 

 principles of geometrical optics shows the intensities of the 

 pencils emerging respectively after two refractions and after 

 total reflexion to be comparable throughout, the intensity 

 of the former being at first greater, then equal and finally 

 less than that of the latter, as the angle of scattering- 

 increases. Thus there is reason to expect that throughout 

 the range in which the scattered light can be observed, the 

 interferences should be strongly marked. 



6. Concluding Remarks. 



Numerical computation of the position of the dark and 

 bright rings in the halo from formula (1) of the preceding- 

 section gives results in general agreement with experiment. 

 The width of the successive rings increases rapidly as 

 we proceed outwards from the centre of the halo. For 

 instance, in the particular case of a film for which the path- 

 difference for normal transmission through the two media is 

 five wave-lengths, the angular radii of the five dark rings in 

 the halo as given by the formula are # = 0°, = 9° 20', 

 (9 = 20° 27', = 37° 12 7 , and = 73°, respectively. These 

 quantities are of the same order as those actually observed. 



A detailed quantitative comparison between experiment 

 and theory, together with a discussion of the theory of 

 the diffraction-haloes due to obliquely-held plates and of the 

 effects observed with" non-uniform plates, as also of the 

 special phenomena observed with dry films of albumen, will 

 be given in the concluding instalments of the paper. 



Calcutta, India, 

 Dated the 14th of October, 1920. 



