the Colours of Mixed Plates. . 685 



patches of imperfect visibility of the rings appear on the film. 

 On farther increasing the angle of observation,, these dis- 

 appear and the rings again become sharp and clear, and 

 continue to move outwards on the film in accordance with 

 formula (1), the second set of rings which move inwards 

 according to formula (2) becoming of negligible intensity. 

 With very oblique observation the dark rings indeed move 

 completely out of the thinner portions of the film, and it is 

 possible to determine the thickness of any part of the film, 

 provided it is not too large, by merely counting the number 

 of rings that pass across it as the angle of observation is 

 gradually increased up to 90°. As the path-differences 

 under which the interferences observed in the film occur 

 decrease with increasing angle of diffraction, it is clear 

 why even a thick film when viewed obliquely shows vivid 

 colours. 



Table II. shows some observations of the angles of 

 diffraction corresponding to various thicknesses of the film 

 at which a dark ring appears on it, and for comparison the 

 theoretical values calculated from formula (1). It is seen 

 that here again the agreement is satisfactory. 



















Table 



II 















(,«-! 



)t. 







An ; 



g\es < 



3f Diffracti 



on at whio 



h a ( 



lark 



ring appea 



rs on 



film. 







10X . 



fobs. 

 " \ calc. 



0° 

 



0' 

 



3° 40' 

 3 48 



8° 

 9 



50' 

 10 



14° 30' 

 14 15 



20° 

 20 



6' 



20 



27° 10' 

 26 50 



35° 

 35 



0' 

 51 



46° 20' 



47 20 



62° 0' 

 68 1 



9\. 



f obs. 

 '" \ oak*. 





 





 



5 

 4 





 44 



10 

 10 



42 



40 



16 

 15 



30 

 49 



21 

 23 



30 

 16 



32 6 

 31 28 



42 

 43 



18 

 10 







7X 



1" obs. 

 " L calc. 





 





 



6 







12 

 15 



13 

 13 



3G 

 40 



22 

 22 



12 

 16 



32 

 33 



54 



10 



50 18 

 50 9 











5A 



f obs. 

 \ calc. 





 





 



9 

 9 



50 



27 



21 

 20 



30 

 27 



36 

 36 



42 



50 

















4 A , 



( obs. 

 *' 1 calc. 





 





 



12 

 12 





 



27 

 28 



42 

 5 



52 

 59 





 40 

















3\ 



f obs. 18 44 27 

 Ic'ale. 16 31 47 20 



In calculating the positions of the dark rings given by 

 formula (1), the phase-change 8 occurring in total reflexion 

 was taken to be given by the formula 



2tt. l + /r- V^s~ (>>-i) 

 cos -— 8 = \ , 



