28 Mr. R. A. Houstoun on Total Reflexion at the 



Therefore 



= (a/I + \/|) si " <-» + ta ° "O + £$)«» <-*> 



Now * + y = a + /3-2L, 



-j- _ 27T^ cos </> 2 



TV, 



Put 



Therefore 



tan 7 = tan 



COS (j) 1 cos <jE> 2 



A COS <£., COS (/>! 



Vk,-\/k; 



_ 47T COS 0o 7 



a+y-'ry=a + p — y— — I 



ire *in — ' l_i 



<£ 1? K 1? K 2 are known ; </> 2 , a, @, y can be calculated ; 

 A is observed ; hence from one observation I can be deter- 

 mined to a multiple of 27r, and if we have a series of obser- 

 vations, I can be definitely determined. 



The method, according to which the silver-iodide film was 

 prepared, was found to be very important. If warm iodine 

 vapour in excess was allowed to act on a silver film, we 

 obtained an opaque dull yellowish film ; but if a small grain 

 of iodine were left near the silver film for ten or twelve hours, 

 a transparent film that gave beautiful interference-colours 

 was obtained. Observations on a film produced according to 

 this method agreed with theory. A set of such observations 

 is given below. <£ l5 the angle of incidence, is calculated from 

 the angle between the directions of the telescope and colli- 

 mator. The thickness of the film, I, was determined by 

 formula (6) from the observations A, and then substituted in 

 formula (5) and A', the theoretical value of the relative 

 phase-difference, calculated. It was found necessary to take 

 the positive value of the imaginary cosine, otherwise a 



