the Black Spot in Liquid Films. 505 



The number of fringes displacement is determined by that 

 of the central black fringe in the white-light fringes, which 

 is shown in the figures broader than the adjacent coloured 

 fringes. The fringes continue vertical within the image of 

 the frames until they reach the boundary between the black 

 and coloured films, and then slant off at a continuously 

 increasing slope as the black films extend lower. When the 

 black films cover the field, which usually occurs within 

 five minutes after the frames are raised, the appearance is 

 shown in (e). 



When the atmosphere about the films has been enclosed a 

 day or more, the tops of the coloured films may occur on the 

 same level, preventing at first the appearance of the sloping 

 portion of the fringes. This would indicate a considerable 

 discontinuity in the thickness at the junction of the black and 

 coloured films. A bodily shift of the sloping portion (c) was 

 often noticed. 



Methods of Measurement. — One of the advantages of this 

 method is that there can be no great difference in the optical 

 path inside and outside of the frames at their tops, except that 

 due to the films ; and the fact that the fringes usually con- 

 tinue vertical within the image of the frames indicates that 

 there is practically none. Another advantage is that the 

 deflexion is the same as that which would be due to a single 

 transmission through twice the number of films. 



The measurements were all taken at the tops of the frames 

 when the fringes were vertical. The calculations were made 

 by using the wave-length of sodium light in the formula, 

 although the white-light fringes were as often used in taking 

 the readings, which were always eye-estimates of the displace- 

 ment of the fringes. 

 The equation 



2N(/k-1) 

 gives the relation for finding the mean thickness of the films 

 where 



£ is the observed displacement of the fringes, 



N the number of films, 



X=5SdfJLfJL, the wave-length of sodium light, 



jm — 1*333, the index of refraction of pure water, and 



D the mean thickness of the films. 



The Two Black Films. — With all solutions a very rapid 

 fall in the thickness occurs when the black films have just 

 been formed, and continues with greater or less rapidity 

 according as the atmosphere about the films is more or less 



