6 5. R. Williams 



incidence on the plate ( 0i=9 r ) ; r will also be a maximum for 

 air. Hence if it can be shown that the angle 6 r does not produce 

 an appreciable error in difference between c and b, which are 

 the lengths of D at normal and oblique incidence, then it can be 

 shown that for a ray incident at an angle 6 t - upon two films, as 

 an air and a liquid film, the difference in D for the two is not an 

 appreciable error, for the difference in the angle of refraction 

 at the surfaces of the two films can never become as large as 0, .; 

 consequently the difference in length can never be as great as 

 c-b in the figure. 



tan $ r =a/b 

 sin 6 r =a/c 



c — b=a — — -: ■ jr- 



[_sin v r tan v,-J 



c — b „ C i i ! ~) „ 



— r-=tan 6 r \ -j— Z"— : 7f =sec 6 r —i. 



b \j>\x\ v r tan v,j 



c—b 

 but — — is the per cent of error introduced. In the apparatus 

 b 



as set up, the light at prism p 1} fig. i, was diaphragmed so that 



6 r was about 25'. Substituting this value in the above equation, 



shows an error of about three parts in a hundred thousand. 



With light incident on two films the error due to difference of 



path D is still less, as shown above. 



In the liquid films with oblique incidence, dispersion produces 

 a variation in D for the different wave-lengths, so that if the 

 index of the substance under examination be smaller than that 

 of the containing cells, the path D for the violet ray will be 

 greater than that of the red, since it will be bent away from the 

 normal more than the less refrangible wave-lengths. We have 

 shown that difference in path, due to refraction, produced a 

 negligible error, and since the angle of deviation is always less 

 than the angle of refraction, no error in difference of D for the 

 various wave-frequencies will occur. 



Again, the length of path D, as determined from the bands in 

 the photographs, will be augmented by change of phase, at reflec- 



134 



