EXPERIMENTS WITH THE DISPLACEMENT INTERFEROMETER. 77 



If for simplicity we put I = R = o (the actual case with the columns in ques- 

 tion, incidence being normal), cos d = \/iX i /D' i and 



dd_ 

 dn 



/I 2 



/I 2 



2D cos e N e - N 2 (N e - N) \/D* - A* 

 If the center of ellipses is at the E line 



AT Tvr 3 dB 



Nc=*Ni and -3- = o 

 dn 



To find the size of the fringes at any other line, the D line, for instance, we 

 may again take the example of a blue column (table 10 below) where 

 N c N=o.2$$ and put X = 5.3X10-*, the grating space D = 2. 5X10-*, whence 



de\ aS.iXio- 10 



= ~, - * /, 

 D 2X^55 X io- V6.25 -.28 



=io~X22.6radians or 4.6' 



At the D line, therefore, the distance between consecutive fringes would be 

 less than 5 seconds of arc, showing the diminutive fringes to be expected. 

 After leaving the center the fringes become more and more nearly equidistant. 

 We may therefore estimate, if the angle between the D and E line is here 

 = 4,380", that somewhat less than 4,360/4.6 = 950 fringes would be encoun- 

 tered between D and E. They would therefore not be useful, except near the 

 center, where d\/dn = oo . 



43. Observations. Qreen glass column. In spite of the clearness of the 

 column, the light absorbed at the ends of the spectrum makes it nearly im- 

 possible to recognize the small, sluggishly moving ellipses. The observations, 

 therefore, are reasonably good only between the D and E lines. In some cases, 

 moreover, it is easy to mistake the lines, from the coincidence of the direct 



TABLE 9. Green column. = 22.87 cm.; e = o.68 cm.; 5=4.6X10-"; 7=15; R- 

 .. = A -i_R/\2 = s j n //sin R- t ( 3 +e cos R+2e/cos R) =70.66; /i = i-53- 



9.7: 



