16 THE INTERFEROMETRY OF 



the glass was found by rotating it around an axis perpendicular to the rays 

 until the direction of motion of the fringes was reversed. In view of the small 

 angle a and the micrometric displacement, it was easy to count single fringes, 

 or fractions as far as about i /3o of a fringe, even though the beam traversed 

 the glass twice. In the first experiment the following data of the horizontal 

 displacement, r, of the wedge were found for successions of 7 fringes: 



0.2044 cm. 0.2042 0.2043 0.2067 

 0.2058 cm. 0.1976 0.1946 0.18888 



Mean, 0.2008 cm. Per fringe, 5^ = 0.0287 cm. 



The last three results are low, the discrepancies probably resulting from 

 slight wabbling of the micrometer slide. In another series made with care 

 as to the normal adjustment, the horizontal displacement, r, of the wedge 

 for successions of 1 1 parallel fringes was 



0.3022 cm. 0.2997 0.2974 0.3002 0.2991 0.3078 

 0.3081 cm. 0.3101 0.3170 0.3183 0.3155 



Mean, 0.3014 cm. Per fringe, ^ = 0.0274 cm. 



If x be the distance from apex of the wedge, its thickness is e = xa, or per 

 fringe 5e = aSx. The index of refraction was found to be ju= 1.526 by total 

 reflection. Thus, without correcting for dispersion, 



and with the above values 



io~ 5 X 5- 



a = 



=0.0020 radian 



2X0.526X0.028 



This is larger than the calipered value because the rays go through the wedge 

 twice obliquely. The reduction, however, would be too complicated here 

 and will be treated later. 



The irregularities above are referable to the micrometer, which was not very 

 accurate, and no particular care was taken with details. The method is inter- 

 esting as allowing of the complete control of a single fringe; i.e., the equivalent 

 of 30 X iQ- 6 cm. As this corresponds to 0.028 cm. on the micrometer, the dis- 

 placement & = 0.001 is equivalent to IO" 6 cm. Furthermore, the method pre- 

 sents an expeditious means of finding a = X/2(// i}dx when a is very small. 



8. Continuation. Revolving plate. In the next place, the revolving com- 

 pensator C, figure 3, was employed. This also proved to be an admirable 

 device for controlling the fringes, and it was much more rapid than the pre- 

 ceding. Unfortunately the computation is inconvenient, as the normal 

 position can not be ascertained with sufficient accuracy. To find it, the plate 

 was revolved until the fringes changed their direction of motion. This is an 

 indication of the insertion of the minimum thickness of glass, but is not sharp 

 enough for precision. Hence data in A, table 4, are not coincident, i denoting 

 the angle of incidence. Another somewhat better and thicker plate was now 

 inserted with the results shown in B. 



