128 



THE INTERFEROMETRY OF 



per fringe, and that is about the mean value obtained in table 33 and else- 

 where. In the present mode of treatment merely practical conveniences are 

 aimed at. A more uniform method will be given in the next chapter. 



66. Angular displacement of fringes. Having for other purposes installed 

 an ocular micrometer in connection with the telescope, it seemed worth while 

 to make a direct test of the equations given elsewhere.* These are apart 

 from signs 



d\ 



dN c cosK ( /i \d\/ d\ 



When n=A-\-B/\ z , \ = D (sin i sin 8}, and when two plates, the half -silver 

 of thickness e and angles of incidence i (constant) and of refraction R, and 

 a compensator of thickness E and at normal incidence are included, these may 

 be changed to 



dd X f i .1 



dN e ~(2B/\*)D cos'0 



I I -2-1- 



X 2 M 



Here dd/dN c is the displacement of the center of ellipses per centimeter of 

 displacement of the normal micrometer at one opaque mirror of the Michel- 

 son device, for the wave-length X. D is the grating constant and 6 the angle of 

 diffraction. In the apparatus used .D = i67Xio- 6 cm., 6 = 20*40' at D line, 

 2 = 30, -R = i9 5' in case of glass and 17 52' in case of carbon-bisulphide 

 plates; X = 58.93 Xicr 6 cm.; B = 4.6Xio~ n or 2#/X 2 = 0.0265, M=i-S3 (gl ass )- 

 Under these circumstances the term 



zB tan 2 .R/XV = 0.002 1 



and may be neglected in comparison with 3. Thus the equation takes the 

 simpler form 



de X i 



dN c ~ (65/X 2 ) D cos 6 E+e/cos R 



The values of E and e are given in table 35. The data marked dd/dN ' c (com- 

 puted) in the table were found from the last equation. 



TABLE 35. Reduction of sensitiveness by glass thickness. D=d/cos r. Incidence at 

 4 = 30, .R = i95' (glass), 17 52' (CS 2 ), compensators normal. Glass: = 1.53; CS 2 , 

 = 1.63. Telescope 19.5 cm. long. 25/X 2 = 0.0265. .D = i67Xicr 6 cm. D = 2O 40'. 



* Carnegie Inst. Wash. Pub. No. 229, 1915, p. 74 et seq., \\ 40, 41. In equations (13) 

 and (18) d\/dN c and dO/dN c should be inverted and D cos 6 in the latter put in the numerator. 



