THE AID OF THE ACHROMATIC FRINGES. 



21 



The mean value AN/A 6 = 0.0042 5 agrees with the theoretical value 

 X/2 cos = 6Xio~ 5 /i. 41 =0.0043 quite as well as the observations warrant. 



Another interesting application of measurement by g g 

 fringes is shown in figure 6. This is concerned with 

 the distance apart, 13, of two objects S and S' ((3 par- 

 allel to 6), both at a distance d from the observer. In 

 passing from 5 to S' the angles at the base b are in- 

 cremented by 8ff and decremented by dcr', where 



if 5 is very distant relatively to b. But 2 8a = 8s; 

 whence 8a = 8ff and fi = d . 8s = d . 8a. Since 2 Aa = 

 2A./V cos i/R = ri\/R, we obtain finally 



if n fringes correspond to 8a, or the passage from -^L 

 S to 5'. 



Thus in case of the spire above, where d = 7 X io 4 cm. 

 or 0.43 mile, about 120 fringes were counted in passing from one side to the 

 other of a conspicuous ledge of rock. Hence, since 2/^ = 9.4. cm., 



= 7Xio 4 



i2oX6Xio 

 - 



9-4 



- 5 



= 54 cm. 



9. Ellipses and hyperbolas. The occurrences of spectrum ellipses and of 

 hyperbolas, the rotation of fringes, centering of ellipses, etc., may be suffi- 

 ciently explained as follows. Let the equation 



(i) n \ = 2e/j. cos r 



refer to the horizontal axis, x, passing through the center of ellipses in the 

 field of the ocular of the telescope. Here n is the order of a given dark 

 fringe in wave-length X, e the thickness, n the index of refraction, and i and 

 r the angles of incidence and refraction, all referring to the half-silver plate. 

 There is no compensator. In the vertical direction in the spectrum the light 

 is homogeneous in X and the equation would be at the center upward or 

 downward wX = 2^^cos /3 . . . . (2), if a and /3 are here the angles 

 of incidence and of refraction (vertical plane). Since the angle a at least 

 is very small, we may consider as an approximation that these equations 

 hold throughout the field of the spectrum. Hence in general the e of equa- 

 tion (i) is to be replaced by e cos & in accordance with equation (i) and an 



