72 THE INTERFEROMETRY OF 



32. Method. Suppose, now, two Fraunhofer lines, X and X' of the spectrum, 

 are selected as the rays between which interference fringes are to be counted. 

 Then, in case of equation (7), if n' is the number of interference rings between 

 X and X', 



(10) n\=(n-\-n'}\' = 2e 



(n) = tt'X'/(X-X') 



(12) 2 = n'X 



In order to measure e, therefore, it is necessary to count the number of fringes 

 n' between X and X', and e varies directly as n'. 



If the mean D and magnesium b lines be taken as limiting the range, io 6 X = 

 58.93 cm., io 6 X'=si.75 cm., Ci= 10^X4-25; then 



11'= i io 3 = 0.21 cm. 



= 10 = 2.1 



= 100 = 21 etc. 



As it will not be convenient to count more than 100 lines ordinarily, the 

 method is thus limited to air-spaces below 0.2 mm. and becomes more avail- 

 able as the film is thinner. Of course, in case of plates which contain specks 

 of dust or lint, or are not optically flat on their surfaces, it is extremely diffi- 

 cult to get e down below 0.002 cm., so that ten fringes between D and b would 

 require very careful preparation. 



If equation (8) is taken, X is to be increased to 



L = X/ cos O m = X/\/i - (m\/DY 



where m is the order of the grating spectrum, whose rays interfere. Thus 

 equations (n) and (12) now become, since nL = (n-\-n'}L' = 2e 



(13) = n'L/(L-L') 



(14) 2e = n'LL'/(L-L'}=C,n' 



If first order of diffractions are in question, m= i, io 6 L = 59.n, 

 '2=10^X4.20. Thus for 



n= i io 3 e= 0.21 cm. 



10 02. i 



100 021. 



scarcely differing from the preceding case, so that one would not know in 

 which series one is working. 



If the diffractions occur in the second order, m = 2 , 



io 6 L 2 = 62.56 io 6 L' 2 = 54.i5 c \= 10^X4-03 



thus again differing but slightly from the above. 



If we inquire into the condition of coincidence and opposition of these 

 fringes, the following results appear: Let the spectrum distance between 

 the G and b line be taken as unity, and let there be n\ and n z first-order fringes 



in this distance. Then in is the difference of distance per fringe. Let 



Hi 2 



