50 



THE INTERFEROMETRY OF 



Table i and fig. 35 show the variation of fringes with the angle of incidence *, 

 equation (5). Hence if the angle of incidence is changed from 5 to + 5, 

 be increases to nearly 3 times its first value. This, therefore, accounts for the 

 large discrepancies of be found in the successive data below. To secure in- 

 creased sensitiveness and to make the apparatus less sensitive to slight changes 

 of i, this angle should be about 25, in which 

 case 8e is about three wave-lengths per fringe. But 

 normal incidence is frequently more convenient. 

 Finally, in figure 34, if the angle of incidence is i 

 and the two faces G and G' make an angle a with 

 each other and are initially at a distance e apart, 

 changing successively to e' and e", the points a, 

 b, c, being in the same phase, the two rays D and 

 D' leaving at d, at an angle 6i, will have a path- 

 difference at d equal to 



cos 0cos a 



whence 

 (6) 



,-(i cos (6 i}) 

 cosi cos (6 a) 



X cost cos (6 a) 

 cos a cos 6 (i cos (6 i)) 

 TABLE i. Wallace gratings. >=io- 4 Xi.75. 



This equation reproduces the preceding equation (5) if a = o and the origi- 

 nal equation (2) if a = i = o. It shows that .a discrepancy or angle between 

 the plates is of minor importance. Hence the change of this angle may be 

 used to bring the sodium lines in coincidence when the gratings differ slightly 

 in their grating constants D. On the other hand, changes of incidence i are 

 of extreme importance. 



Experiments made with the film grating showed that equation (2) not only 

 fits very badly, but that de per fringe is a fluctuating quantity. Table 2 

 gives some results obtained by measuring the successive values obtained for 

 5eXio s , corresponding to 10 fringes. Fringes were distinctly seen within 

 3 cm. of displacement by an ordinary telescope. 



TABLE 2. 

 Gratings 15,050 lines to inch; computed values io 3 5e=o.94 cm. per fringe. 



First sample: Second sample: 



io*= i .22 cm. 10^=0.98 cm. 



1.16 



I.2I 



1. 06 

 I. II 



(norma] inddence) 



> (oblique incidence) 



