<!4 C. Barns — Rotation of Interference Fringes. 



It is interesting to inquire into the frequency of fringes, n, 

 when the angle of diffraction, #, is changed. From the original 

 equation e = n\/(l — cos#), since dX/dO = Dcos 6, the rate of 

 change 



(hi _ e 1 e 



ltd ~ J) 1 + cos 6 ~ D+ ^/2?T\* ' 



where e is the distance apart of the rulings and D the grating 

 space. Since cos 6 varies but slowly with 6 and is additionally 



Fig. 1. 



Fig. 2. 



<jLL±X±. 



augmented by 1, dn/dQ is nearly constant and about equal to 

 e/2D. 



The fringes and slit images are thus given by the two sides 

 of the parallelogram cgc'h, for the two colors X and X'. The 

 diagonal cc represents dd\ the diagonal gh has no signification. 

 On the other hand the normal distance apart D' and D" of 

 ^'audyy and ab and ed are both important. 



The equations useful elsewhere* have very little immediate 

 value here, because the experimental variables, figure 1, are B, 

 the distance between two consecutive colored fringes, and 

 b" and b', the corresponding distance between the fringes in 

 case of homogeneous light in each case X, X' and the angle y', 

 which indicates the inclination of the slit. Thus Bb'b" are 

 given by computation and y' is specified at pleasure. Ob- 



*This Journal, xli, p. 428, 1916. 



