54 THE INTERFEROMETRY OF 



If the grating G' is displaced be parallel to itself, however, the path-difference 

 will again be increased by X whenever 



X cos i 



fu? 



i-cos(0'-H) 



Since i is small, this equation will not differ appreciably from equation (2), 

 with which it coincides for the central fringes. 



If the sodium lines are not superposed, these fringes may still be seen, but 

 they are not in the principal focal plane and the new focal plane changes con- 

 tinually, as the fringes grow in size. Examples are given in table 4. The 

 large values of de show that i was not actually negligible. Experiments 

 similar to the above, bearing on the reason for the discrepancy (equation 6) , 

 were tried with the thin Wallace gratings, and the results are given in table 5. 



TABLE 5. Thin Wallace grating. 



i negative (within 10) 5'Xio 3 =2.6o cm. 5eXio 3 =2.4O cm. 



Ocular in, 2.34 2.45 



2-57 



z'=o, normal incidence, 5eXio 3 =i-48 cm. 5eXio 3 =i.37 cm j (small 



Ocular set for principal 1.50 1.37 '\ fringes) 



focal plane, 1.37 1.32 ((large 



1.19 ^fringes) 

 i positive (within I o) SeXio 3 =o.86 cm 8eXio 3 =o.<)6 



Ocular out, .88 .86 cm, 



85 

 .87 

 .96 



(small 

 fringes) 



(large 



fringes) 



As before, the effect of i passing from negative (through zero) to positive 

 values is enormous, de increasing nearly threefold for a change of i estimated 

 as within 20. Here, however, the drawn-out ocular (towards the observer) 

 corresponds to the small values of de, whereas above the reverse was the case. 

 This depends upon which of the spaces D or D' is the greater. 



22. Homogeneous light. Fine slit. Transverse axes not coincident. To 



obtain this group of interferences, the two sodium lines from a very fine slit 

 are thrown slightly out of coincidence; i.e., by not more than the DiD 2 dis- 

 tance. In the principal focal plane, therefore, these doublets are seen sharply, 

 while if the ocular is drawn sufficiently forward or reanvard, an interesting class 

 of fringes soon appears which resemble Fresnel's fringes for two virtual slits. 

 These fringes may be seen, however, on both sides of the focal plane and in- 

 crease in size with the distance of the plane of observation (focus of ocular) 

 in front or behind the principal focal plane. In figure 37 the two gratings, 

 G and G', are struck by parallel pencils from the collimator at different angles 

 of incidence (o and i). The two diffracted pencils of parallel rays are 

 caught by the objective L of the telescope and condensed at the principal 

 foci, F and F f , appearing as two bright yellow lines. In front and behind the 

 plane FF', therefore, are two regions of interference, I and I', throughout 

 which the Fresnellian phenomenon may be seen in any plane parallel to 

 FF', observed by the ocular. When the electric arc is used with a very fine 



