Refleded-Diffracted and Difraded-Rejiected Rays. 53 



If the glass plate ff gg is removed and a mirror M used, 

 as in the interferometer, the fringes may be enormously 

 enlarged by decreasing e and the measurements made with 

 any degree of accuracy ; but such measurements were 

 originally impracticable and have now little further interest. 



7. Interferometer. 



The final test of the above equation is given by the last 

 part of the table for different thicknesses of glass, £ = *48 

 and e = '17 cm. The results are in perfect accord. 



These data suffice to state the outlook for the interferometer. 

 In this case n and e are the only variables, so that equation (8) 

 becomes 



8e = \/2fi(cos — cos r), 



where Be is the thickness of glass corresponding to the 

 passage of one fringe across the cross-hairs of the telescope. 



If instead of glass in the grating above, an air space inter- 

 venes between the film of the grating and the auxiliary 

 mirror M (fig. 1), the equation reduces to 



Se = tJ7 w t: , .... (20) 



2(cos0 — cost) ' v J 



where i and 0' are the angles of incidence and diffraction in 

 air. 



These equations (20) embody a curious circumstance. 

 Inasmuch as 6 and 6' change as i increases from 0° to 90° 

 from negative to positive values at about £==13° and i = 20°, 

 respectively, the denominator of either equation (20) will 

 pass through infinity (for air at about i= 10°). Hence at this 

 value of i the motion of the mirror M produces no £- effect 

 (stationary fringes), while on either side of it the fringes 

 travel in opposite directions in the telescope when e changes 

 by the same amount. In the negative case the sensitiveness 

 for airspaces passes from 8e= — *000,489 to 8e= — <x> per 

 fringe. In the positive case from Be= -f-oo to Se — '000,039 

 per fringe, or to a limit of about a half wave-length in case 

 of 15,000 lines to the inch. This limiting sensitiveness may 

 be regarded as practically reached even at z = 40°, where 

 ^ = •000,155 cm. per fringe and an angle of about i = 45° is 

 most convenient in practice. 



The addition to the large fringes the fine set appears 

 when e is small or not more than a few tenths of a milli- 

 metre. The sensitiveness of these is naturally much more 



