REVERSED AND NON-REVERSED SPECTRA. 



71 



In the present apparatus I have made i = r = o, a more convenient plan 

 of testing the method, though not necessary and, in fact, often inconvenient 

 in practice. The equations are, finally, 



(7) n\ = ze 



(8) 



(9) 



-cos m = 2<?i - - 



n\ = 



if D is the grating space, and the interference in question is due to the grating 

 spectrum of the mih order. 



The meaning of the equations (7), (8), and (9) is given in figure 52. The 

 case of equation (7) may be seen in the direct white ray, figure 52 a, provided 

 the light of the focussed slit-image is resolved by direct-vision spectroscope. 

 For this purpose Mr. Ives's grating with attached direct grating prism may 

 conveniently be placed in front of the telescope T, figure 50, focussed on the 

 slit. After adjustment these fringes appear strong. Of course, H and G 



a 



I 



d 



V\ 



ge 





52 



53 



must be parallel and all but touch. Under the same conditions the fringes 

 may be seen laterally in any order of spectrum, as in figure 52 b. Figure 

 52 c illustrates equation (8) and figure 52 b equation (9). Figure 53, finally, 

 illustrates the general case of incidence, i. 



The first and second orders of spectra are alone intense enough to pro- 

 duce marked effects. In case oii o, a double diffraction of the first order, 

 6' reinforces a single diffraction of the second order, 2 , since 



\/D = (sin 9' sin 6} =sin 2 /2, 



(sin 0'-X/>) = (2\/>)/2 or sin 6' = 2\/D 



Probably for this reason they are visible. The general case, equations (4), 

 (5), and (6), is illustrated in figure 53, the rays /, I', and /" being incident, 

 R reflected, and D diffracted. The retardations are ef and df, respectively. 

 If the diffractions differ by a whole number of wave-lengths the total diffrac- 

 tion is obtained. One would be tempted to resolve the case by aid of a wave- 

 front ab, in which case the equations would be different; but they do not 

 reproduce the phenomenon. 



