Baribs — U&e of the Grating in Interferometry . 1G7 



gratinfT- In other words, it was convenient to move the grat- 

 ing at the center of tlie spectrometer, rather than the mirrors 

 M and N adjustably attached near the edge of the plate grad- 

 uated in degrees. 



In group A at 124. the short air path is to M^ the long path 

 to N ; in group Cat 76, the reverse is true. In group B at 

 100, the system is self-compensating and the air paths about 

 equal. 



In all cases the angle of diifraction, ^, is less than the angle 

 of incidence, *. There are, of course, corresponding cases, 

 B > {, which have not been drawn, because they merely dupli- 

 cate tlie cases given, at a different angle. It is assumed that 

 after more than one direct reflection or one diffraction, the 

 interferences are no longer observable. 



The diagrams 124 and 76 show that the two reflections of 

 the component rays at the grating take place at the same sur- 

 face. Hence the occurrence of centered figures or rings. On 

 the contrary, the reflections in diagram 100 take place at the 

 two different faces of the grating, respectively. Hence the 

 angle of the grating is included and liable to produce eccentric 

 ring systems. The center may be so far off that the dark lines 

 are nearly straight, but they change their inclination as the 

 vertical projection of the center moves horizontally through 

 the field. 



Some of these cases may coalesce in practice or they may 

 destroy each other, more or less. I have taken a single inci- 

 dent ray from which may come two parallel emergent rays, 

 which are brought to interfere by the telescope. It would have 

 been just as convenient to have taken the two corresponding 

 incident rays which interfere in a single emergent ray. Fi'om 

 the position of the mirrors it is clear that the regularly re- 

 fracted rays are not returned. Only rays first diffracted at 

 the grating (where they may also be reflected) are returned by 

 the mirrors. 



As a whole we may distinguish two typical cases, — those in 

 which both component rays are diffracted as in number 1 or 

 refracted as in number 2, and those in which one component 

 ray is refracted and the other diff'racted. If * and Q' are the 

 angles of incidence and diffraction in air, and r and Q the cor- 

 responding angles of refi-action and diffraction in glass, the j)ath 

 differences l\x are as follows : 



No. 1. Aa;=2/Ae/ cos 6=2-2™. 



" 2. =2/xe/ cos r-l-2e sin 6' (tan r— tan 6) = 2-5='°. 



" 3. =2/xe/ cos 6=2-2™. 



" 4. =Zero. 



" 5. = — 2/Ae/ cos Q -I- 2/x,e / cos r -i- 2e tan r sin & . 



