with the Aid of a Grating. 419 



and reflected obliquely at the mirrors M and 1ST, thus 

 angle 2 a in air and 2j3i in glass and issuing 

 Fin-. 3. 



enclosing an 



toward q. These component rays are drawn in full and 

 dotted respectively. There may be two incident rays for a 

 single emergent ray, or, as in rig. 3, a single incident ray 

 for two emergent rays interfering in the telescope. The 

 treatment of the two cases is different in detail ; but as the 

 results must be the same they corroborate each other. 



The notation used is as follows : — Let e be the normal 

 thickness of the grating, e' the effective thickness of the 

 compensator when used. Let distance measured normal to 

 the mirror be termed y, y n and y m being the component 

 air-paths passing on the glass and on the air side of the 

 grating gg, so that y m > y n . Let y=y m -y n be the air-path 

 difference. Similarly let distances z be measured normal to 

 the grating, so that z may refer to displacements of the 



rating. 



Let i be the angle of incidence, r the angle of refraction, 

 and fi r the index of refraction for the given colour, whence 



sin i=fJt> r sin r. 



Similarly, if © is the angle of diffraction in air of the y rays 

 and ®! the corresponding angle in glass, 



sin ® = yu, sin ©! ; (1) 



and if 6 is the angle of diffraction of any oblique ray in air 

 and 6i the corresponding angle in glass, 



sin 6= sin (® + «)=/£tf sin Q v . . . . (2) 



