in Theory and Practice. 399 



where _ L r V I "1 



K ~ * L */-sp ■+ y 2 + z ri + v 7 ?' 2 +y* + 2 "d ' 



and 



i*=a* + tf + f. 



This equation applies to light in any direction. In the 

 special case of parallel light, for which k = 0, falling on a 

 plane grating with lines in the direction of z, one condition 

 will be that this expression must be the same for all values of z. 



Hence A 



If N is the order of the spectrum and a the grating-space, 

 we shall see further on that we also have the condition 



ba/jb = 27rN= -j—fi. 



The direction of the diffracted light will then be defined by 

 the equations 



a ,2 + /3' 2 + 7 ' 2 =0, 



i 7 +iy=o, 



I/3 + I'/3'=-N. 

 a 



Whence 



"W~»>-£ 



r/3'=-N-I/3, 



a ' 



iy=-i 7 . 



In the ordinary case, where the incident and diffracted rays 

 are perpendicular to the lines of the grating, we can simplify 

 the equations somewhat. 



Let be the angle of incidence and ^ of diffraction as 

 measured from the positive direction of X. 



\= I' cos <f> + 1 cos yjr, 

 - N=/a= I' sin <ft + 1 sin 'vjr, 



h 27r 



where I is the wave-length in vacuo. 



In case of the reflecting-grating 1 = 1', and we can write 



\ = I{cOS<|> + COS^}, 



-N = //, = I{sin <f> + sin-^r}. 

 2 E 2 



