400 Prof. Henry A. Kowland on Gratings 



This is only a very elementary expression, as the real value 

 would depend on the nature of the obstacle, the angles, &c, 

 but it will be sufficient for our purpose. 



The disturbance due to any grating or similar body will 

 then be very nearly 



where ds is a differential of the surface. For parallel rays, k = 0. 



Plane Gratings. 



In this case the integration can often be neglected in the 

 direction of z, and we can write for the disturbance in case of 

 parallel rays, 



Case I. — Simple Periodic Puling. 



Let the surface be divided up into equal parts, in each of 

 which one or more Hues or grooves are ruled parallel to the 

 axis of z. 



The integration over the surface will then resolve itself into 

 an integration over one space, and a summation with respect 

 to the number of spaces. For in this case we can replace y 

 by na+y, where a is the width of a space, and the displace- 

 ment becomes 



but . ba/j, 



sinn 



.baa' 



sin T 



Multiplying the disturbance by itself with — i in place of +i, 

 we have for the light intensity, 



ib(\x+w) 



ds^e+W^Wds]. 



The first term indicates spectral lines in positions given by 

 the equation 



. baa ft 

 sin -~ = 0, 



with intensities given by the last integral. The intensity of 

 the spectral lines then depends on the form of the groove as 



