GRATINGS IN THEORY AND PRACTICE 531 



A77 



<p = 0, I =1(1 + cos v'O and // = / sin = 11 . 



The last term in the intensity will then be 



As an example, let the green of the second order vanish. In this case, 

 Z= -00005. N = 2. Let a =-0002 cm. and 7=1. 



Then, ^[20000 + V (20000) 2 - (10000) 2 ] = n. 



Whence, -% _ n 



~ 37300. ' 



where n is any whole number. Make it 1. 



Then the intensity, as far as this term is concerned, will be as 

 follows : 



Minima where Intensity is 0. Maxima where Intensity is 1. 



Wave-lengths. Wave-lengths. 



1st spec. -0000526 -0000268 -0001000 -00003544 -00002137 



2nd " -0000500 -0000266 -0000833 -00003463 -00002119 



3rd " -0000462 -0000263 -0000651 -00003333 -00002089 



4th -0000416 -0000259 -0000499 -00003169 -00002050 



5th " etc. etc. etc. 



The central light will contain the following wave-lengths as a 

 maximum : 



0001072 -00003575 -0000214, etc. 



Of course it would be impossible to find a diamond to rule a rectangu- 

 lar groove as above and the calculations can only be looked upon as a 

 specimen of innumerable light distributions according to the shape of 

 groove. 



Every change in position of the diamond gives a different light dis- 

 tribution and hundreds of changes may be made every day and yet the 

 same distribution will never return, although one may try for years. 



EXAMPLE 2. TRIANGULAR GROOVE 



Let the space a be cut into a triangular groove, the equations of the 

 sides being x = cy, and x = c'(y a), the two cuttings coming 

 together at the point y = u. Hence we have cu = c'(u a), and 

 ds = dy V 1 + <? or dy ^1+c 12 . Hence the intensity is proportional to 



