402 Prof. Henry A. Rowland on Gratings 



and the intensity of the light becomes proportional to 



It is to be noted that this expression is not only a function 

 of N but also of I, the wave-length. This shows that the 

 intensity in general may vary throughout the spectrum ac- 

 cording to the wave-length, and that the sum of the light in 

 any one spectrum is not always white light. 



This is a peculiarity often noticed in gratings. Thus one 

 spectrum may be almost wanting in the green, while another 

 may contain an excess of this colour; again, there may be 

 very little blue in one spectrum, while very often the similar 

 spectrum on the other side may have its own share and that 

 of the other one also. For this reason I have found it almost 

 impossible to predict what the ultra-red spectrum may be, for 

 it is often weak even where the visible spectrum is strong. 



The integral may have- almost any form, although it will 

 naturally tend to be such as to make the lower orders the 

 brightest when the diamond rules a single and simple groove. 

 When it rules several lines or a compound groove, the higher 

 orders may exceed the lower in brightness, and it is mathe- 

 matically possible to have the grooves of such a shape that, 

 for given angles, all the light may be thrown into one spectrum. 



It is not uncommon, indeed very easy, to rule gratings with 

 immensely bright first spectra, and I have one grating where 

 it seems as if half the light were in the first spectrum on one 

 side. In this case there is no reflexion of any account from 

 the grating held perpendicularly : indeed, to see one's face the 

 plate must be held at an angle, in which case the various 

 features of the face are seen reflected almost as brightly as in 

 a mirror but drawn out into spectra. In this case all the 

 other spectra and the central image itself are very weak. 



In general it would be easy to prove from the equation 

 that w r ant of symmetry in the grooves produces want of 

 symmetry in the spectra — a fact universally observed in all 

 gratings, and one which I generally utilize so that the light 

 may be concentrated in a few spectra only. 



Example 1. — Square Geooves. 



When the light falls nearly perpendicularly on the plate, 

 we need not take the sides into account but only sum up the 

 surface of the plate and the bottom of the groove. Let the 



depth be X and the width equal to — . 



1 vrt 





