GRATINGS ix THEORY AND PRACTICE 529 



Now na is the width of the grating. Hence, using a grating at a 

 given angle, the defining power is independent of the number of lines 

 to the inch and only depends on the width of the grating and the wave- 

 length. According to this, the only object of ruling many lines to the 

 inch in a grating is to separate the spectra so that, with a given angle, 

 the order of spectrum shall be less. 



Practically the gratings with few lines to the inch are much better 

 than those with many, and hence have better definition at a given 

 angle than the latter except that the spectra are more mixed up and 

 more difficult to see. 



It is also to be observed that the defining power increases with shorter 

 wave-lengths, so that it is three times as great in the ultra violet as 

 in the red of the spectrum. This is of course the same with all optical 

 instruments such as telescopes and microscopes. 



The second term which determines the strength of the spectral lines 

 will, however, give us much that is new. 



First let us study the effect of the shape of the groove on the bright- 

 ness. If N is the order of The spectrum and a the grating space we 

 have 



Nl 



/j. = /(sin <p + sin 0) = - 

 a 



since sin*? = 



<i 



and the intensity of the light becomes proportional to 



^ ' + ^ y) ds e ~ K " (> + ^ v) 



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 according 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 color; again there may be very little blu^ 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 

 34 



