
Some Spectroscopic Notes. 463 
‘deviation 2 depends on 8. Suppose this factor expressed as 
a function of @ and plotted as a curve. Let the value of the 
ordinate decrease and the gradient increase with @.. Then 
the shape of the diffraction maximum will be obtained by 
Fig. 16. multiplying it by the appropriate portion 
of this curve. ‘The apparent displacement 
of the diffraction maximum depends on the 
gradient, and the diminution of the intensity 
on the ordinate of this obliquity curve. 
The loss of the intensity has also another 
D : , 
more important cause. f is more than ten 
times e. Consequently, as 7 or @ increases, 
the proportion of light that is wasted in 
es diffuse reflexion on the opaque faces f 
f increases very rapidly. 
§ 4. The second or interference factor 
aes 
siv@n(E+F). ,. : foe 
pet i discussed in Preston, § 157, where it is shown 
sin?(K+ F) { ile 
that there are maxima of intensity 
l=7 
in the direction given by H+ F=p7 or 
e(ucosi— cos @)+f (sind—psinz)=pr. . . (2) 
If we put 1=0, this equation becomes 
Fig. 17. the ordinary equation for the echelon 
spectroscope. It can be derived di- 
rectly by considering two rays which 
leave corresponding points in. two 
neighbouring apertures. Their path 
difference is 
p{e cosi—f sin z) —(e cos O—f sin 6), 
And @ is the direction of an image 
when the path difference is equal to an 
integral number of wave-lengths, 7. e. 
= px. 
In addition to these principal maxima the interference 
factor has (n—2) subsidiary maxima between every two ad- 
jacent principal maxima. The ratio of the intensity of one 
of these secondary maxima to the intensity of one of the 
chief maxima is 

1 
1+(n?—1) sin H+ F)’ : | 
Rewrite equation (2), putting @=w+Adé,. Then A@ is 
