462 Mr. R. A. Houstoun: 
which travels through D 
; 2K 
e( Cos 2 —Cos 8) aoe 
Now all the rays for which @ is the same will terminate in 
one point in the focal plane of the telescope. The amplitude 
and phase in that point will be obtained by compounding 
the amplitudes and phases due to the different paths. Then 
by Preston’s ‘ Light,’ § 150, the resultant amplitude due to 
one aperture (i. e. e, the faces / are ground) is proportional 
fo fs EF 
gest 
we disregard that at present. By analogy with Preston’s 
‘ Light,’ p. 266, I, the resultant intensity in the direction 8, is 
given by 
It will depend also on the angles 7 and 6, but 
__ f?sin’F sin ?n(E + F) 
bi Yo sm {hE i) 7) eae (1) 
The variation of the first factor with F is discussed in 
Preston, § 151. It gives the ordinary diffraction effect. If 
the intensity of the first maximum is 1, the intensities of the 
succeeding maxima are 55, sg, and ,1,. The principal 
maximum corresponds to  =Q, 2. e. 

sin @—psin7=0 
This equation gives the “no deviation ” 
position. For if we consider the ray repre- 
sented in the diagram its deviation is 0—r. 
But sinv=ypsini, hence its deviation is 
@—sin—wsinz, and this is zero when 
sin@— wsin¢=0. ‘The principal diffraction 
maximum should always appear in the centre 
of the field, no matter what the angle 7 is, 
z.e.no matter how the echelon is rotated. I 
tested this by rotating the echelon, so that 
r increased from 0° to about 5°, which was 
all the range that the adjustment permitted. The diffraction 
maximum did not, however, remain always equally bright 
and equally broad exactly in the same place; the intensity 
diminished so that the visible breadth became less, and there 
was a slight motion of the maximum in the direction in 
which @ grows smailer. The width of the maximum de- 
creased more on the one side. This apparent motion can be 
explained by adding an obliquity factor, depending on 2 and 
9, to the expression for the intensity, to represent the effect 
that was disregarded above. For the positions of minimum 
Fig. 15. 

