of the Secondary Maxima of Grating Spectra, 



479 



different values of P.D. The first-order spectrum comes in 

 such a direction that the P.D. is 360° or the path difference is 

 A,; consequently the point for which P.D. = 180° is midway 

 between the " central image " and the first spectrum, and 

 the diffraction pattern is symmetrical about it. We thus see 

 that there is a secondary maximum at this point, as shown in 

 the lower part of fig. 1. 



From now on we shall only determine the positions of the 

 minima when more than three lines operate. The complete 

 curve can be calculated in the same manner. 



In the case of a four-line grating we have intensity 16 at 

 the centre, zero when the P.D. is 90° or 180°, and unity 

 when the P.D. is 120°. This gives us two secondary maxima 

 between the principal maxima, their intensity being about 

 ^ that of the latter ; these maxima occur when the P.D. 

 is 135° and 225°. In fig. 2, I have given the positions of the 



/°///?s£ Difference: 



o 20 W 60 



80 



Fiflr. 2. 



100 120 



140 



160 180 



4 L//VES 



5 Lines 



6 Lines 



7 L/A/E s 



8 L/NES 



\Z Lines 



minima and the form of the closed amplitude figure at each, 

 for gratings of 4, 5, 6, 7, 8, and 12 lines. The ordinates of 

 the amplitude curves are not drawn to a scale of course. 



With a five- line grating we get our first minimum when 

 the five amplitude lines form a pentagon^ the phase difference 

 being 72°, and a second when they form a star, the phase 



2K2 



