OBJECT-GLASS WITH A TRIANGULAR APERTURE. 



441 



from the centre; and therefore when at any point in them the light is 

 too feeble for vision, at every more distant point the light is still more 

 feeble. Hence it would appear that, according to theory, the six rays 

 are not interrupted by a dark ring, or band, in any part. In this particular, 

 therefore, there is a decided disagreement between theory and the experi- 

 ment recorded by Sir J. Herschel. 



4. Let us now examine the intensity in that part of the screen which 

 is situated between any two of the six rays. As we have already seen 

 the results when 6 = 0, and when = 30', we shall now suppose the values 

 of to lie between 0° and 30». 



Since — — : is a factor of equation (B), it follows that the general 



brightness of the spectra will decrease very rapidly from the centre ; and 

 at a given distance from the centre the brightness is less the more 9 differs 

 from 0", and is least when 9 = 30". The places and extent of the spectra 

 are pointed out by the other factor of equation (J?), viz. 



sin - [m s in 9) sinM»« sin (60" + 0)$ ^ sin- \m .(60' - 9)\ 



sin 9 



sin (60^ + 9) 



6)\ sin- ] m . (60' 

 "*" sin (60" - 9) 



.(C). 



This expression vanishes entirely whenever tn and 9 are such that 

 (m sin 9) and (m -y/3 cos 9) are simulta- 

 neously both odd or both even multiples 

 of TT. If 3f he such a point, and 3IG, 

 MH be drawn parallel to OA, OB, two 

 of the six rays, then the distance of HM 

 from OA, and the distance of MG from 



OB are both multiples of ( — | . Hence 



there will be an infinite number of per- 

 fectly dark spots situated in the farther 

 corner of parallelograms, such as HMGO, 

 whose sides are parallel to OA, OB. 



If the line HM be such that its distance from OA is an even multiple 



of — , then for every point in that line, the principal factor in the ex- 



