Prof. Miller on the appearance of a Luminous Point, Sj-c. 459 



the shape of the sand-pipes in the chalk would operate to fill 

 them with the superincumbent strata. We find the order in 

 which the materials lie in the pipes corresponding precisely 

 with that of the superimposed strata on the surface of the 

 chalk, the clayey and ochry matter first ; the sand and 

 gravel next ; then the water- worn pebbles ; and, lastly, in 

 many cases, boulders. The whole appears arranged like the 

 table of contents in a book, and tells the tale as well. 

 I remain, dear Sirs, yours truly, 

 Norwich, Oct. 15, 1839. Wm. Stark. 



LXX. On the Appeat-a?ice of a Luminous Point seen through 



a telescope, the object-glass of "which has an aperture of the 



form of a scalene triangle. By W. H. Miller, M.A., 



F.R.S., F.G.S., Fellow and Tutor of St. John's College, and 



Professor of Mineralogy in the University of Cambridge. 



VITHEN a point of light is seen through a telescope having 

 • ' a small triangular aperture, the telescope having been 

 adjusted so as to show the point distinctly with its undiminish- 

 ed circular aperture, there will be seen, in place of a well- 

 defined image of the luminous point, a bright disc, from which 

 proceed, in directions perpendicular to the sides of the aper- 

 ture, six rays, accompanied on each side, when the light is 

 sufficiently strong, by parallel rows of bright points, decreasing 

 in intensity as they recede from the principal rays. The in- 

 tensity of the light at any point in the field of view may be 

 expressed by a formula of great simplicity, considering the 

 complicatednatureof thephaenomenon it represents, which first 

 appeared in Professor Schwerd's elaborate treatise on diffrac- 

 tion (Die Beugungserscheinungen aus den Fundamentalgese- 

 tzen der Undulationstheorie analytisch entwickelt und in 

 Bildern dargestellt. Mannheim, 1835.). This formula maybe 

 deduced in the following manner. 



Let K be the centre of the object-glass ; O the geometric 

 focus to which the rays proceeding from the luminous point 

 converge, after I'efraction, through the object-glass; M any 

 point in a plane through O perpendicular to O K ; ABC the 

 triangular aperture. Draw M H parallel to O K meeting the 

 plane of A B C in H, and D A E, B F, C G, Q P R perpen- 

 dicular to H K. Let F G, G E, E F, the orthogonal pro- 

 jections of B C, C A, A B upon H K, be equal to a, /3, y re- 

 spectively ; S the area of A B C, O K = ^», K H = j9, K R 

 = j;, A D = e. Then (Airy's Tracts, Undulatory Theory of 

 Optics, art. 80.) the wave transmitted through an aperture 

 A P Q D would caUse at M a displacement. 



