" On the Inflexion of Light:' 431 



ing off in an hyperbolic form, and not approaching each other 

 so as to form any junction at the sides: the moment the aper- 

 ture was sufficiently widened to allow of their thus joining into 

 continuous curves (as in Mr. Barton's diagram), the dark space 

 entirely disappeared, and the progress of its disappearance 

 was always that a faint light appeared Jirst at the centre, and 

 thence extended to the edges. 



In all my experiments I invariably find that with very nar- 

 row apertures, up to the degree of approach which gives the 

 coalescing of shadows, the centre is always a point of relative 

 brightness : just before the formation of the shadow the whole 

 becomes dull, but the centre the least so; the actual formation 

 of the shadow commences by the approach of the two shadows 

 from the edges, which at length unite in the centre. 



Now in comparing these results with theory, we must confine 

 ourselves to the case of rectilinear edges ; for the slightest con- 

 sideration will show, that, with curved edges, the portion of 

 light at the wider parts, may, according to theory, conspire to 

 the production of the effect, at the narrower part, in a degree 

 dependent on the increase of breadth or degree of inclination 

 or curvature of the edges ; a case in which the analytical inves- 

 tigation would become immensely complicated. Taking then 

 the formula as given in Prof. Airy's Tract (p. 317), and sup- 

 posing an aperture with parallel rectilinear sides, it will be 

 readily seen from the expressions for the values of (5), between 

 which the integrals are to be taken (assuming such distances, 

 &c. as will afford convenience of calculation), we shall easily 

 find that commencing from the central part of the screen, and 

 reckoning thence to lateral distances (which it will be con- 

 venient to measure in terms of the breadth which the geome- 

 trical shadow would have at the screen), we shall have for the 

 limits of integration, successively, at the centre, at the edge of 

 the shadow, and at 1, 2, &c. whole breadths of the shadow 

 beyond the edge successively, when the aperture is very nar- 

 row, the values of (5) as in the following table ; and with these, 

 by means of the table of integrals, we shall find the quantities 

 which are proportional to the brightness of the corresponding 

 points of the screen. 



Values of s. Brightness. 



(i'JJ) (-D 3 +C0002)* 



(^) (-0999) 2 +(-0006) 9 



(".j) ('0999) 2 + (-0036)* 



