442 Astronomical and Nautical Collections. 



can suppose all those, which are essentially concerned in the 

 effect, to be nearly of equal intensity. It is not, however, 

 surprising that the same formulas will give the position of 

 the fringes with sufficient accuracy at small distances from 

 the screen, when its edges are thin, since, the mean breadth 

 of an undulation being but about one fifty thousandth of an 

 inch, a tenth of an inch becomes comparatively a very consi- 

 derable distance. 



These are the three principal kinds of phenomena presented 

 to us by diffraction, when the edges of the screen, or of the 

 opening made in it, are sufficiently extensive to afford fringes 

 independent of any effect from their terminations: and in 

 such cases it is sufficient to make the integral calculation for 

 the plane perpendicular to the edges of the screen only, in 

 order to determine the position of the dark and bright 

 stripes, and their comparative intensities. But when the 

 screen or the opening are of small dimensions in every direc- 

 tion, it becomes necessary to extend the integration to the 

 effects produced in two perpendicular planes: and the results 

 of the calculation agree perfectly v/ith observation, as will 

 appear from two curious instances. 



. When the screen is circular, the calculation leads to this 

 singular result, that the centre of the shadow projected by 

 it must be as much enlightened as if the screen were not in 

 existence. It was Mr. Poisson that first pointed out this 

 consequence of my formulas, which I did not at first observe, 

 though it is immediately deducible from the theory by very 

 simple geometrical considerations, Mr. Arago made the 

 experiment with the- shadow of a screen -jVth of an inch in 

 diameter, perfectly round, and fixed on a plate of glass. The 

 result confirmed the fact which had been announced by the 

 theory. It is only the centre itself that possesses this pro- 

 perty, and the same brightness is only extended to a sensible 

 distance from this mathematical point when the screen is of 

 very small diameter, and when its shadow is observed at a 

 great distance : for the wider that the screen becomes, the 

 more the little bright circle is contracted; and when the 

 screen is four tenths of an inch in diameter, we only see a 

 single point of light, at the distance of a yard, even with a 

 powerful magnifier. It must be observed, that if the screen 



