Astronomical and Nautical Collections. 443 



were too large, the reasoning, from which the formulas have 

 been deduced, would no longer be rigorously applicable to 

 the rays inflected into the shadow, because of their too great 

 obliquity, which would render it impossible to consider their 

 effects as equal in intensity to those of the direct rays. 



When we calculate, by the same formulas, the intensity of 

 the light in the centre of the projection of a small circular 

 aperture, made in a large screen, we find that this centre 

 will exhibit alternately a bright and a dark appearance, ac- 

 cording to the distance at which the shadow is viewed ; and 

 that in homogeneous light this darkness must be perfect. 

 This new inference from the general formulas may be deduced 

 from the theory by very simple geometrical considerations. 

 Thus we find that the values of the successive distances, at 

 which the centre of the shadow becomes completly dark, are 



b = ^^' -, b = ^^' , b = _^?1_ ; andsoforth; 

 2ad- r' 4ad - r^' 8ad -r^ 



r being the semidiameter of the aperture, a and b its respec- 

 tive distances from the luminous point and from the micro- 

 meter, and d the length of the undulation of the light em- 

 ployed. Now, if we place the micrometer at the distances 

 indicated by these formulas, we observe, in fact, that the 

 centre of the projection of the opening is so completely de- 

 prived of light, that it appears like a spot of ink in the middle 

 of the illuminated part, at least with respect to the minimums 

 of the first three orders, as indicated by the formulas here 

 inserted : those of the subsequent orders, which are nearer 

 to the screen, exhibiting no longer the same degree of dark- 

 ness, on account of the want of homogeneity of the light 

 employed. 



There is still a multitude of other phenomena of diffrac- 

 tion, such as those of multiplied and coloured images, 

 reflected by striated surfaces, as seen through a texture of 

 fine fibres, as well as the coloured rings, produced by an 

 irregular collection of such fibres, or of light powders, 

 consisting of particles nearly equal, placed between the 

 eye of the spectator and a luminous object; all of which 

 may be explained and rigorously computed by means of the 

 theory which has been laid down. It would, however, oc- 

 cupy too much of our time to describe them here, and to 



