440 Adronomical and Nautical Collections, 



The general formula gives the position of the maxima and 

 minima for any distances whatever of the luminous point from 

 the screen, and from the screen to the micrometer, when the 

 length of the undulation of the light employed is known. 

 In order to submit the theory to a decisive test^ instead of 

 determining the length of the undulation by measures of the 

 external fringes, and then employing it in calculations of the 

 same kind, I deduced it from an experiment on diffraction of 

 a very different kind ; and after having first verified it by 

 the fringes obtained from two mirrors, of which it repre- 

 sented the breadth within a hundredth part of the truth, I 

 introduced it into the formula which I afterwards compared 

 with 125 measurements of exterior fringes, made under very 

 different circumstances ; for the distance of the radiant point 

 from the screen was varied from four inches to six or seven 

 yards, and the distance between the screen and the microme- 

 ter was varied from -jVth of an inch to more than four j^ards : 

 and the results of all these comparisons were perfectly satis- 

 factory, as may be seen in the comparative table published 

 in the Xlth volume of the Annales de Chimie et de Phy-i-i 

 sique, p. 339, 343. 



When the screen, instead of extending infinitely on one 

 side, is narrow enough to admit some light on that side, not 

 too much weakened by the rapid decrease of intensity pro- 

 duced by obliquity, we must take into the calculation the 

 light on both sides, and find, for each point of the shadow, 

 the general result of all the elementary undulations derived 

 from the points on the right and left. We thus demonstrate 

 that the interior parts of the shadow must be divided by a series 

 of dark and bright stripes, nearly equal in breadth, of which 

 the situations differ very little from those which would be 

 deduced from the approximative formula which has already 

 been given for the same purpose, when they are still separated 

 from the borders of the shadow by an i aterval of .several iof 

 their breadths. But when the opaque body is narrow enough, 

 and the micrometer far enough removed for the. observed 

 stripes to be. very near, the exterior stripes, tlien the /results 

 of this more exact calculation, as well as those of experiment, 

 show that the approximation is no longer accurate. The cal- 



