48^ Astronomical and Nautical Collections, 



been employed for one section, and thus demonstrate tliat 

 the rays which have a marked obliquity must destroy each 

 other. 



These strata, in the case here considered, being all parallel 

 to the edge of the screen, and infinitely extended, while the 

 undulation is intercepted but on one side ; the intensity of 

 the result of all the impressions, which they transmit to P, 

 will be the same for each of them : for the rays emanating 

 from them must be considered as of equal intensity, at least 

 for the very small extent of the generating undulation, which 

 has a sensible influence on the light received at P. Besides, 

 each elementary result will evidently be retarded by the 

 same quantity, with respect to the ray derived from the 

 point of the stratum nearest to P, that is to say, to the 

 point in which it cuts the plane of the figure : consequently 

 the intervals between these elementary results will be equal 

 to the differences of the paths described by the rays AP, 

 mP, mF, and so forth, which are in the plane of the 

 figure, and their intensities will be proportional to the arcs 

 Am, m', m, mM, and so forth. We may therefore con- 

 sider the intensity of the general result as determined by the 

 calculation already mentioned, as belonging to the section of 

 the undulation made by a plane perpendicular to the margin 

 of the screen. 



While the outline of the screen remains rectilinear, it is 

 sufficient, in order to determine the situations of the dark 

 and light stripes, and their relative intensities, to consider 

 the section of the undulation made by a plane perpendicular 

 to that outline : but when it is curved, or composed of lines 

 meeting at any angles, it becomes necessary to obtain the 

 integral effect for two directions at right angles to each other, 

 or for a circle surrounding the point considered. This last 

 method is the most simple in some particular' cases, as when 

 we have to calculate, for example, the intensity of the light 

 in the projection of the centre of a circular screen or opening: 

 [a simplification which, thougli sufficiently obvious, had per- 

 haps not occurred to Mr. Fuesnel, until it was pointed out 

 to him by the Translator of this paper.] 



It will now be easy to form a distinct idea of the method 



