Astronomical and Nautical Collections. 439 



which must be followed, in order to calculate the situation 

 and the intensity of the dark and bright stripes, in the dif- 

 ferent circumstances under which it is proposed to compare 

 the theory with experiment. When the screen is infinitely 

 extended on one side, or is broad enough to allow us to 

 neglect the rays which pass beyond it, we are to determine, 

 for any point P at the distance of the place at which the 

 fringes are to be observed, the result of all the elementary 

 undulations coming from the part AMF only of the incident 

 wave ; and comparing the intensities at different collateral 

 points, P, F, P", we are to find the situation of the darkest 

 and the brightest points. In this manner we find, for a 

 screen closed on one side, 1st, that the intensity of the light 

 decreases rapidly within the [shadow] beginning from the 

 tangent CAB, and so much the more rapidly as the undula- 

 tion is smaller ; and this in a continuous manner, without 

 any alternations of maxima and minima ; 2ndly, that out of 

 the shadow, the intensity of the light, after augmenting con- 

 siderably to a certain point, which may be called a maximum 

 of the first order, decreases to another point, which is the 

 minimum of the first order : that it increases again to a 

 second maximum, to which succeeds a second minimum, and 

 so forth ; 3rdly, that none of these minimums completely 

 vanish, as in the case of fringes produced by the concourse 

 of two luminous pencils of equal intensity, and that the dif- 

 ference between the maxima and minima diminishes in pro- 

 portion as we go further from the shadow ; whence we may 

 understand why the fringes which surround shadows in a 

 homogeneous light, are less marked and less numerous, than 

 those which are obtained by a combination of two mirrors, 

 and those in white light much les^ brilliant ; 4thly, that 

 the intervals been the maxima and minima are unequal, and 

 diminish, as we depart from the shadow, in proportions 

 which remain unaltered, whatever may be the distance from 

 the screen at which we measure them ; and .5thly, that the 

 same maxima and minima, calculated for different distances 

 from the screen, are situated in hyperbolas of a sensible cur- 

 vature, of which the foci are the edge of the screen, and the 

 luminous point. All these consequences of the theory are 

 precisely confirmed by experiment. 



