Astronomical and Nautical Collections. 441 



culation determines also, with remarkable precision, the sin- 

 gular alterations which the exterior fringes often undergo, 

 wlien the other series extends beyond the shadow, and mixes 

 its eftects with those of the exterior. 



I have also verified the theory by examining the fringes 

 derived from a narrow slit of indefinite length; and deter- 

 mining, for the different points enlightened by the luminous 

 pencil, the result of all the elementary undulations derived 

 from the part of the primitive wave comprehended in the 

 breadth of the slit; and I have found a satisfactory agree- 

 ment between the calculation and the observations, even 

 when the fringes thus obtained afforded the most capricious 

 and apparently irregular appearances. 



In this mode of considering the problems relating to dif- 

 fraction, we have not taken into the calculation the greater or 

 less thickness of the edges of the screen, but merely the 

 extent of the primitive wave which is capable of sending 

 elementary undulations to the points for which we are to find 

 the intensity of illumination; and the opaque substance has 

 no other effect than simply to intercept a part of the wave : 

 for this reason the result is necessarily independent of the 

 nature of the body, of its mass, and of the thickness of its edges. 

 Nevertheless, if the surface of the edges were very extensive, 

 it would be impossible to consider the portion of the wave as 

 quitting the slit without having received some previous mo- 

 dification, and it would be necessary to take into the calcula- 

 tion the small fringes derived from the eff'ect of the remoter 

 parts of the slit. But while the thickness is moderate, or 

 the edges rounded oft* into a well marked curve, the small 

 fringes derived from this cause may be neglected, and the 

 emerging wave may be considered as of equal intensity through- 

 out, at the moment of its quitting the screen, especially if the 

 intensity of the light is to be calculated for a pretty consi- 

 derable distance from the screen. We must not, indeed, for- 

 get, that according to the reasoning which has been emplo)^ed, 

 the formulas for diffraction are only sufficiently exact when 

 this distance is very considerable, in comparison with the 

 breadth of an undulation, since it is in this case only that 

 we can neglect the rays that are decidedly oblique, and 



