432 Astronomical and Nautical Collections. 



a narrow body, it will be easy' to apply similar arguments to 

 other cases of diffraction. 



The middle of the central band, which is always formed by 

 the simultaneous arrival of rays, which depart at the same 

 instant from the luminous point, must be found in the plane 

 drawn through this point and the line bisecting the narrow 

 body ; because, since every thing is symmetrical on each 

 side of this plane, the rays which unite in it Xnust have passed 

 through equal routes on each side, and must consequently 

 arrive at the same instant, unless they have passed through 

 diflPerent media, which is not the case, to be considered at 

 present. The situation of the middle stripe being deter- 

 mined, that of every other stripe must also be determined 

 accordingly. Now it is evident that if the luminous point 

 should change its situation a little, and be moved to the 

 right, for example, the plane, which has been supposed, 

 would incline to the left, and would carry with it all the 

 fringes which accompany the middle stripe. And if, instead 

 of supposing such a motion, we suppose the luminous point 

 to become of sensible dimensions ; the integral points of 

 which it is composed will each produce a group of fringes, 

 and their "Situations will be so much the more remote as the 

 luminous object is larger ; and ultimately, if its size is suffi- 

 ciently increased, they will extinguish each other and disap- 

 pear. This is the reason that, when the rays cross each other 

 at sensible angles, as in all the phenomena of diffraction, it 

 becomes necessary to employ a very fine luminous point, in 

 order to discover their mutual influence: and the point must 

 be so much the finer as the angle formed by the rays is 

 greater. 



However minute the luminous point may be, it is always 

 composed, in reality, of an infinite number of centres of oscil- 

 lations, and it is of each of these centres that we must under- 

 stand what has been said of a luminous point. But as long 

 as they are very near to each other in comparison with the 

 breadth of the fringes, it is obvious that the different groups 

 of fringes which they produce, instead of mixing with each 

 other in a confused manner, will be superposed almost ex- 

 actly, and instead of extinguishing, will co-operate with each 

 other. 



