Astronomical and Nautical Collections, 133 



different kinds by the full lines n'o\ no, no, no : these latter 

 representing the successive positions or the trajectories of 

 the middle points of the dark stripes^ an^^ \]xf ^i^vmer the 

 trajectories of the bright bands, , , ,{ • t .. ', ,,. 



It has been necessary to magnify very greatly in this 

 figure the real length of the luminous undulations, and to 

 exaggerate the mutual inclination of the two mirrors, so that 

 we must not expect an exact representation of the pheno- 

 menon, but merely a mode of illustrating the distribution of 

 the interferences, in undulations which cross each other with 

 a slight inclination, h nto 



It is easy to deduce from geometrical considerations, that 

 the length of these fringes is in the inverse ratio of the mag- 

 nitude of the angle made by the two pencils which interfere, 

 and that the interval, comprehended between the middle 

 points of two consecutive dark or bright bands, is as much 

 greater than the length of the undulation, as the radius is 

 greater than the sine of the angle of intersection. 



In fact the triangle b7ii, formed by the right line bi, and 

 the two circular arcs ni and nb, may be considered as recti- 

 linear and isosceles, on account of the smallness of the arcs ; 

 and the sine of the angle b n i, considered as very small, may 



lb 

 be called — : so that bn being the radius, ib will represent 

 bn 



the sine of the angle b n i, which has its legs perpendicular 



to those of the angle AbB: consequently, these angles being 



equal, one of them may be substituted for the other ; and 



representing by i the angle A ^ B, formed by the reflected 



rays, we have bn == — — ; consequently nn, which is twice 



bn^ wm be equal to -r— .. But nn is the distance between 



the ihfddle points of two consecutive dark stripes, and is 

 the distance which has been called the breadth of a fringe ; 

 and i5 being the breadth of a semiundulation, according to 

 the construction of the figure, 2ib will be that of a whole 

 undulation ; consequently the breadth of a fringe may be 

 said to be equal to the length of an undulation divided by 

 the [numerical] sine of the angle made by the reflected rays 



