134 Astronomical and Nautical Collection^.. 



with each other, whicli is also the angle under which the 

 interval AB would appear to an eye placed at b. We find 

 another equivalent formula, by remarking that the two tri- 

 angles, b 711 and AbB, are similar, whence we have the pro- 



portion ^w: ^2 = A^:AB, and bn = — ,or2bn =: 



^ AB 



: which implies that we may find the numerical 



breadth of a fringe by multiplying the length of an undula- 

 tion by the distance of the images A and B from the plane 

 on which the fringes are measured, and dividing the product 

 by the distance of the two images. 



It is sufficient to inspect the figure, in order to be con- 

 vinced of the necessity of having the two mirrors nearly in 

 the same plane, if we wish to obtain fringes of tolerably large 

 dimensions ; for in the little triangle b n z, the side b ^, which 

 represents the length of a semiundulation, being little more 

 than the hundred thousandth of an inch for the yellow rays, 

 for example, the side bn^ which measures the half breadth of 

 a fringe, can only become sensible when bn \% very little 

 inclined to 2 7i, so that their intersection may be remote from 

 ib ; and the inclination oi bn to in depends on the distance 

 AB, which is the measure of the inclination of the mirrors. 



If A and B, instead of being the images of the luminous 

 point, were the projections of two very fine slits cut in a 

 screen RN, through which the rays of light were admitted 

 from a luminous point placed behind the screen in the conti^ 

 nuation of the line ^DC, the two paths described between 

 the point and the slits A and B being equal, it would be suf- 

 ficient to compute the paths described by the rays, beginning 

 from A and B, in order to have the differences of their 

 lengths; and it is obvious in this case, that the calculation^ 

 which we have been making of the breadth of the fringes, 

 produced by the two mirrors, would remain equally applir 

 cable, at least as long as each slit remained narrow enough 

 to be considered as a single centre of undulation, relatively 

 to the inflected rays which it transmits. It may therefore 

 be said that the breadth of the fringes, produced by two very 

 fine slits, is equal to the length of an undulatioij supposed 



