In fact the triangle _bni_, formed by the right line _bi_, and the two circular arcs _ni_ and _nb_, may be considered as rectilinear and isosceles, on account of the smallness of the arcs; and the sine of the angle _bni_, considered as very small, may be called _ib_/_bn_: so that _bn_ being the radius, _ib_ will represent the sine of the angle _bni_, which has its legs perpendicular to those of the angle A_b_B: consequently, these angles being equal, one of them may be substituted for the other; and representing by _i_ the angle A_b_B, formed by the reflected rays, we have _bn_ = _ib_/sin _i_; consequently _nn_, which is twice _bn_, will be equal to 2_ib_/sin _i_. But _nn_ is the distance between the middle points of two consecutive dark stripes, and is the distance which has been called the breadth of a fringe; and _ib_ being the breadth of a semiundulation, according to the construction of the figure, 2_ib_ 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 [p134] with each other, which 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 triangles, _bni_ and A_b_B, are similar, whence we have the proportion _bn_: _bi_ = A_b_ : AB, and _bn_ = (_bi_ × A_b_)/AB, or 2_bn_ = (2_bi_ × A_b_)/AB: which implies that we may find the numerical breadth of a fringe by multiplying the length of an undulation 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 convinced 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 _bni_, the side _bi_, 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_ is very little inclined to _in_, so that their intersection may be remote from _ib_; and the inclination of _bn_ to _in_ depends on the distance AB, which is the measure of the inclination of the mirrors.