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 continuation of the line _b_DC, the two paths described between the point and the slits A and B being equal, it would be sufficient 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 calculations which we have been making of the breadth of the fringes, produced by the two mirrors, would remain equally applicable, 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 undulation supposed [p135] to be multiplied by the interval between the two slits, and divided by the distance of the screen from the wires of the micrometer employed for measuring the fringes. This formula is also applicable to the dark and bright stripes which are observed in the shadow of a narrow substance, substituting the breadth of this substance for the interval which separates the two slits, as long as the stripes are far enough from the edges of the shadow: for when they approach very near to the edges, it is shown, both by theory and by experiment, that this calculation does not represent the facts with sufficient accuracy; and it is not perfectly correct in all cases, either for the fringes within the shadow, or for those of the two slits, but only for the fringes produced by the mirrors, which exhibit the simplest case of the interference of rays slightly inclined to each other. In order to obtain from the theory, a rigorous determination of the situation of the dark and light stripes in the two former cases, it is not sufficient to calculate the effect of two systems of undulations, but those of an infinite number of similar groups must be combined, according to a principle which will shortly be explained, in treating of the general theory of diffraction. ii. _Rule for the Correction of a_ LUNAR OBSERVATION. _By_ Mr. WILLIAM WISEMAN, _of Hull_. RULE. Add together the reserved logarithm (found as directed, page 111 and 112 of the Appendix to the third edition of the Requisite Tables) the log. sines of half the sum, and half the difference of the apparent distance, and difference of apparent altitudes, and 0.3010300, the log. of 2. Then, to the natural number corresponding to the sum of these four logarithms, add the natural verse sine of the difference of true altitudes, and the sum will be the natural verse sine of the true distance.