In the course of supplying the numerous wants of navigation, it will often be found necessary to _cut off_, on a given bearing, the beam proceeding from a Lighthouse, as a guide to the seaman to avoid some shoal, or as a hint to put about and seek the opposite side of a channel. This is attended with some little practical difficulty, especially in lights from reflectors arranged externally on a circle, because a certain portion of light, chiefly due to the divergence caused by the size of the flames, and partly from the effects of the diffraction or inflexion of the light, spreads faintly over a narrow sector between the light arc and the dark one. It becomes necessary, of course, to make allowance for this penumbral arc by increasing the masked portion of the lantern; and, where a very sharp line of demarcation is required, a board is sometimes placed on the outside of the Lightroom, in such a position, and of such length, that while it does not enter the boundaries of the luminous sector, it prevents the more powerful part of the penumbral beam from reaching the observer’s eye. This effect is, of course, more conveniently produced, where the circumstances admit of its adoption, by distributing the reflectors round the concave side of the lantern, towards the land; but such an arrangement is inapplicable when the illuminated sector exceeds the dark one. I have found, by observation, that the sector intercepted between the azimuth on which the lantern is masked and that on which total darkness is produced to an observer, at moderate distances, may be estimated at not less than 3° for dioptric, and 7° for catoptric lights of the highest class.[79] [79] The method which I adopted for determining those quantities, was to mask a certain portion of the lantern of a lighthouse subtending an horizontal sector of about 30° or 40°, and at night to fix, by actual observation, at the distance of 5 or 6 miles, two points on the coast between which the light so masked was obscured. The angle included between the lines joining those points and the centre of the lantern was then determined by triangulation next day, and _half the difference_ between the observed angle (which is always the _lesser_ of the two) and the computed subtense of the masked sector of the lantern, is, in each case, the amount of the allowance stated in the text. Those quantities may therefore serve to guide the Lighthouse engineer to approximate more rapidly to his object, as he will generally be safe in increasing the dark sector, by one or other of the above constants, according to the kind of apparatus employed. I need not add, that in a matter of this kind, a final appeal to actual observation is, in all cases, indispensable. ~Double Lights.~