An ingenious modification of the fixed apparatus is also due to the inventive mind of FRESNEL, who conceived the idea of placing one apparatus of this kind in front of another, with the axis of the cylindric pieces crossing each other at right angles. As those cylindric pieces have the property of refracting all the rays which they receive from the focus, in a direction perpendicular to the mixtilinear section which generates them, it is obvious that if two refracting media of this sort be arranged as above described, their joint action will unite the rays which come from their common focus into a beam, whose sectional area is equal to the overlapped surface of the two instruments, and that they will thus produce, although in a disadvantageous manner, the effect of an annular lens. It was by availing himself of this property of crossed prisms, that FRESNEL invented the distinction for lights, which he calls _a fixed light varied by flashes_; in which the flashes are caused by the revolution of cylindric refractors with vertical axes, ranged round the outside of the fixed light apparatus already described. ~True Cylindric form given to the Refractors and other improvements in their Construction.~ Having been directed by the Commissioners of the Northern Lighthouses to convert the fixed catoptric light of the Isle of May, into a dioptric light of the first order, I proposed, that an attempt should be made to form a true cylindric, instead of a polygonal belt for the refracting part of the apparatus; and this task was successfully completed by Messrs COOKSON of Newcastle in the year 1836. The disadvantage of the polygon lies in the excess of the radius of the circumscribing circle over that of the inscribed circle, which occasions an unequal distribution of light between its angles and the centre of each of its sides; and this fault can only be fully remedied by constructing a cylindric belt, whose generating line is the middle mixtilinear section of an _annular_ lens, revolving about a vertical axis passing through its principal focus. This is, in fact, the only form which can possibly produce an equal diffusion of the incident light over every part of the horizon.