Such an apparatus is shewn in Plate XVII.; and the accompanying diagram (fig. 70) shews an elevation ABCD, a section BD, and a plan ABD, of a single pannel of this improved compound belt. AC and BD are the diagonal joints above described. Time and perseverance, and the patience and skill of Monsieur FRANÇOIS SOLEIL, whom I urged to undertake the task, were at length crowned with success; and I had the satisfaction at last of seeing a fixed light apparatus, having its form truly cylindric, and its central belt in one piece, while the joints were inclined to the horizon at such an angle as to render the light perfectly equal in every azimuth. ~Catadioptric Zones.~ The loss of light by reflection at the surface of the most perfect mirrors, and the perishable nature of the material composing their polish, induced me, so far back as 1835, in a Report on the Light of Inchkeith, which had just been altered to the dioptric system, to propose the substitution of _totally reflecting_ prisms, even in lights of the first order or largest dimensions. In this attempt I was much encouraged by the singular liberality of Mr LEONOR FRESNEL, to whose friendship (as I have often, with much pleasure, acknowledged) I owe all that I know of dioptric Lighthouses. He not only freely communicated to me the method pursued by his distinguished brother AUGUSTIN FRESNEL, in determining the forms of the zones of the small apparatus, introduced by him into the Harbour Lights of France, and his own mode of rigorously solving some of the preliminary questions involved in the computations; but put me in possession of various important suggestions, which substantially embrace the whole subject. Another friend also helped me, by pointing out certain less direct methods of determining some of the elements, which greatly abridged the labours of computation. Mr FRESNEL agreed with me in anticipating a considerable increase of the light derived from the accessory part of the apparatus; but he expressed his opinion, that in order to prevent great absorption, the rings should not greatly exceed those of the small apparatus in their sectional area. This would have required about _forty_ rings to intercept the same quantity of light acted upon by the curved mirrors; and, although the difficulties of grinding were somewhat similar to those which had already been encountered in forming the cylindric belt for the Isle of May apparatus, there were also some special difficulties attending the formation of the catadioptric zones, which appeared so formidable as to deter me by the expense of grinding so many zones, and led me to think of adopting flint glass. Considerable masses, of a very pure and homogeneous appearance, had been shewn to me by the late Dr RITCHIE of the London University, who calculated upon the uniform and permanent success of his process; but, whatever foundation there might have been for this hope, it was