ORDINARY optical apparatus adapted for a lighthouse which has to illuminate the whole horizon, as at rock or insular stations, is unsuitable for stations situate on the coast line, or in narrow sounds, where the light has in some azimuths to be seen at great distances, in others at smaller, and where towards the land no light is wanted at all. The problem in such cases is to allocate the rays in the different azimuths in proportion to the distances and breadths of sea in which the light requires to be seen in those directions by the sailor. Before 1855 no attempt was made to deal with this question, excepting the simple expedient of placing a spherical mirror on the landward side, where no light was wanted, and thus the rays intercepted by the mirror were reflected back again through the flame, so as to be ultimately acted on by the apparatus at the seaward side. But this device did not in any way fulfil the condition of allocating the rays proportionally to the varying, distances at which the light had to be seen in the different azimuths, nor to the amplitude of the arcs. What was required was a system by which the whole light from the lamp should be spread horizontally and with strict equality over any given arc in azimuth; and at a light of unequal range, which must be seen at different distances in different azimuths. the rays should he allocated to each of such arcs in the compound ratio of the number of degrees and the distances from which the light has to be seen in such arcs.
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STEVENSON, T. On an Improved Optical Arrangement for Azimuthal Condensing Apparatus for Lighthouses . Nature 12, 333–335 (1875). https://doi.org/10.1038/012333c0