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Rh of mean horizontal divergence, and C = constant varying between .9 and .75 according to the description of apparatus. The factor H/h must be eliminated in the case of fixed lights. Deduction must also be made in the case of coloured lights. It should, however, be pointed out that photometric measurements alone can be relied upon to give accurate values for lighthouse intensities. The values obtained by the use of Allard’s formulae, which were largely used before the necessity for actual photometric measurements came to be appreciated, are considerably in excess of the true intensities. —Île Vierge Apparatus and Lantern. Plan at focal plane. Optical Calculations.—The mathematical theory of optical apparatus for lighthouses and formulae for the calculations of profiles will be found in the works of the Stevensons, Chance, Allard, Reynaud, Ribière and others. Particulars of typical lighthouse apparatus will be found in tables VI. and VII.

4. —The earliest form of illuminant used for lighthouses was a fire of coal or wood set in a brazier or grate erected on top of the lighthouse tower. Until the end of the 18th and even into the 19th century this primitive illuminant continued to be almost the only one in use. The coal fire at the Isle of May light continued until 1810 and that at St Bees lighthouse in Cumberland till 1823. Fires are stated to have been used on the two towers of Nidingen, in the Kattegat, until 1846. Smeaton was the first to use any form of illuminant other than coal fires; he placed within the lantern of his Eddystone lighthouse a chandelier holding 24 tallow candles each of which weighed of a ℔ and emitted a light of 2.8 candle power. The aggregate illuminating power was 67.2 candles and the consumption at the rate of 3.4 ℔ per hour.

Oil.—Oil lamps with flat wicks were used in the Liverpool lighthouses as early as 1763. Argand, between 1780 and 1783, perfected his cylindrical wick lamp which provides a central current of air through the burner, thus allowing the more perfect combustion of the gas issuing from the wick. The contraction in the diameter of the glass chimney used with wick lamps is due to Lange, and the principle of the multiple wick burner was devised by Count Rumford. Fresnel produced burners having two, three and four concentric wicks. Sperm oil, costing 5s. to 8s. per gallon, was used in English lighthouses until 1846, but about that year colza oil was employed generally at a cost of 2s. 9d. per gallon. Olive oil, lard oil and coconut oil have also been used for lighthouse purposes in various parts of the world.

Mineral Oil Burners.—The introduction of mineral oil, costing a mere fraction of the expensive animal and vegetable oils, revolutionized the illumination of lighthouses. It was not until 1868 that a burner was devised which successfully consumed hydrocarbon oils. This was a multiple wick burner invented by Captain Doty. The invention was quickly taken advantage of by lighthouse authorities, and the “Doty” burner, and other patterns involving the same principle, remained practically the only oil burners in lighthouse use until the last few years of the 19th century.

The lamps used for supplying oil to the burner are of two general types, viz. those in which the oil is maintained under pressure by mechanical action and constant level lamps. In the case of single wick, and some 2-wick burners, oil is supplied to the burner by the capillary action of the wick alone.

The mineral oils ordinarily in use are petroleum, which for lighthouse purposes should have a specific gravity of from .820 to .830 at 60° F. and flashing point of not less than 230° F. (Abel close test), and Scottish shale oil or paraffin with a specific gravity of about .810 at 60° F. and flash point of 140° to 165° F. Both these varieties may be obtained in England at a cost of about 6d. per gallon in bulk.

Coal Gas had been introduced in 1837 at the inner pier light of Troon (Ayrshire) and in 1847 it was in use at the Heugh lighthouse (West Hartlepool). In 1878 cannel coal gas was adopted for the Galley Head lighthouse, with 108–jet Wigham burners. Sir James Douglass introduced gas burners consisting of concentric rings, two to ten in number, perforated on the upper edges. These give excellent results and high intensity, 2600 candles in the case of the 10–ring burner with a flame diameter at the focal plane of 5 in. They are still in use at certain stations. The use of multiple ring and jet gas burners is not being further extended. Gas for lighthouse purposes generally requires to be specially made; the erection of gas works at the station is thus necessitated and a considerable outlay entailed which is avoided by the use of oil as an illuminant.

Incandescent Coal Gas Burners.—The invention of the Welsbach mantle placed at the disposal of the lighthouse authorities the means of producing a light of high intensity combined with great focal compactness. For lighthouse purposes other gaseous illuminants than coal gas are as a rule more convenient and economical, and give better results with incandescent mantles. Mantles have, however, been used with ordinary coal gas in many instances where a local supply is available.

Incandescent Mineral Oil Burners.—Incandescent lighting with high-flash mineral oil was first introduced by the French Lighthouse Service in 1898 at L’Île Penfret lighthouse. The burners employed are all made on the same principle, but differ slightly in details according to the type of lighting apparatus for which they are intended. The principle consists in injecting the liquid petroleum in the form of spray mixed with air into a vaporizer heated by the mantle flame or by a subsidiary heating burner. A small reservoir of compressed air is used—charged by means of a hand pump—for providing the necessary pressure for injection. On first ignition the vaporizer is heated by a spirit flame to the required temperature. A reservoir air pressure of 125 ℔ per sq. in. is employed, a reducing valve supplying air to the oil at from 60 to 65 ℔ per sq. in. Small reservoirs containing liquefied carbon dioxide have also been employed for supplying the requisite pressure to the oil vessel.

The candle-power of apparatus in which ordinary multiple wick burners were formerly employed is increased by over 300% by the substitution of suitable incandescent oil burners. In 1902 incandescent oil burners were adopted by the general lighthouse authorities in the United Kingdom. The burners used in the Trinity House Service and some of those made in France have the vaporizers placed over the flame. In other forms, of which the “Chance” burner (fig. 44) is a type, the vaporization is effected by means of a subsidiary burner placed under the main flame.

Particulars of the sizes of burner in ordinary use are given in the following table.