mirrors are very far from being a correct theoretical solution of this problem; and the practical departures from theory, in so far as they correct the abstract faults, annul the abstract merits of the arrangement. Both in theory and practice, every simple metallic reflector is radically faulty; for it must waste much of the reflected light, and must leave the front radiation wholly uncorrected. Except for this loss of light and front radiation, a series of lamps on faces of a revolving frame, each lamp with its paraboloid mirror attached, would make up a satisfactory revolving light; but no satisfactory fixed light is thus possible.

As might be supposed, it was not till the Argand lamp had given an intense concentrated light that spherical or paraboloidal mirrors were to any extent used in light-houses. Some rude trials of plane mirrors, and paraboloids built of plane glass facets, preceded Borda's arrangement of Argand burners with paraboloid reflectors on a revolving frame, first set up in the Corduan tower, in 1784; but, practically, the great merit of this combination belongs either to Teulère or to Borda, who, aided by Lenoir's skill, really initiated the existing catoptric system. Probably no essential advance from Borda's arrangement will ever be made by using metallic reflection only. None has thus far been realized; and, from the nature of the case, all metallic catoptric arrangements must leave much of the light unutilized. Borda's plan, though still much in use, only survives by virtue of organic inertia, and it is now rapidly giving place to one vastly superior.

A strict geometric law also governs the refraction of light at the surfaces of transparent bodies. The sines of the two angles made by the incident and refracted portions of a ray with the normal at the point of incidence, bear a constant ratio to each other, for each substance, whatever be the angle of incidence. Each refracting medium, placed in vacuo, is characterized by its own special value of this ratio, called its index of refraction, which may once for all be experimentally determined for each substance. Knowing the indices of refraction for the various media of a given combination, as a telescope, microscope, or a light-house refracting system, the entire course of any ray

a

therein can be accurately traced. Given, then, glass of a known index of refraction, how can all the rays of a central light-house lamp be strictly utilized by its use, and what shapes and positions must be given it?

To Augustin Fresnel the world owes enduring gratitude, for his elegant and almost faultless solution of this practical problem. Prior to his research, lenses had been tried for giving direction to light-house illumination; but these trials were very faulty, either optically or mechanically. In England and Ireland, simple spherical lenses were placed before lights a hundred years ago; but their great thickness, and the bad quality of the glass, made them, on the whole, injurious to their effect. Buffon, who was much engaged in forming burning-glasses by which the sun's parallel rays are focalized, proposed to cut away the central mass of glass, and to reduce the lens to a series of rings placed around the central lens in echelon order. As his idea was to make all these in a single connected piece of glass, its supreme mechanical difficulty made it virtually impracticable. Condorcet was the first to indicate the plan of a separate formation of the rings, with which large annular lenses might then be built up. Brewster, when treating of burning-glasses, in 1811, presented a clear exhibit of the composition and action of annular lenses, and advocated their use in the inverse problem of parallelizing the rays diverging from a light-house lamp flame as a focus. As he did not fully embody his ideas in practical forms, and as he, apparently inspired with less than his accustomed ardor, failed to procure responsive action by the inert light-house commissioners, no fruit resulted from his advanced conceptions. Brewster, of all men living, can best afford to spare a single optical laurel, but even this he is not bound wholly to forego. In 1819, Arago of fered to undertake for the light-house commission a systematic series of researches, with the express object of improving light-house illumination, and for this he applied to have Mathieu and Fresnel assigned as co-laborers. It was through the acceptance of this proposal that Fresnel, being duly detailed as an officer of Ponts et Chaussées, was led to that brilliant train of researches and inventions so admirably detailed in his Memoir, read before the Academy July

29, 1822, in which, not knowing of Brewster's conceptions, he takes up the whole problem de novo. He was already recognized as the profoundest optical philosopher of his age, and as a perfect master of the most difficult analytical implements. Among the many illustrious opticians since Newton and Huygens, we think not one has possessed so excellent a blending of all the qualities and powers needed for fruitful and complete research as Augustin Fresnel. As with Snellius and Malus, his brilliant career of research was prematurely closed, yet each of this illustrious trio made fundamental discoveries which only Young has equaled since Newton and Huygens. To them we may apply Newton's saying when Coates died: "Had these men lived, we should have known something." Huygens originated the watch, and the undulatory theory of light; Fresnel approached his merit, by inventing his light-house apparatus, and by discovering the formulæ of interference, double refraction, and polarization. Before the trained powers of such a man, the difficulties of lighthouse optics vanished forever. Not content with vaguely indicating desirable combinations, he determined, with precision, their exact form, dimensions, and modifications. He left but few improvements to be made, and even these he had indicated the mode of effecting. It is not amiss, therefore, to call the dioptric or catadioptric light-house apparatus, now in general use, the Fresnel lens-a name than which no worthier or more enduring monument could be erected. We will now indicate briefly the prevailing forms of these lenses.

The light is produced by a single central lamp-flame, proceeding from concentric wicks, varying in number from one to five, the focus being the central point of flame. Around this are arranged, for a fixed light of the first order, horizontal hoops or rings of glass, so shaped and placed as to throw out in a horizontal direction all the light received on them. Thus while the horizontal divergence is duly preserved, the vertical divergence is counteracted, and nearly all the rays are brought into a flat, star-like horizontalism (as when a chestnut burr is pressed flat), and the illumination is equally diffused over all points in the horizon. The number of these rings varies with the order of the light, and, in all cases, the thickness of

glass to be penetrated is so small that absorption produces only a slight loss. The middle ring, at the level of the flame, is plane-convex in cross-section, with the convexity outwards, and is of considerable breadth above and below the focal level. The rings just above and below this have a four-sided, approximately-trapezoidal section, and with the precise curvature on the exterior for parallelizing and horizontalizing the emerging rays. The several rings, above and below, are similarly determined. All these rings are limited by horizontal top and bottom surfaces, and their interior surfaces together make up a vertical cylinder: thus all the curvatures are thrown into the outer surfaces. The horizontal glass surfaces in contact are cemented, and the segments of the rings are sustained by metal ribs placed radially, and connected with the main supporting-frame. This cylindrical refractor receives the rays for about 30° above and 30° below the horizontal plane, through the focus. It is surmounted by a domelike arrangement of prismatic zones, so adjusted as to receive and horizontalize the rays between about 30° and 80° above the horizontal. These zones give a spherical triangle in cross-section. The light enters at the under side, passes to the superior face, where it is intervally reflected, and, after a second refraction at the outer surface, it emerges duly horizontalized. It is fortunate that interval reflection is attended with far less loss of light than in metallic reflection, provided it take place as in these zones, within the angle called the angle of total reflection. The cylinder of the main cylindrical refractor is extended downward by several zones of spherical triangular cross-section, operating like the upper zones, and receiving the light from 30 to 52° below the horizontal. Thus all the rays, except an upper cone of 10° angle, and a lower one of 38° angle, are received on glass rings, and thrown out horizontally and uniformly in each azimuth. The upper opening is needed for the chimney, and the lower for the lamp and lamp-attendance-very little light being thrown down in that space any way, because it is eclipsed by the lamp and wick. Such, in general terms, is a fixed catadioptric lens-the cylindrical refractor simply bending the rays horizontally, while the upper and lower zones combine

two refractions with one interval reflection. A cylinder of glass rings is underpinned with glass rings, and is crowned with a dome of glass rings, and all are upheld by vertical or slightly oblique metal ribs, horizontally connected. Sometimes there are thirtysix or forty of these rings in one apparatus. Any focal light in this magnificent glass cage-six feet in interior diameter, and nine or ten feet highmust shine, exclusively, for the benefit of those outside wanderers who skirt the horizon, and cannot waste its splendors on aeronauts and hovering angels. Star-gazing is under prohibition, and each ray must acknowledge king utility.

There are several important variations from this fixed-light combination, besides the modifications for different orders of fixed-lights. For a revolving lens-light, a regular polygon is assumed as a basis, on which to erect faces of glass refractors and prisms, operating as in the fixed-light, except, that all the light, incident on each face, issues as a single parallel beam, or nearly so. A central circular lens, at the level of the focus, is placed in each face, and is so surrounded by ring-lenses as with them completely to fill the rectangle of the face. This rectangle is surmounted by a dome segment of curved prisms, and is extended downward, by several like internally reflecting prisms. All these parts are determined by the condition, that the transmitted rays shall emerge parallelized horizontally as well as vertically. If the primary plan were an octagon, eight such beams would be produced simultaneously. To the whole arrangement, a clock-work gives a regular rotation around a vertical axis, thus bringing the beams successively to bear on an eye in the horizon, which sees a regular series of blazes or long flashes succeeding at stated intervals, characteristic for each light. A considerable duration is essential to the flash, hence the rotation must not be very rapid. There is, however, opportunity to give a considerable variety of distinctly recognizable appearances to different revolving lights, so as to avoid mistaking one for another.

The fixed-light, varied with flashes, is produced by revolving a combination of vertical prisms around a fixed lenslight, so as to parallelize a portion of the horizontally diverging rays, or it

might be made by inserting one face of a revolving-lens apparatus in the fixedlight apparatus, and giving a revolution to the whole. Such a light is seen most of the time, as if a steady fixed one; but a bright flash, preceded and followed by a short eclipse, occurs once during each revolution. This ingenious device of Fresnel gives one of the best characteristic distinctions of a light. There are many cases where the land-action of a light causes the waste of about half the rays. This is in part remedied by what are called holophotal arrangements, in inventing which, Alan and Thomas Stevenson have been distinguished. By placing spherical reflectors or prismatic combinations for effecting a like result, by two interval reflections behind the lamps, the landward rays may be thrown back through the flame, whence they will emerge as if original light issuing seaward. Innumerable devices, modifications, adaptations, and details of lighthouse optical apparatus have been made, to which we cannot take space to allude.

Suffice it to specify the sizes and character of the six orders of lens-apparatus. The first order lamp has four or five wicks, and the lens-apparatus or glass-cage is six feet in internal diameter, and from nine to ten feet high. This is eminently the sea-coast light, and it is adapted to the greatest ranges. The second order lamp has three concentric wicks, and the apparatus is four feet seven inches in inner diameter. The third order lamp has two wicks, and its apparatus is three feet three and one-third inches diameter. The fourth order has one or two wicks, and one foot seven and three-fourth inches diameter; the fifth, one wick, and one foot two and three-fourth inches diameter, and the sixth, one wick, and eleven and threefourth inches inner diameter. These lights may be either fixed, fixed, varied with flashes, or revolving. These distinctions, with those derived from times of revolution, are chiefly relied on, and are quite sufficient, except in some overcrowded localities. Double lights, or two lights, either on the same tower or on two adjacent towers, are sometimes used for distinction; but this mode has the fault of requiring two lights to do what one may be made to accomplish. Besides, at a distance of one mile for each six feet of vertical

separation, two lights run together, and if they are on two towers, not only are they liable to blend at the same rate, but their opening varies with their bearing. Range-lights, consisting of two lights covering vertically to indicate a channel, or other important right line, are of great value in certain cases. Tide-lights, to show the height and stage of tide, are much used in Europe, but not yet in the United States. Thomas Stevenson gives the name of apparent light to his combination, constructed at Stornoway, by which a lamp on the shore illuminates a beacon, supporting a reflecting apparatus 530 feet from the light, whereby the beacon is made to show as a light to a distance of over a mile in a certain sector.

From what has been said, it will be seen that the catoptric and diacatoptric systems of apparatus are the only two generally available. Theoretically, the diacatoptric system has a very great superiority over the parabolic mirror system. Practically and economically, this advantage is equally great, as is proved by a vast array of comparative statistics, and by the fact that every. where, where the subject is understood, lenses are rapidly replacing mirrors, but nowhere so rapidly as in our own country. The gain experienced from substituting lenses for reflectors, in some of the smaller lights of our establishment, has been found to be enormous: indeed, the cost of maintaining reflectors and providing oil and supplies of all kinds, was actually, in these cases, about ten times greater than for the regular supply of lenses, giving more effective lights. When all our lights are fitted with lenses, the quantity of oil consumed will be only from one-fourth to one-fifth what it would be with equivalent reflectors under the old system. Thus a reflector light of ten lamps consumed over 400 gallons yearly, while a fourth order lens only burns about fifty gallons. The importance of this economy will be better appreciated from the fact that our authorized lights would, if all fitted with reflectors, require 5,110 lamps, burning forty gallons each, or 204,400 gallons in all, yearly; while the actual estimate for the year only calls for 148,150 gallons, giving an absolute saving, by the present lenses, of 56,250, which, at $225 per gallon, makes $126,562 as the pecuniary saving for a year. Of course, as our supply of lenses is increased, this sum

will undergo a proportionate increase. The oil saving for our 494 lights, in 1854, anticipated from a complete substitution of lenses for reflectors, was estimated at 130,720 gallons, or, at present prices, a value of $394,120. Have we not good reason for pronouncing Fresnel a public benefactor? When the annual advantage to us alone, for a single scientific invention, is thus expressed in hundreds of thousands, we may well demand honor and recognition for those more abstract and recondite fields of investigation whence Fresnel drew his power to become a benefactor. Nor should we here forget to express our admiration for that excellent mastery of glass fabrication and manipulation, and for that tasteful skill in mechanical adjuncts, which has centralized in Paris the manufacture of light-house illuminating apparatus and lamps. Not only patronage but honor is justly awarded to men like Soleil, the mechanical and operative assistant of Fresnel in his inventive career, as also to such as Lepante and Letourneau.

If we have succeeded in conveying a tithe of the interesting information concerning light-house administration, construction, and illumination, which has been at our command, our expectation is fully answered. The superabundance of riches has been a great embarrassment, and the amplitude of the subject has made our effort seem like a hopeless attempt to coerce the towering and expanding genius in the Arabian Nights within his box-prison. A light-house not only epitomizes the arts of the engineer, mechanic, and optician, but it is an exponent of administrative organization; it is an expression of honorable commercial enterprise, it is an embodiment of national majesty, and, prouder than all, it is an untiring assertor of the common brotherhood and united humanity of the nations upon earth. Its friendly invitations, and still more friendly warnings, as, in faithful steadfastness, it shines out over the varying phases of the deep, give to it almost a human and vital interest. The quiet star-light which comes to us from remotest worlds, testifies to some unknown affinities which bridge the very depths of space; so, when the solitary ocean-rover sees, glimmering along the far horizon, a beacon-star of man's kindling, he knows that humanity, and kindness, and real philanthropy, have there a home.