Chapter IX (3)

What I have stated above as to the use of mirrors with a short focal distance for lights of great divergence, proceeds on the assumption, that the penumbral portion of the light on each side of the strongest beam (which is confined within the limits of the least divergence, due to that portion of the mirror where the focal distance is the greatest) is to be pressed into service in the illumination of the horizon; and it is the chief inconvenience which attends the application of paraboloïdal mirrors to fixed lights, that because it is impracticable to apply a number of mirrors sufficient to light the whole horizon with an equally strong light, spaces occur on either side of each reflector in which the mariner has a light sensibly inferior to that which illuminates the sector near the axis of each mirror. This will be best explained by stating the numerical results of the computations of the divergence of the mirrors used in the Northern Lights for this purpose, both at the vertex and the sides. In a mirror whose focal distance is 4 inches, and its greatest double ordinate 21 inches, illuminated by a flame 1 inch in diameter, we find by computation, that the greatest divergence is 14° 22′, and that the strongest arc of light is only 5° 16′; a difference so great, that while the one may admit of the horizon being imperfectly illuminated by means of 26 reflectors, the superior light which would result from confining the duty of each instrument within the range of its best effect, could only be obtained by the use of 68 reflectors, and the expenditure of a proportionately great quantity of oil, not to speak of the great practical difficulty which would attend the arrangement of so many lamps in a lantern of moderate size. In revolving lights, the mirrors are not, as in fixed lights, inconveniently taxed for horizontal divergence, because each portion of the divergent beam visits successively each point of the horizon. In this view of the merits of _fixed_ and _revolving_ lights, I should be disposed to recommend, in any new organisation of lights with parabolic reflectors, the adoption, in fixed lights, of reflectors with a short focal distance and small span, so as to admit of many being ranged around the frame; while in revolving lights, it would be my aim to approach the largest size of reflector that could be made, so as if possible to illuminate each face of the revolving frame by means of a large lamp in a single mirror, with a great focal distance, thereby diminishing the difference between the divergence of the powerful cone of rays reflected from the more distant parts of the mirror and that of the feebler and more diffuse light from its apex.

~Effect of Paraboloïdal mirrors.~

The maximum luminous effect of the reflectors ordinarily employed in fixed lights, as determined by observation, is generally equal to about 350 times the effect of the unassisted flame which is placed in the focus; while for those employed in revolving lights, which are of larger size, it is valued at 450. This estimate, however, is strictly applicable only at the distances at which the observations have been made, as the proportional value of the reflected beam must necessarily vary with the distance of the observer, agreeably to some law dependent upon the unequal distribution of the light in the illuminous cone which proceeds from it. The effect also varies very much in particular instruments. The ordinary burners used in lighthouses are one inch in diameter, and the focal distance generally adopted is 4 inches, so that the extreme divergence of the mirror in the horizontal plane may be estimated at about 14° 22′; while the divergence of the most luminous cone is 5° 16′ for the small reflectors, and 4° 25′ for the larger size. In arranging reflectors on the frame of a fixed light, however, it is advisable to calculate upon a less amount of effective divergence, for beyond 11° the light is very feeble; but the difficulty of placing many mirrors on one frame, and the great expense of oil required for so many lamps, have generally led to the adoption of the first valuation of the _effective_ divergence.

~Power of Paraboloïdal Mirrors.~

The measure of the illuminating power of a paraboloïdal mirror may be estimated as the _quotient of the_ SURFACE _of the circle which cuts it in the plane of its greatest double ordinate, divided by the surface of the largest vertical section of the flame, and diminished by the loss of light in the process of reflection_. This estimate will be found near enough for all practical purposes; but it is obviously inaccurate, inasmuch as it overlooks the circumstance of the focal distance of each portion of the mirror being different, and the consequent increase in the length of the various trajectories at each point of the surface as you recede from the axis; and the only correct rule, therefore, is, to find an imaginary focal distance which must be the radius of a spherical segment which shall answer the double condition of having its surface equal to that of the greatest cross section of the mirror, and of including, at the same time, a number of degrees equal to those which are brought under the influence of the reflecting action of the paraboloïd. This subject, however, as I have already hinted, is not of great practical importance; and I shall not therefore dilate on it farther, but content myself with saying, that such a line will be found to be a _mean proportional_ between the _greatest_ and _least_ focal distances of the mirror.[44] The large mirrors used in the Northern Lights have about ¹²⁄₁₇ths of the whole light of the lamp incident on their surface; the rest escapes in the comparatively useless state of naturally radiating light.

[44] This subject is treated in detail in M. BARLOW’S Paper already
noticed. (London Transactions for 1837, p. 212.)

~Manufacture of Reflectors.~

The reflectors used in the best lighthouses, are made of sheet-copper plated in the proportion of six ounces of silver to sixteen ounces of copper. They are moulded to the paraboloïdal form, by a delicate and laborious process of beating with mallets and hammers of various forms and materials, and are frequently tested during the operation by the application of a mould carefully formed. After being brought to the curve, they are stiffened round the edge by means of a strong bizzle, and a strap of brass which is attached to it for the purpose of preventing any accidental alteration of the figure of the reflector. Polishing powders are then applied, and the instrument receives its last finish. The details of this manufacture are given in the Appendix.

~Testing of Mirrors.~

Two gauges of brass are employed to test the form of the reflector. One is for the back, and is used by the workmen during the process of hammering, and the other is applied to the concave face as a test, while the mirror is receiving its final polish. It is then tested, by trying a burner in the focus, and measuring the intensity of the light at various points of the reflected conical beam. Another test may also be applied successively to various points in the surface, by masking the rest of the mirror; but as it proceeds upon the assumption that the surface of the reflector is perfect, and that we can measure accurately the distance from a radiant coincident with the focus to the point of the mirror to be tried, it is in practice almost useless. For such a trial we must place a screen in the line of the axis of the mirror at some given distance from it, and ascertain whether the image of a very small object placed in the conjugate focus, which is due to the distance of the screen in front of the focus, be reflected to any point considerably distant from the centre of the screen through which the prolongation of the axis of the mirror should pass. We thus obtain a measure of the error of the instrument. For this purpose, we must find the position of the conjugate focus, which corresponds to the distance of the screen. If _b_ be the distance to which the object should be removed outwards from the principal focus of the mirror, _d_ the distance from the focus to the screen, and _r_ the distance from the focus to that point of the mirror which is to be tested, we shall have

_r_²
_b_ = ----
_d_

as the distance to which the object must be removed outwards from the true focus on the line of the axis.[45]

[45] The truth of this equation may be easily ascertained as follows
(See fig. 27):--Let AP be the mirror, F its principal focus, and PH
the line of reflection of the ray FP; then an object at I will be
reflected at P to the conjugate focus O, where the screen is supposed
to be placed. But by construction, FPI = HPO = POF, and the angle at
F being common, the triangle FPI is similar to FPO, and hence FO ∶
PF ∷ PF ∶ FI, and

PF²
FI = ---;
FO

and substituting the letters in the text, we get _d_ ∶ _r_ ∷ _r_ ∶
_b_, and

_r_²
_b_ = ----.
_d_

~Argand Lamps used in Reflectors.~

The flame generally used in reflectors, is from an Argand fountain-lamp, whose wick is an inch in diameter. Much care is bestowed upon the manufacture of the lamps for the Northern Lighthouses, which sometimes have their burners tipped with silver to prevent wasting by the great heat which is evolved. The burners are also fitted with a sliding apparatus, accurately formed, by which they may be removed from the interior of the mirror at the time of cleaning them, and returned exactly to the same place, and locked by means of a key. This arrangement, which is shewn in figs. 28, 29, and 30, is very important, as it insures the burner always being in the focus, and does not require that the reflector be lifted out of its place every time it is cleaned; so that, when once carefully set and screwed down to the frame, it is never altered. In these figs. _a a a_ represents one of the reflectors, _b_ is the burner, and _c_ a cylindric fountain, which contains 24 ounces of oil. The oil-pipe, the fountain _c_ for supplying oil, and the burner _b_, are connected with the rectangular frame _d_, which is moveable in a vertical direction upon the guide-rods _e_ and _f_, by which it can be let down, so that the burner may be lowered out of the reflector, by simply turning the handle _g_ (as will be more fully understood by examining figs. 28 and 29), which has the effect of forcing a _thread_ (like that of a screw) on the outside of the guide into a groove in the frame, or withdrawing it, and thus allows it to slide down or locks it at pleasure. An aperture of an elliptical form, measuring about two inches by three, is cut in the upper and lower part of the reflector, the lower serving for the free egress and ingress of the burner, and the upper, to which the copper tube _h_ is attached, serving for ventilation; _i_ shews a cross section and a back view of the main bar of the chandelier or frame on which the reflectors are ranged, each being made to rest on knobs of brass, one of which, as seen at _k k_, is soldered to the brass band _l_, that clasps the exterior of the reflector. Fig. 28 is a section of the reflector _a a_, shewing the position of the burner _b_, with the glass chimney _b′_, and oil-cup _l_, which receives any oil that may drop from the lamp. Fig. 30 shews the apparatus for moving the lamp up and down, so as to remove it from the reflector at the time of cleaning it. In the diagram (fig. 30) the fountain _c_ is moved partly down; _d d_ shews the rectangular frame on which the burner is mounted, _e e_ the elongated socket-guides through which the guide-rods slide, and _f_ the guide-rod, connected with the perforated sockets on which the _checking-handle g_ slides. The oil-cup _l_ (covered with a lid and wick-holder, as shewn in fig. 31) also serves as a _frost-lamp_ during the long nights of winter, when the oil is apt to turn thick. It is attached to the lower part of the oil-tube by the arm _h_; and is lighted about an hour before sunset, so as to prepare the reflector lamp for lighting at the proper time. The communication between the burner and the fountain is easily opened or shut in the burners used in the Scotch Lighthouses, by simply giving the fountain a turn of one quadrant of the horizon round its own vertical axis by means of the round knob at its top, and thereby moving a simple slide-valve, which shuts off the communication between the fountain-tube and lamp-tube. By this mode, the oil is cut off about fifteen minutes before extinguishing the lights, so that when that is done, the burner is quite free of oil.

~Arrangements for Raising or lowering the Argand Wick.~

It would needlessly occupy much time and space to describe the various means (many of them sufficiently clumsy) which have been employed, and in many places are still in use, for raising and depressing the wick; it will be enough to say, that they all involve some application of the rack and pinion. I shall, therefore, only describe the method (invented, it is believed, by M. VERZY) which is adopted in all the Lighthouses in the district of the Commissioners of Northern Lights. The arrangement is as follows (see figs. 32, 33, 34, 35, 36):--The inner tube _t_ of the burner is enclosed by a strong tube _s_, which fits to it tightly, so as not to be easily moved. This strong tube has a spiral groove cut on its outer or convex surface. The wick-holder has two small pegs projecting from it, the one on the inside (not seen), and the other on the outside at _a_ (fig. 33). That on the inside works in the spiral groove of the tube S (figs. 32 and 33), already described as embracing the inner tube _t_; and all that is required for raising the wick is to make the wick-holder turn round on its vertical axis. This is effected by means of the small external peg _a_ of the wick-holder (fig. 33), which moves in a vertical slit _a_ (figs. 32 and 34), cut in a tube standing in the burner, and concentric with it, and which also moves freely round its axis. Small knobs _n_ _n_ (figs. 32, 34, and 36), at the top of this tube, fit into a notch in the upper ring of the gallery, which supports the glass chimney. By turning this gallery _g_ (see figs. 33 and 36), therefore, motion is given to the tube, with its knobs _n_ _n_, whose vertical slit _a_ (while it holds the external peg of the wick-holder, and also turns it round along with it) permits that peg _a_ to slide upwards or downwards, and thus the wick-holder rises or falls, according as its own internal peg moves up or down the spiral groove in the tube S. In fig. 32, C shews the glass chimney resting on the gallery _g g_.

~Flowing of the Lamp.~

An important point in the economy of the Argand lamp, is the level at which the outlet for the oil, in its passage from the fountain to the burner, should be cut. The cutting of this hole (generally called the _flow-hole_) in the pipe is termed the _flowing_ of the lamp, and is commonly done by successive trials, until the oil stands at the proper level of the burner, before the wick is put in. A more ready and accurate method of accomplishing this object and at once determining the level at which the _flow-hole_ should be cut, was introduced by Mr JAMES MURDOCH, the Foreman of Lightroom Repairs to the Scotch Board, and is generally employed in the Northern Lighthouses. Its nature will be readily understood by a reference to the accompanying diagram, No. 37:

The _hatched_ surface represents a metallic ruler, with a spirit-level at L; C is the cup in which the bottom of the fountain _f_ (shewn in dotted lines) rests. When the fountain is removed, and the ruler rests on the edge of the cup C, the screw at A is used to adjust the level at L; and a gauge GG is allowed to fall until a notch in it at _x′_ rests on the outer tube of the burner F; the pinching-screw B retains this ruler in its place, and the point _x′_ indicates the level at which the oil should stand in the burner. The level line _x′ x_ indicates the level on which the top of the _flow-hole_ H should be cut in the fountain-tube, which is shewn in dotted lines within the outer tube, or _body_ of the lamp. In other words, _y′ x′_ measures the level at which the oil should stand in the burner _below_ the lower edge of the metallic ruler, while the corresponding line _y x_, at the opposite end, shews the level of the top of the _flow-hole_ H, below the edge of the cup C. The gauge GG applied to that point of the fountain which coincides with the edge of the cup (so that _y′_ coincides with _y_) measures the length _yx_ = _y′ x′_; and a _set-square_ applied at _x_ gives the position of H on the fountain-tube. The round dot at _a_ shews the position of the air-hole in the body of the lamp, which establishes a connection between the external air and the surface of the oil. The rods SS′ shew the sliding gear (described as _d_ and _f_, page 221), and are only introduced to identify this diagram with those of the fountain and burner which have preceded it.

The most advantageous level of the flow-hole depends on many circumstances too obscure and complicated to admit of any systematic elucidation; and it is enough for all practical purposes, to know that the capillary powers of the wick, and the greater or less viscidity of the oil, are the chief circumstances which determine that level. Actual experience is the only sure guide to the best practice in this respect; and I therefore content myself with stating, that it is generally found that the sperm oil should stand in the empty burner at about ³⁄₈ inch below its top. For colza oil ²⁄₈ inch is sufficient. In summer, owing to the oil being more fluid, there is sometimes a tendency to overflow the burner; but any inconvenience arising from it is avoided by the plan adopted in the Northern Lights, of shutting off the oil (by means of the apparatus already alluded to on p. 222) about fifteen minutes before extinguishing the lights in the morning.

The arrangement for cutting off the oil is very simple, as will be seen from the annexed diagram (fig. 38), in which F is the fountain, T the oil-tube leading to the burner, and V the _flow-hole_, with its sliding valve. By turning the handle H one quadrant of the circle, the whole fountain F and tube T turn round their vertical axis, while the valve V, which rests in a notch in the cup of the lamp, remains still, and sliding over T, opens the _flow-hole_. S is the screw-plug which retains the oil in the fountain, and which is unscrewed and removed when the fountain is to be filled.

~Placing the Lamp in the Focus.~

In the reflecting apparatus of the Northern Lighthouses, the focal position of the lamp is not, as we have already seen, liable to derangement, by the removal of the burner for the purpose of cleaning, as the sliding gear described at p. 221 insures the return of the lamp to its true place. The burner is originally set by means of a gauge, which touches four points of the mirror’s surface (one of them being its vertex, and the other three in the vertical plane of its greatest double ordinate). This gauge being provided with a short tube or collar properly placed for the purpose of receiving the burner, at once verifies its true position, both vertical and horizontal. The diagrams 39 and 40 shew the nature of the apparatus for adjusting the burners, the one being a plan and the other a section. The four points which touch the curve are one _g_ at the vertex, two in the same horizontal plane with the focus, and near the edge of the mirror at PP, and the fourth, also near the edge, and in the same vertical plane with the focus. F is the focus. The horizontal arms are graduated, and fitted with sliding pieces and clamping screws at R, so as to admit of being varied with the width of the mirror; but each gauge applies only to curves of the same focal distance; the distance F _g_ being fixed. The gauge, when applied to the mirror, is properly secured by the screws at R, R, and R′; and the burner which is attached to the oil-tube in a temporary manner at A, is raised into the interior of the mirror. If the tube of the burner ascends into the circular tube at F until (when fixed by the checking handle already noticed at p. 221) its upper edge just touches a narrow projection inside the tube F (so placed that the rim of the burner should just touch it when it is on the level required for putting the brightest part of the flame in the focus), then the burner is in the proper position; but if, on the one hand, the axis of the burner stands beyond F, at some point between it and N (which lies in the plane of the mirror’s edge), the bent tube O from the fountain must be shortened at A; and if it rise too high, that tube must be bent down (and _vice versa_), until, by successive trials, it shall exactly fit into the tube F, and stand at the proper level. A skilful workman soon comes to guess those quantities very accurately; and, almost at the first trial, curtails the tube to the proper length, and bends it to the suitable level. All that is needful is to proceed cautiously, so as not to cut the tube too short, for this leads to some trouble.

~Distinctions of Catoptric Lights.~

The great advantage derived by seamen from the establishment of lights on a coast, soon makes the calls for additional lights so frequent, that their very number itself produces a new evil, in the difficulty of distinguishing the lights from each other. As the object of a light is to make known to the benighted mariner the land he has made, with as much certainty as the sight of a hill or tower would shew him his position during the day, it becomes an object of the first importance to impress upon each light a distinctive character, which shall effectually prevent the possibility of its being mistaken for any other.

Catoptric lights are susceptible of nine separate distinctions, which are called _fixed_, _revolving white_, _revolving red and white_, _revolving red with two whites_, _revolving white with two reds_, _flashing_, _intermittent_, _double fixed lights_, and _double revolving white lights_. The first exhibits a steady and uniform appearance, which is not subject to any change; and the reflectors used for it (as already noticed) are of smaller dimensions than those employed in revolving lights. This is necessary, in order to permit them to be ranged round the circular frame, with their axes inclined at such an angle, as shall enable them to illuminate every point of the horizon. The revolving light is produced by the revolution of a frame with three or four sides, having reflectors of a larger size grouped on each side, with their axes parallel; and as the revolution exhibits once in two minutes, or once in a minute, as may be required, a light gradually increasing to _full strength_, and in the same gradual manner decreasing to total darkness, its appearance is extremely well marked. The succession of _red_ and _white_ lights is caused by the revolution of a frame whose different sides present red and white lights; and these, as already mentioned, afford three separate distinctions, namely, alternate red and white; the succession of two white lights after one red, and the succession of two red lights after one white light. The _flashing_ light is produced in the same manner as the _revolving_ light; but owing to a different construction of the frame, the reflectors on each of eight sides are arranged with their rims or faces in one vertical plane, and their axes in a line inclined to the perpendicular, a disposition of the mirrors which, together with the greater quickness of the revolution, which shews a flash once in five seconds of time, produces a very striking effect, totally different from that of a revolving light, and presenting the appearance of the flash alternately rising and sinking. The brightest and darkest periods being but momentary, this light is farther characterised by a rapid succession of bright flashes, from which it gets its name. The _intermittent_ light is distinguished by bursting suddenly into view and continuing steady for a short time, after which it is suddenly eclipsed for half a minute. Its striking appearance is produced by the perpendicular motion of circular shades in front of the reflectors, by which the light is alternately hid and displayed. This distinction, as well as that called the _flashing light_, is peculiar to the Scotch coast, having been first introduced by the late Engineer of the Northern Lights Board. The double lights (which are seldom used except where there is a necessity for a _leading_ line, as a guide for taking some channel or avoiding some danger) are generally exhibited from two Towers, one of which is higher than the other. At the Calf of Man, a striking variety has been introduced into the character of leading lights, by substituting, for two _fixed_ lights, two lights which revolve in the same periods, and exhibit their flashes at the same instant; and these lights are, of course, susceptible of the other variety enumerated above, that of two revolving red and white lights, or flashing lights, coming into view at equal intervals of time. The utility of all these distinctions is to be valued with reference to their property of at once striking the eye of an observer and being instantaneously obvious to strangers.

The introduction of colour, as a source of distinction, is necessary, in order to obtain a sufficient number of distinctions; but it is in itself an evil of no small magnitude; as the effect is produced by interposing coloured media between the burner and the observer’s eye, and much light is thus lost by the absorption of those rays, which are held back in order to cause the appearance which is desired. Trial has been made of various colours; but red, blue, and green alone have been found useful, and the two latter only at distances so short as to render them altogether unfit for sea-lights. Owing to the depth of tint which is required to produce a marked effect, the red shades generally used absorb from ⁴⁄₇ths to ⁵⁄₆ths of the whole light, an enormous loss, and sufficient to discourage the adoption of that mode of distinction in every situation where it can possibly be avoided. The red glass used in France absorbs only ⁴⁄₇ths of the light; but its colour produces, as might be expected, a much less marked distinction to the seaman’s eye. In the Lighthouses of Scotland, a simple and convenient arrangement exists for colouring the lights, which consists in using chimneys of red glass, instead of placing large discs in front of the reflectors.

~Arrangement of Reflectors on the Frame.~

After what has been already said on the subject of divergence, it will at once be seen, that in revolving lights the reflectors are placed with their axes parallel to each other, so as to concentrate their power in one direction; whilst in fixed lights it is necessary, in order to approach as near as possible to an equal distribution of the light over the horizon, to place the reflectors, with their axes inclined to each other, at an angle somewhat less than that of the divergence of the reflected cone. For this purpose, a brass gauge (see fig. 41), composed of two long arms, AM, AM, somewhat in the form of a pair of common dividers, connected by a means of a graduated limb A, is employed. The arms having been first placed at the angle, which is supplemental to that of the inclination of the axes of the two adjacent mirrors at O, are made to span the faces of the reflectors, one of which is moved about till its edges are in close contact with the flat surface of one of the arms of the gauge.

Figs. 42 and 43 shew an elevation and plan of a revolving apparatus on the catoptric principle. In these figures, _n n_ shews the reflector frame or chandelier; _o o_, the reflectors with their oil-fountains _p_ _p_. The whole is attached to the revolving axis or shaft _q_. The copper tubes _r_ _r_ convey the smoke from the lamps; _s_ _s_ are cross bars which support the shaft at _t t_; _u u_ is a copper pan for receiving any moisture which may accidentally enter at the central ventilator in the roof of the light-room; _l_ is a cast-iron bracket, supporting the cup in which the pivot of the shaft turns; _m_ _m_ are bevelled wheels, which convey motion from the machine to the shaft. The machinery does not require any particular notice, being that of common clock-work, moved by the descent of a weight.

Fig. 44 shews a plan of one tier of reflectors arranged in the manner employed in a fixed catoptric light; _n_ _n_ shews the chandelier, _q_ the fixed shaft in the centre, which supports the whole, _o_ _o_ the reflectors, and _p_ _p_ the fountains of their lamps. In this figure (in order to prevent confusion) only one tier of reflectors is shewn; the other tiers are so arranged, that their axes divide into equal angles the arcs intercepted between the axes of the adjoining reflectors on the first tier, thereby producing the nearest approach to an equal distribution of the light, which is attainable by this arrangement.

In lighthouses of moderate height, the proper position for the reflector itself is perfect horizontality of its axis, which may be ascertained with sufficient accuracy, by trying with a plummet, whether the lips of the instrument, which we may conclude to be at right angles to the plane of its axis, be truly vertical. In lightrooms very much elevated above the sea, however, the dip of the horizon becomes notable; and a slight inclination forwards should be given to the face of the reflectors, so that their axes produced may be tangents to the earth at the visible horizon of the light-room. This, however, must not be permitted to interfere with the perfect horizontality of the top of the burner, which is indispensable to its proper burning.

~Bordier Marcet’s Reflectors.~

~Fanal Sidéral.~

Various forms of the parabolic mirror were invented by M. BORDIER MARCET, the pupil and successor of ARGAND, who has laboured with much enthusiasm in perfecting catoptric instruments, more especially with a view to their application in the illumination of lighthouses and the streets of towns. Amongst many other ingenious combinations, he has invented and constructed an apparatus which is much used in harbour-lights on the French coast, where it is known by the fanciful name of _Fanal[46] sidéral_. The object is to fulfil, as economically as possible, the conditions required in a fixed light, by illuminating, with perfect equality, every part of the horizon, by means of a single burner; and M. BORDIER MARCET has in his work-shop an instrument of this kind, eight feet in diameter, which he constructed on speculation. The apparatus used in harbour-lights, on the French coast, is of much smaller dimensions, and does not exceed fifteen inches in diameter. A perfect idea of the construction and effect of this instrument may be formed, by conceiving a parabola to revolve about its parameter as a vertical axis, so that its upper and lower limbs would become the generating lines of two surfaces possessing the property of reflecting, in lines parallel to the axis of the parabola, all the rays incident upon them, from a light placed in the point where the parameter and axis of the generating parabola intersect each other. This point being the focus of each parabolic section of this apparatus, light is equally dispersed in every point of the horizon, when the axis of the parabolic section is in a plane perpendicular to a vertical line. But however perfectly this apparatus may attain its important object, it necessarily produces a feeble effect; because as its action is entirely confined to the vertical direction, the light distributed by it decreases directly as the distance of the observer. This beautiful little instrument is shewn at fig. 45, in which _b_ shews the burner, _p p_ the upper reflecting surface, and _p′ p′_ the lower reflecting surface, both generated in the manner above described by the revolution of a parabola about its parameter _x b_; F is the focus of the generating parabola; and _l_ _l_ are small pillars, which connect the two reflecting plates, and give strength to the apparatus.

[46] Fanal, from φανεν, a lantern.

~Fanal à double effet.~

M. BORDIER MARCET has also prepared an ingenious modification of the paraboloïdal mirror, which he has described under the name of _fanal à double effet_; and the object of which is to obtain a convenient degree of divergence from parabolic mirrors, by the use of two flames and two reflecting surfaces, each of which is acted upon by its own flame, and also by that of the other. This modification consists in the union of two portions of hollow paraboloïdal mirrors, generated by the revolution of two parabolas about a common horizontal axis, and illuminated by two lamps placed in the focus of each. The first surface is generated by the revolution on its axis of a segment of a paraboloid intercepted between the parameter and some double ordinate greater than it, and may, from its form, be called the ribbon-shaped mirror. The second surface is that of a parabolic conoid, which is cut off by a vertical plane passing through a double ordinate, which is equal to the parameter of the parabolic ribbon, which is placed in front of it. The elements of the curve which forms the conoïdal mirror, must be so chosen as to have its focus at a convenient distance in _front_ of that of the ribbon-shaped mirror, so as to admit of placing the two lamps separate from each other, as well as to produce the necessary degree of divergence, which is to be obtained by the action of these mirrors respectively on the flame placed in the focus of the other. These two mirrors are joined together in the line of the parametric section of the ribbon, which coincides with the lips of the conoid at some double ordinate _behind_ its parameter. Each mirror produces, by means of the lamp placed in its focus, an approach to parallelism of the reflected rays, which M. BORDIER MARCET has not inaptly termed the _principal effect_; whilst the action of each surface on the lamp which is placed in the focus of the other, causes what the inventor calls the _secondary_ or _lateral effect_. Their secondary action may be described thus: The lamp, which is in the focus of the ribbon, is much nearer the vertex of the conoid than its own focus; so that its rays making, with normals to the surface of the conoid, angles greater than those which are formed by the rays proceeding from its focus, are of necessity reflected in lines diverging from the axis of the mirror. Those, on the contrary, which proceed from the focus of the conoid, meet the ribbon-shaped surface, so as to make angles with its normals more acute than those which the rays from its own focus could do, and which are, therefore, reflected in lines converging to the axis of the mirror. Those reflected rays must therefore cut the axis, and diverge from it on the other side. This apparatus has been used at La Hève and some other lights on the French coast; but it is impossible not to perceive the great loss of light which results from the use of two flames in one mirror; and it must not be forgotten, that the divergence which is obtained by means of it is not confined to the horizontal direction in which only it is wanted; but that the light is at the same time scattered in every direction round the edge of the mirror.

Arrangements of a similar kind were proposed and executed for the same purpose of uniting greater divergence with considerable power in the central parts of the resultant beam, by ARGAND himself, in 1806, and also in 1808, by M. HAUDRY, _Ingénieur des Ponts et Chaussées_. ARGAND proposed the union of a paraboloid, and an ellipsoid having their foci coincident in one point, which being the posterior focus of the latter curve, was illuminated by the rays reflected to it by means of the ellipsoïdal surface from the lamp placed in the anterior focus. From the _optical focus_ thus obtained, some rays would fall on the paraboloïdal surface and produce, by reflection, a cylinder of parallel rays, while the rest would diverge from the axis, and form a zone of spreading rays. M. HAUDRY’S plan consisted of a combination of a conical with a paraboloïdal mirror, so placed, that the rays from the front part of the hollow cone might be nearly parallel to those sent out by the paraboloid; while the rays from its base diverging from the axis might produce a ring of divergent rays, similar to that obtained from the ellipsoid of ARGAND’S apparatus.

It would occupy much time to exhibit all the disadvantages of the arrangements in the _fanal à double effet_ of M. BORDIER MARCET, and also in those of ARGAND and HAUDRY; and I shall therefore dismiss the subject by observing, that the loss of light due to the position of the flame in the apparatus of ARGAND, is so great as to induce one to wonder that such combinations should ever have been attempted. There can be no doubt, that the most efficient mode of obtaining due divergence from mirrors, is to adopt the paraboloid, with a short focal distance, which has the double advantage of increasing the divergence which is due inversely to the focal distance, and, at the same time, subjecting to the action of the mirror a larger portion of the luminous sphere proceeding from the flame.

~Fanal à double face.~

Lastly, I shall notice M. BORDIER MARCET’S _fanal à double face_, which consists of two paraboloïdal mirrors, truncated in the vertical plane of the parameter, and united together back to back, so as to be illuminated by the same lamp placed in their common focus. To save the light which would otherwise escape the catoptric action, he adds a parabolic conoid of greater focal distance, and so placed, that while its focus may coincide with the common focus of the other mirrors, its size may be so restricted, that it shall not interfere with the effect of the truncated mirror opposite which it is placed. The obvious consequence of such an arrangement is, that the rays (see fig. 46) produced from a lamp in the common focus of the three mirrors, will produce in opposite directions a luminous ring from each of the truncated mirrors AC, BC, and A′C′, B′C′, while the central or conoïdal mirror MN will fill the interior of one of those luminous rings with a cone of rays, whose intensity will be in the inverse ratio of MN² to _a_ _b_² (or FM² to F _a_²), which latter surface represents the whole amount of naturally divergent rays, which strike on _a_ _b_, and which are spread over MN. Two sets of reflectors of this form facing in opposite directions (each set arranged in one plane, and fixed on a frame which could be made to revolve round a vertical axis), would thus present their brightest effect after considerable intervals of darkness; but, by arranging them with their axes slightly inclined, they were made to prolong the light periods and curtail the dark ones. M. BORDIER MARCET speaks of this apparatus with all the satisfaction generally felt by inventors; but it is no difficult matter to identify its effect with that of the common paraboloïdal mirrors. It is obvious, that all the rays which fall from a true focal point on the three reflectors AC, BC, A′C′, B′C′, and MN, are merely those which would fall on a single reflector, whose double ordinate and the portion of the abscissa between that ordinate and the focus, are equal to those of the first reflector of the compound system, so that the quantity of light reflected by the three reflectors is neither more nor less than that which would be projected by one. All the difference that can exist is, that in the case of a flame which has a notable size, the surface MN being farther distant than _a_ _b_, would produce less aberration and, consequently, a very slight increase of intensity in the small portion of the reflected beam of parallel rays due to that part of the compound mirror. We cannot, therefore, sensibly err in rejecting any advantage to be derived from this arrangement as insignificant.[47]

[47] See Peclet′s Traité de l′Eclairage, p. 302, from which fig. 46
is copied.

~Mr Barlow′s Spherical Mirrors.~

Spherical mirrors have been employed in Lighthouses chiefly when they can be introduced to aid the effect of refracting apparatus: and it will not be necessary to say much of them in this place. I must, however, notice an ingenious proposal of Mr W. H. BARLOW,[48] who suggests placing in front of the flame a small spherical reflector, whose centre is coincident with the focus of a paraboloïd, and whose subtense is the parameter of the generating curve. The small mirror, being somewhat less than a hemisphere, would cause the light falling upon it to be returned through the focus so as to reach the paraboloïdal surface and to be finally reflected from that portion of it which is embraced between the limits of its extreme divergence. If there were no loss of light at the surface of the small mirror, its effect would be to increase the power of the beam of parallel rays by an amount equal to the sum of the rays incident on the spherical surface, but at the same time to diminish it by intercepting a portion of the light reflected from the paraboloïd. I am not aware that such a combination has been tried, as it applies most advantageously to reflectors whose span does not exceed the parameter of the generating curve, a form rarely adopted in lighthouses; but it might also be adapted to reflectors which intercept a larger portion of light, by making the spherical reflector some segment less than the hemisphere.

[48] In an excellent paper above noticed, on the Illumination of
Lighthouses, in the London Transactions, for 1837.

~Captain Smith’s Mirrors in the form of a parabolic spindle.~

CAPTAIN SMITH of the Madras Engineers, has described in the “Professional papers of the ‘Corps of Royal Engineers,’[49] a new system of fixed lights,” which consists in placing a flat wick in the focus of one-half of a hollow parabolic spindle generated by the rotation of a parabola about its parameter as a vertical axis. The action of the instrument is obvious, for each vertical section being parabolic, effects a change only in the _vertical_ divergence of the rays incident on it from the focus, and suffers their horizontal direction to remain unaltered; thus each vertical plate of reflected rays passes through the parameter of the curve and illuminates the opposite point of the horizon by means of a narrow strip or line of light. Two hollow spindles of that form, each lighting 180° and facing opposite azimuths, would, therefore, be sufficient to illuminate the whole horizon. The author of the paper, however, appears to contemplate the employment of a series of those mirrors ranged one above another and _breaking joint_ vertically, somewhat in the manner already described in speaking of the arrangement of the paraboloïdal mirrors used in fixed lights. The advantages of this mode of illumination are much overrated by CAPTAIN SMITH, who seems to magnify beyond its real importance the risk attending the use, in the dioptric apparatus, of a single lamp, whose sudden extinction would deprive at once the whole horizon of the benefit of the light; while, on the contrary, he reckons the security obtained by his arrangement as an advantage of the highest value. In certain situations, where no regular establishment of trained light-keepers is maintained, that security may be an object of more importance and may warrant a greater sacrifice, than is necessary in Great Britain; but I have no hesitation in saying, that I know of no situation in which the plan proposed by CAPTAIN SMITH could bear comparison with the mode of illumination for fixed lights by means of the catadioptric instruments of FRESNEL.

[49] Vol. v., p. 56.

DIOPTRIC[50] SYSTEM OF LIGHTS.

[50] Most probably directly derived from the Greek διόπτρον, an
optical instrument with holes for looking through, whose name is a
compound of διὰ, through, and ὄπτομαι, _I see_.

One of the earliest notices of the application of lenses to lighthouses is that recorded by SMEATON in his Narrative of the Eddystone Lighthouse, where he mentions a London optician, who, in 1759, proposed grinding the glass of the lantern to a radius of seven feet six inches; but the description is too vague to admit of even a conjecture regarding the proposed arrangement of the apparatus. About the middle of the last century, however, lenses were actually tried in several lighthouses in the south of England, and in particular at the South Foreland in the year 1752; but their imperfect figure and the quantity of light absorbed by the glass, which was of impure quality and of considerable thickness, rendered their effect so much inferior to that of the parabolic reflectors then in use, that after trying some strange combinations of lenses and reflectors, the former were finally abandoned. Lenses were also tried at the lights of Portland, Hill of Howth, and Waterford, by Mr Thomas Rogers, a glass manufacturer in London; who possessed, it is said, the art of blowing mirrors of glass, “and by a new method silvered over the convex side without quicksilver.”[51]

[51] Hutchinson’s Practical Seamanship, p. 200. See also the notice
of the spherical mirrors made by Messrs François and Letourneau of
Paris in a subsequent part of this volume.

The object to be attained by the use of lenses in a Lighthouse is, of course, identical with that which is answered by employing reflectors; and both instruments effect the same end by different means, collecting the rays which diverge from a point called the _focus_, and projecting them forward in a beam, whose axis coincides with the produced axis of the instrument. We have already seen that, in the case of _reflection_, this result is produced by the light being _thrown back_ from a surface so formed as to make all the rays to proceed in one and the same required direction. In the case of _refraction_, on the other hand, the rays pass through the refracting medium, and are _bent_ or _refracted_ from their natural course into that which is desired.

The celebrated BUFFON, to prevent the great absorption of light by the thickness of the material, which would necessarily result from giving to a lens of great dimensions a figure continuously spherical, proposed to grind out of a solid piece of glass, a lens in steps or concentric zones. This suggestion of BUFFON regarding the construction of large burning glasses, was first executed, with tolerable success, about the year 1780, by the Abbé ROCHON; but such are the difficulties attending the process of working a solid piece of glass into the necessary form, that it is believed the only other instrument ever constructed in this manner, is that which was made by Messrs COOKSON of Newcastle-upon-Tyne, for the Commissioners of Northern Lighthouses.

The merit of having first suggested the building of lenses in separate pieces, seems to be due to CONDORCET, who, in his _Eloge de Buffon_, published so far back as 1773, enumerates the advantages to be derived from this method. Sir DAVID BREWSTER also described this mode of building lenses in 1811, in the _Edinburgh Encyclopædia_; and in 1822, the late eminent FRESNEL, unacquainted with the suggestions of CONDORCET or the description by Sir DAVID BREWSTER, explained, with many ingenious and interesting details, the same mode of constructing those instruments. To FRESNEL belongs the additional merit of having first followed up his invention, by the construction of a lens and, in conjunction with MM. ARAGO and MATHIEU, of placing a powerful lamp in its focus, and indeed of finally applying it to the practical purposes of a Lighthouse.

The great advantages which attend the mode of construction proposed by CONDORCET are,--the ease of execution, by which a more perfect figure may be given to each zone and spherical aberration in a great measure corrected, and the power of forming a lens of larger dimensions than could easily be made from a solid piece. Both BUFFON and CONDORCET, however, chiefly speak of reducing the thickness of the material, and do not seem to have thought of determining the radius and centre of the curvature of the generating arcs of each zone, having contented themselves with simply depressing the spherical surface in separate portions. FRESNEL, on the other hand, determined those centres, which constantly recede from the vertex of the lens in proportion as the zones to which they refer are removed from its centre; and the surfaces of the zones of the annular lens, consequently, are not parts of concentric spheres, as in BUFFON’S lens. It deserves notice, that the first lenses constructed for FRESNEL by M. SOLEIL had their zones polygonal, so that the surfaces were not annular, a form which FRESNEL considered less accommodated to the ordinary resources of the optician. He also, with his habitual penetration, preferred the plano-convex to the double-convex form, as more easily executed.[52] After mature consideration, he finally adopted crown glass, which, notwithstanding its greenish colour, he preferred to flint glass, as being more free from _striæ_. All his calculations were made in reference to an index of refraction of 1·51, which he had verified by repeated experiments, conducted with that patience and accuracy for which, amidst his higher qualities, he was so remarkably distinguished.[53] The instruments have received the name of _annular_ lenses, from the figure of the surface of the zones.

[52] The plano-convex lens, with its curved side towards the parallel
rays, is also a form producing small spherical aberration, a
circumstance which may also have influenced his choice.

[53] My friend, Mr WILLIAM SWAN, carefully examined, by his new
and ingenious method, described in the Edinburgh New Philosophical
Journal, January 1844, several specimens of the St Gobain glass
(which is now used in the manufacture of the lenses), and found its
refractive index to be 1·51793, the _difference_ between the greatest
and least values being only 0·00109.

~Refraction.~

A ray of light, in passing _obliquely_ from one transparent body into another of different density, experiences at the point of the intersection of the common surface of the two planes, a sudden change of direction, to which the name of _refraction_ has naturally been given, in connection with the most familiar instance of the phenomenon, which is exhibited by a straight ruler with one half plunged into a basin of water while the other remains in the air. The ruler no longer appears straight, but seems to be _bent_ or _broken_ at the point where it enters the water. It may not be out of place to call attention to the laws which regulate the change of direction in the incident light, which are _three_ in number.

1. Incidence and refraction, in uncrystallized media of homogeneous structure such as glass, always occur in a plane perpendicular to that of the refracting surface.

2. In the same substances, the angle formed with the perpendicular by the ray at its entering the surface of the second medium, has to the angle which it makes with the normal after it has entered the surface, such a relation, that their sines have a fixed ratio, which is called the _refractive index_. When a ray falls normally on the surface of any substance, it suffers no refraction.