CATOPTRIC[39]SYSTEM OF LIGHTS.

CATOPTRIC[39]SYSTEM OF LIGHTS.[39]From the Greek κατοπτρον, amirror; a compound of κατα,opposite to, and ὂπτομαι,I see.

[39]From the Greek κατοπτρον, amirror; a compound of κατα,opposite to, and ὂπτομαι,I see.

For those defects a simple remedy is found in the well known power possessed by most bodies, ofreflectingor throwing back from them the light which falls upon them. This property is not possessed by all reflecting bodies in an equal degree, some absorbing more and some less of the incident light. Perhaps the earliestattempts to apply this property as a corrective for the direction of the rays from a Lighthouse, would be confined to placing plane mirrors behind each lamp; yet this would prove but a partial remedy, as it would still leave the greater part of the light to stray above and below the proper direction. Hollow mirrors of a spherical form might next be tried; and if properly placed with reference to the flame, would constitute a very great improvement in lighthouse illumination. But those steps in the march of improvement are more imaginary than real; and I am not aware of any well authenticated records of such gradual attempts having preceded the adoption of the right mode of applying reflection as a means of rectifying the direction of the rays emerging from a lighthouse. There is, on the contrary, distinct evidence that the impulse given byArgand’sinvention, led to an immediate adoption of the most perfect form of reflecting instruments.

Application of Paraboloïdal Mirrors into Lighthouses.The name of the inventor of paraboloïdal mirrors and the date of their first application to Lighthouses, have not been accurately ascertained. The earliest notice which I have been able to find, is that by MrWilliam Hutchinson, the pious and intelligent author of a quarto volume on “Practical Seamanship” (published at Liverpool in 1791), who notices (at p. 93) the erection of the four lights at Bidstone and Hoylake, in the year 1763, and describes large parabolic moulds, fashioned of wood and lined with mirror-glass, and smaller ones of polished tin-plate, as in use in those Lighthouses. MrHutchinsonseems to have understood the nature, properties, and defects of the instruments which he describes, and has shewn a good acquaintance with many of the most important circumstances to be attended to in the illumination of Lighthouses. Many claims to inventions rest on more slender grounds than might be found in MrHutchinson’sbook for concluding him to have first invented the paraboloïdal mirror and applied it to use in a Lighthouse;[40]but, in the absence of any statement as to the date whenthe mirrors were really adopted, the merit of the improvement must, in justice, be awarded to others.

[40]MrHutchinsonseems also (“Practical Seamanship,” p. 198) to have tried speculum metal as a material for Lighthouse reflectors.

M.Teulere, a member of the Royal Corps of Engineers of Bridges and Roads in France, is, by some, considered the first who hinted at the advantages of paraboloïdal reflectors; and he is said, in a memoir dated the 26th June 1783, to have proposed their combination with Argand lamps, ranged on a revolving frame, for the Corduan Lighthouse. Whatever foundation there may be for the claim of M.Teulere, certain it is that this plan was actually carried into effect at Corduan, under the directions of theChevalier Borda; and to him is generally awarded the merit of having conceived the idea of applying paraboloïdal mirrors to lighthouses. These were most important steps in the improvement of lighthouses, as not only the power of the lights was thus greatly increased, but the introduction of a revolving frame proved a valuable source of differences in the appearance of lights, and, in this way, has since been the means of greatly extending their utility. The exact date of the change on the light of the Corduan is not known; but as it was made byLenoir, the same young artist to whomBorda, about the year 1780, entrusted the construction of his reflecting circle, it has been conjectured by some that the improvement of the light was made about the same time. The reflectors were formed of sheet-copper, plated with silver, and had a double ordinate of 31 French inches. It was not long before these improvements were adopted in England, by the Trinity-House of London, who sent a deputation to France to inquire into their nature. In Scotland, one of the first acts of the Northern Lights Board in 1786, was to substitute reflectors in the room of the coal-light then in use at the Isle of May in the Frith of Forth, which, along with the light on the Cumbrae Isle in the Frith of Clyde, had, till that period, been the only beacons on the Scotch coast. The first reflectors employed in Scotland were formed offacetsof mirror glass, placed in hollow paraboloïdal moulds of plaster, according to the designs of the late MrThomas Smith, the Engineer of the Board,who (as appears from the articleReflector, in the Supplement to the third edition of the Encyclopædia Britannica) was not aware of what had been done in France, and had himself conceived the idea of this combination. The same system was also adopted in Ireland; and in time, variously modified, it became general wherever lighthouses are known.

To enable us to enter on the subject of the proper forms of reflectors, we must glance very briefly at theReflection.laws of reflection. Those laws are two in number.1st, The ray which falls on a reflecting surface, called theincidentray, and the ray which leaves the reflector, called thereflectedray, are always in oneplane, which plane is perpendicular to thereflecting surface.2d, The angle which thereflectedray makes with the reflector is always equal to the angle which theincidentray makes with it, or, in other words, the angle ofincidenceis equal to the angle ofreflection.[41]

[41]This will be more readily understood by referring to the accompanying figure (No. 22), in which CDEF is the reflecting surface; GHOKI the plane of reflection perpendicular to that surface; BO a line perpendicular ornormalto the surface CDEF; and AO the incident ray. Then if in the plane GHOKI, the angle BOI be made equal to AOB, OA′ is the reflected ray; BOG is then the angle of incidence; and BOI the angle of reflection. GOH and IOK, which are the complements of those angles, are, indeed, more strictly speaking, the angles of incidence and reflection; but in cases where the reflecting surface is curved, it is more convenient to refer the angles to the normal BO.Fig. 22.Reflecting light

Fig. 22.Reflecting light

Fig. 22.

It would lead to prolixity altogether superfluous in this place, to explain, in a rigorous manner, the effects produced by various reflecting surfaces on the direction of the rays incident on them; as any one who comprehends the laws of reflection just enumerated, may easily satisfy himself of the following truths:1st, That a plane mirror makes no change on the divergence of the rays, but merely causes them to emerge from its surface in the same direction as if they had come from a point as much behind the mirroras the luminous body lies in front of it.2d, A convex reflecting surface increases divergence, and disperses the rays in the same manner as if they had come directly from a point behind it, whose distance from the mirror increases with the distance of the luminous body from its surface, and diminishes with the degree of convexity of the mirror.3d, A concave surface diminishes the divergence of the rays incident upon it from a point between the surface and its centre of curvature; the distance of the point in which the reflected rays converge diminishing as the distance of the radiant point or the concavity of the mirror is increased. It is obvious, therefore, that concave mirrors are those which are required to produce a correction of the path of the rays, so as to apply them to most advantage in a lighthouse, the object to be attained being that of throwing the greatest amount of light towards given points in the horizon, and collecting the divergent rays, which, as we have already seen, are scattered above and below it.

To simplify our view of this matter, I shall, in the first place, suppose that the object to be attained is to throw the whole rays of a single lamp, with an infinitely small flame, to a given mathematical point at a moderate distance; and, as this is a case which can hardly occur in the practice of Lighthouse illumination, I content myself with observing that this object may be attainedapproximatelyby placing the lamp in front of a spherical mirror at any distance greater than half the radius of the curve surface, oraccuratelyby placing it in one focus of an elliptical mirror; in all those cases the rays would meet in the opposite, or, as they are termed,conjugate foci. Let us next suppose that our object is to illuminate, by means of a mathematical point of light, a small circular space on the horizon equal in diameter to the mirror employed; this object will be rigorously attained only by placing the light in the focus of a paraboloïdal reflector. The same object may be approximately attained by placing the light in a spherical mirror, at a pointhalf-waybetween the centre of curvature and the surface of the mirror, provided the surface of the mirror shallsubtend only a small angle at the centre of curvature. The paraboloïdal mirror, on the contrary, has the property of converging to the focus parallel rays falling upon every point of its surface, however extended it may be.

Paraboloïdal Mirrors.Any one practically acquainted with this subject, must at once perceive that the paraboloïdal mirror completely fulfils one great object required in a lighthouse; and to render this more obvious to the general reader, I shall, for the present, confine my remarks to the case of those lighthouses which exhibit to the mariner in every part of the horizon, pencils of light at certain intervals of time, separated by periods of darkness, reserving the consideration of Lights which are continually in sight all round the horizon or over a given portion of it, for a subsequent part of these Notes. In doing this, I am aware that I may appear to be departing from the strict order of investigation, by suddenly introducing the idea of motion; but a little consideration will, I think, satisfy the reader that this is, in reality, the more convenient mode of treating the subject. Let us suppose, then, that our object is to give occasional flashes of light, separated by intervals of darkness, to seamen in various azimuths and at various distances from a lighthouse. It is obvious that this may be most efficiently done by causing concave mirrors, which collect the rays from lamps placed in them and thereby increase the light in front of the mirror, to revolve round a vertical axis with a velocity suited to produce the required number of flashes in a given time. The paraboloïdal mirror is best adapted for producing this effect, for the following reasons:1st, Because it alone produces a rigorous parallelism of all rays proceeding from its focus, and falling upon any point of its surface, however distant the point of reflection from that focus, or however farin frontof it.2d, Because it therefore embraces in its action the greatest number of the whole rays coming from the focus, and,cæteris paribus, will produce the strongest light.3d, Because thetheoreticalobject to be attained is to make those flashes equally powerful at any distance, an effect which wouldbe rigorously fulfilled by placing an infinitely small flame in a perfect paraboloïdal mirror. And,4th, Because, although absolute equality of luminousness at any distance is not attainable, and, in practice, is inconsistent with other conditions required in a useful light, we still, by using the parabolic mirror, make the nearest approach to parallelism of the reflected rays, and consequently obtain the strongest light which is consistent with a due regard to a certain duration of the flash on the eye of a distant observer, which is measured by the angle of the luminous cone projected to the horizon.

Having thus so far anticipated what some might think would more naturally have occurred in a subsequent part of these Notes, I return to a more detailed consideration of the parabola itself, and its product, the paraboloïdal mirror. I content myself, however, with describing the parabola, by that property which peculiarly adapts it to the purposes of a lighthouse. The parabola, then, is a curve of the second order, obtained by cutting a cone in a plane parallel to one side, which possesses this remarkable property,that a line drawn from the focus to any point in the curve, makes, with a tangent at that point, an angle equal to that which a line parallel to the axis of the curve makes with that tangent.[42]

[42]See third corollary to Proposition III. of Wallace’s Conic Sections, which shews that a tangent to the parabola makes equal angles with the diameter which passes through the point of contact and a straight line drawn from that point to the focus. The curve may be traced in two different ways, both dependent on the property,that the distance of any point in the parabola from the focus is equal to its distance from the directrix.To draw the curve mechanically (fig. 23), let F be the focus, MF the focal distance (chosen at pleasure according to rules which I shall afterwards notice), KMX is the axis, and AB the directrix (the dotted linefFe, bounded by the curve at either end, would then be theparameterorlatus rectum). Place the edge of the straight ruler AKHB along the directrix; and let LHB be a square ruler which may slide along the fixed ruler AKHB, so that the edge HL may be constantly perpendicular to AB, or parallel to MX, the axis; let LDF be a string equal in length to HL, and having one end fixed in F, and the other at L, a point in the sliding square. Then if the string be stretched by a pencil D, so as to keep the part DL close to the edge of the square, and if at the same time the square be gently pushed along the line AB, the point D will be forced to move along the edge LH of the square, and will trace out a curve which will be the required parabola. This is obvious from the consideration, that the string LDF being equal in length to LH, and LD being common to both, the remainder DF must be equal to the remainder DH, so that the point which traces the curve being equidistant from the directrix and the focus must, in terms of the above definition, describe a parabola.Fig. 23.Mechanical construction of curveIn the second place, the same property, as already stated, furnishes us with the means of tracing the curve by finding successive points therein. Draw a linea bperpendicular to the axis OX, and the position in this line, of a pointpthrough which the curve passes, is easily found thus: Describe from F the focus as a centre with a radius equal to the perpendicular distance Odof the linea bfrom the directrix AB, a circle cutting the linea bin two pointspandp′; then both these points are in the curve. By repeating the same process, any number of points in the curve may be obtained.Fig. 24.Tracing of curveLastly, from the equation to the curve, the lengthyof any ordinate may be computed, in terms ofmits principal focal distance, and x its abscissa, by the simpleexpression,—y= √4m x.

To draw the curve mechanically (fig. 23), let F be the focus, MF the focal distance (chosen at pleasure according to rules which I shall afterwards notice), KMX is the axis, and AB the directrix (the dotted linefFe, bounded by the curve at either end, would then be theparameterorlatus rectum). Place the edge of the straight ruler AKHB along the directrix; and let LHB be a square ruler which may slide along the fixed ruler AKHB, so that the edge HL may be constantly perpendicular to AB, or parallel to MX, the axis; let LDF be a string equal in length to HL, and having one end fixed in F, and the other at L, a point in the sliding square. Then if the string be stretched by a pencil D, so as to keep the part DL close to the edge of the square, and if at the same time the square be gently pushed along the line AB, the point D will be forced to move along the edge LH of the square, and will trace out a curve which will be the required parabola. This is obvious from the consideration, that the string LDF being equal in length to LH, and LD being common to both, the remainder DF must be equal to the remainder DH, so that the point which traces the curve being equidistant from the directrix and the focus must, in terms of the above definition, describe a parabola.

Fig. 23.Mechanical construction of curve

Fig. 23.

In the second place, the same property, as already stated, furnishes us with the means of tracing the curve by finding successive points therein. Draw a linea bperpendicular to the axis OX, and the position in this line, of a pointpthrough which the curve passes, is easily found thus: Describe from F the focus as a centre with a radius equal to the perpendicular distance Odof the linea bfrom the directrix AB, a circle cutting the linea bin two pointspandp′; then both these points are in the curve. By repeating the same process, any number of points in the curve may be obtained.

Fig. 24.Tracing of curve

Fig. 24.

Lastly, from the equation to the curve, the lengthyof any ordinate may be computed, in terms ofmits principal focal distance, and x its abscissa, by the simpleexpression,—

y= √4m x.

It is easy to see, that if this curve revolve about its axis, it will generate a parabolic conoid, which we may conceive to be concave or convex, as we please. If the surface be concave, we obtain the mirror of which we are in search; for every principal section, or that passing through the axis of such a mirror, will necessarilypossess the same properties as that of the plane curve, and will each have a focus meeting in one and the same point; the union of all these sections will therefore form a mirror capable of reflecting, in a direction parallel to the axis and to each other, all the rays of light which fall on its surface.

We have already seen that a perfect paraboloïdal mirror, with a point of light infinitely small placed in the focus, would project a beam equally intense at any distance, every transverse section of which would be of the same superficial extent.Divergence of Paraboloïdal Mirrors.In practice, these conditions can never be rigorously fulfilled. No perfect instrument can come from the hands of man, and every mirror must of necessity possess many defects. To obtain a true mathematical point of light is also impossible; and for the purposes of a lighthouse, it would be completely useless, as will appear from the following simple considerations. Let us suppose that a true paraboloïdal mirror, having a double ordinate or space of two feet, and illuminated by a point of light, projects a truly cylindric beam of light to the horizon, and that it revolves horizontally round a vertical axis, with such a velocity as to cause the beam to pass over the eye of an observer stationed at the distance of 100 feet in one second of time, and we shall find that another observer, at a distance of 15 miles from the mirror, would not see the light at all, although of equal size, because its velocity at that distance would be so great as only to be present to his eye for ¹⁄₇₉₂d of a second, a space of time far too short to make a perceptible impression on the eye of a distant observer. This is no mere hypothesis unsupported by facts; for I shall have occasion, in another part of these Notes, to describe certain experiments, by which it was ascertained that a beam of light emerging from a lens, and passing over the eye of an observer at 14 miles distance, in a space of time equal to ¹⁄₁₆₆th of a second, became altogether invisible at that distance.

For this evil, happily a very simple and efficient remedy may be found in what may be said to constitute atheoreticaldefect in the combination of the Argand burner with the reflector. The burner, instead of being a mathematical point, has generally a diameter of about one inch, and a ray proceeding from the edge of the flame to any point on the surface of the mirror, makes with the line joining that point and the principal focus an angle which,being repeated by reflection, gives the effective divergence ofeachside of the mirror at that point.[43]

[43]This is easily understood by reference to the accompanying figure (No. 25.), in which AOB is a central section of a paraboloïdal mirror.Fig. 25.Divergence of lightPF = distance from the focus F to a point in the curve P, and PG a tangent drawn from P to the surface of the flame at G;FG = radius of the wick or flame;and GPF = G′PF′ = divergence of one side of mirror, and consequently 2 GPF = the whole effective divergence of the mirror at that cross section.Now sin GPF =GFPFor the sine of the divergence from each point =Radius of flame.Distance from focus to point of reflection.Fig. 26.Divergence of lightIt is obvious that this quantity which variesinverselywith the distance of the reflecting surface from the focus, is greatest at the vertex of the curve, and least at the sides or edges of the paraboloïd. The most useful part of the light, or that which conduces to the strongest part of the flash in a revolving light, is that which is derived from the cone of rays which is bounded by the limits of thisminimumdivergence; for the faint light which first reaches the eye of a distant observer, in the revolution of a reflector, is not that which is reflected by the sides or edges, as might at first be supposed, but proceeds from the centre. The light, in fact, gradually increases in power in proportion as additional rays of reflected light are brought to bear on the observer’s eye, until, last of all, the extreme edge of the mirror adds its effect. The light continues in its best state until the opposite limit of minimum divergence has been reached, when it begins gradually to decline, receding from the margin of the mirror towards the centre, and, having at length reached the limit of its maximum divergence, it finally disappears at the centre. The increase and decline of the power of a mirror in the course of its movement round the circle of the lantern, as seen by a distant observer, will, therefore, in all its different states, be measured by the areas of a series of circles described from its focus, with radii equal to the distance of the focus from the point of the mirror which reflects to the observer’s eye the extreme ray which can reach him in any given position of the mirror. This will be more easily understood by referring to the accompanying diagram,Fig. 26, in whiche a e′is the principal section of a paraboloïdal mirror, F its focus, αFA its axis, and FK the radius of the flame. If the reflector revolve round a vertical axis at O, an observer placed in front of it (at a distance so great that the subtense of the mirror’s width would be small enough to allow us safely to consider the lines drawn fromeande′to his eye as parallel), would receive the first ray of light in the directionaD, as reflected ata, from a single point on the edge of the flame (where a tangent to the flame would pass througha); and conversely he would lose the last ray at D′, as reflected ata, from a single point on the opposite margin of the flame; and hence, as above, the greatest divergence is measured by the angle which the flame subtends at the vertex a of the mirror, being the sum of the anglesαandα′. We shall next suppose the mirror to move a little, so that the observer may receive at G a ray of light from some other point in the flame which is reflected atb; while another ray from an opposite point reflected atb′would be seen in the parallel directionb′G′, thus indicating the boundary of a circular portion of the mirrorb a b′, the whole of which would reflect light to the distant observer’s eye. Again, let us suppose a ray to come from another part of the flame, and be reflected at the mirror’s edgeeinto the directioneH, and another from the opposite side of the flame to be reflected at its opposite edgee′, into the directione′G″, and we obtain the full effect of the whole reflecting surface, which will continue unabated until the mirror in the course of its revolution shall reflect ate′to the observer’s eye, a ray from a point in the margin of the flame (through which a tangent drawn frome′to the flame would pass) in such a direction, that the angle which it makes with the axis of the mirror is equal to that subtended by the radius of the flame at the distance Feor Fe′. After this the light would recede from the edges of the mirror in the same gradual manner, until it should vanish in the directionaD′, which is the opposite limit of the extreme divergence of the instrument. In the above explanation, I have confined myself simply to the effects of the outer ring of the flame, which is the source of divergence; but I need not remind the reader that every portion of the flame radiates light, which, being reflected, conduces to the effect. Some rays also are passing from the opposite sides of the flame through the true focus, so as to be normally reflected in lines parallel to its axis. The solid lines in the diagram shew the theoretical reflection of rays proceeding from F tob,b′,e,e′, where they are diverted into the directionsbB,b′B′,eE, ande′E′; and by contrast with the dotted lines, serve to render more perceptible the path of the divergent rays which come from the edge of the flame. The Greek letters indicate the angles of divergence, and point out their relations to each other on either side of the mirror. The arcs of greatest and least divergence are marked in the diagram. This subject will be found treated less directly, but, certainly, more concisely and neatly, by MrW. H. Barlow, in a paper on the Illumination of Lighthouses in the London Transactions for 1837, p. 218.

[43]This is easily understood by reference to the accompanying figure (No. 25.), in which AOB is a central section of a paraboloïdal mirror.

Fig. 25.Divergence of light

Fig. 25.

PF = distance from the focus F to a point in the curve P, and PG a tangent drawn from P to the surface of the flame at G;

FG = radius of the wick or flame;

and GPF = G′PF′ = divergence of one side of mirror, and consequently 2 GPF = the whole effective divergence of the mirror at that cross section.

Now sin GPF =GFPFor the sine of the divergence from each point =Radius of flame.Distance from focus to point of reflection.

Fig. 26.Divergence of light

Fig. 26.

It is obvious that this quantity which variesinverselywith the distance of the reflecting surface from the focus, is greatest at the vertex of the curve, and least at the sides or edges of the paraboloïd. The most useful part of the light, or that which conduces to the strongest part of the flash in a revolving light, is that which is derived from the cone of rays which is bounded by the limits of thisminimumdivergence; for the faint light which first reaches the eye of a distant observer, in the revolution of a reflector, is not that which is reflected by the sides or edges, as might at first be supposed, but proceeds from the centre. The light, in fact, gradually increases in power in proportion as additional rays of reflected light are brought to bear on the observer’s eye, until, last of all, the extreme edge of the mirror adds its effect. The light continues in its best state until the opposite limit of minimum divergence has been reached, when it begins gradually to decline, receding from the margin of the mirror towards the centre, and, having at length reached the limit of its maximum divergence, it finally disappears at the centre. The increase and decline of the power of a mirror in the course of its movement round the circle of the lantern, as seen by a distant observer, will, therefore, in all its different states, be measured by the areas of a series of circles described from its focus, with radii equal to the distance of the focus from the point of the mirror which reflects to the observer’s eye the extreme ray which can reach him in any given position of the mirror. This will be more easily understood by referring to the accompanying diagram,Fig. 26, in whiche a e′is the principal section of a paraboloïdal mirror, F its focus, αFA its axis, and FK the radius of the flame. If the reflector revolve round a vertical axis at O, an observer placed in front of it (at a distance so great that the subtense of the mirror’s width would be small enough to allow us safely to consider the lines drawn fromeande′to his eye as parallel), would receive the first ray of light in the directionaD, as reflected ata, from a single point on the edge of the flame (where a tangent to the flame would pass througha); and conversely he would lose the last ray at D′, as reflected ata, from a single point on the opposite margin of the flame; and hence, as above, the greatest divergence is measured by the angle which the flame subtends at the vertex a of the mirror, being the sum of the anglesαandα′. We shall next suppose the mirror to move a little, so that the observer may receive at G a ray of light from some other point in the flame which is reflected atb; while another ray from an opposite point reflected atb′would be seen in the parallel directionb′G′, thus indicating the boundary of a circular portion of the mirrorb a b′, the whole of which would reflect light to the distant observer’s eye. Again, let us suppose a ray to come from another part of the flame, and be reflected at the mirror’s edgeeinto the directioneH, and another from the opposite side of the flame to be reflected at its opposite edgee′, into the directione′G″, and we obtain the full effect of the whole reflecting surface, which will continue unabated until the mirror in the course of its revolution shall reflect ate′to the observer’s eye, a ray from a point in the margin of the flame (through which a tangent drawn frome′to the flame would pass) in such a direction, that the angle which it makes with the axis of the mirror is equal to that subtended by the radius of the flame at the distance Feor Fe′. After this the light would recede from the edges of the mirror in the same gradual manner, until it should vanish in the directionaD′, which is the opposite limit of the extreme divergence of the instrument. In the above explanation, I have confined myself simply to the effects of the outer ring of the flame, which is the source of divergence; but I need not remind the reader that every portion of the flame radiates light, which, being reflected, conduces to the effect. Some rays also are passing from the opposite sides of the flame through the true focus, so as to be normally reflected in lines parallel to its axis. The solid lines in the diagram shew the theoretical reflection of rays proceeding from F tob,b′,e,e′, where they are diverted into the directionsbB,b′B′,eE, ande′E′; and by contrast with the dotted lines, serve to render more perceptible the path of the divergent rays which come from the edge of the flame. The Greek letters indicate the angles of divergence, and point out their relations to each other on either side of the mirror. The arcs of greatest and least divergence are marked in the diagram. This subject will be found treated less directly, but, certainly, more concisely and neatly, by MrW. H. Barlow, in a paper on the Illumination of Lighthouses in the London Transactions for 1837, p. 218.

It is still more obvious that a perfect paraboloïdal figure, and a luminouspointmathematically true, would render the illumination of the whole horizon by means of a fixed lightimpossible; and it is only from the divergence caused by the size of the flame which is substituted for thepoint, that we are enabled to render even revolving lights practically useful. But for this aberration, the slowest revolution in a revolving light would be inconsistent with a continued observable series, such as the practical seamen could follow, and would, as we have seen, render the flashes of a revolving light too transient for any useful purpose; whilst fixed lights, being visible in the azimuths only in which the mirrors are placed, would, over the greater part of the distant horizon, be altogether invisible. The size of the flame, therefore, which is placed in the focus of a paraboloïdal mirror, when taken in connexion with the form of the mirror itself, leads to those important modifications in the paths of the rays and the form of the resultant beam of light, which have rendered the catoptric system of lights so great a benefit to the benighted seamen.

In order to obtain a mirror capable of producing a given divergence of the reflected beam, therefore, we must proportion its focal distance to the diameter of the flame in such a manner, that the sine ofone-halfof the whole effective divergence of the mirror, may be equal to thequotient of the radius of the flame, divided by the distance of a given point on the surface of the mirror from the focus. The best proportions for paraboloïdal mirrors depend on the objects which they are meant to attain. Those which are intended to give great divergence to the resultant beams, as in fixed lights, capable of illuminating the whole horizon at one time, shouldhave a short focal distance; while those mirrors which are designed to produce a nearer approach to parallelism (as in the case of revolving lights which illuminate but a few degrees of the horizon at any one instant of time), will have the opposite form. Those two objects may, no doubt, be attained with the same mirror, by increasing or diminishing the size of the burner; but that is by no means desirable, as any change on the size of a burner, which is found to be the best in other respects, must be considered as to some extent disadvantageous.

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 whichwould 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 offixedandrevolvinglights, 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 advisableto 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 theeffectivedivergence.

Power of Paraboloïdal Mirrors.The measure of the illuminating power of a paraboloïdal mirror may be estimated as thequotient of theSURFACEof 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 amean proportionalbetween thegreatestandleastfocal 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’sPaper 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, bya 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. Thedetailsof 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. Ifbbe the distance to which the object should be removed outwards from the principal focus of the mirror,dthe distance from the focus to the screen, andrthe distance from the focus to that point of the mirror which is to be tested,we shall haveb=r²das 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 (Seefig. 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 FI =PF²FO; and substituting the letters in the text, we getd∶r∷r∶b, andb=r²d.Fig. 27.Reflection of parabolic mirror

Fig. 27.Reflection of parabolic mirror

Fig. 27.

Fig. 28.Details of lamp assemblyFig. 29.Details of lamp assemblyFig. 30.Details of lamp assembly

Fig. 28.Details of lamp assembly

Fig. 28.

Fig. 29.Details of lamp assemblyFig. 30.Details of lamp assembly

Fig. 29.Details of lamp assembly

Fig. 29.

Fig. 30.Details of lamp assembly

Fig. 30.

Fig. 31.Oil cup

Fig. 31.

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 infigs. 28,29, and30, 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 arepresents one of the reflectors,bis the burner, andca cylindric fountain, which contains 24 ounces of oil. The oil-pipe, the fountaincfor supplying oil, and the burnerb, are connected with the rectangular framed, which is moveable in a vertical direction upon the guide-rodseandf, by which it can belet down, so that the burner may be lowered out of the reflector, by simply turning the handleg(as will be more fully understood by examiningfigs. 28and29), which has the effect of forcing athread(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 tubehis attached, serving for ventilation;ishews 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 atk k, is soldered to the brass bandl, that clasps the exterior of the reflector.Fig. 28is a section of the reflectora a, shewing the position of the burnerb, with the glass chimneyb′, and oil-cupl, which receives any oil that may drop from the lamp.Fig. 30shews 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 fountaincis moved partly down;d dshews the rectangular frame on which the burner is mounted,e ethe elongated socket-guides through which the guide-rods slide, andfthe guide-rod, connectedwith the perforated sockets on which thechecking-handle gslides. The oil-cupl(covered with a lid and wick-holder, as shewn infig. 31) also serves as afrost-lampduring 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 armh; 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.

Fig. 32.Argand burner details

Fig. 32.

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.Arrangements for Raising or lowering the Argand Wick.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 (seefigs. 32,33,34,35,36):—The inner tubetof the burner is enclosed by a strong tubes, 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 ata(fig. 33). That on the inside works in the spiral groove of the tube S (figs. 32and33), already described as embracing the inner tubet; 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 pegaof the wick-holder (fig. 33), which moves in a vertical slita(figs. 32and34), cut in a tube standingin the burner, and concentric with it, and which also moves freely round its axis. Small knobsnn(figs. 32,34, and36), 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 galleryg(seefigs. 33and36), therefore, motion is given to the tube, with its knobsnn, whose vertical slita(while it holds the external peg of the wick-holder, and also turns it round along with it) permits that pegato 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. Infig. 32, C shews the glass chimney resting on the galleryg g.

Back to Index Next