Catoptric [39] System of Lights.
[39] From the Greek κατοπτρον, a mirror; 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, of reflecting or 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 earliest attempts 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 by Argand’s invention, 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 Mr William 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. Mr Hutchinson seems 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 Mr Hutchinson’s book 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 when the mirrors were really adopted, the merit of the improvement must, in justice, be awarded to others.
[40] Mr Hutchinson seems 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 the Chevalier 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 by Lenoir, the same young artist to whom Borda, 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 of facets of mirror glass, placed in hollow paraboloïdal moulds of plaster, according to the designs of the late Mr Thomas Smith, the Engineer of the Board, who (as appears from the article Reflector, 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 the Reflection. laws of reflection. Those laws are two in number. 1st, The ray which falls on a reflecting surface, called the incident ray, and the ray which leaves the reflector, called the reflected ray, are always in one plane, which plane is perpendicular to the reflecting surface. 2d, The angle which the reflected ray makes with the reflector is always equal to the angle which the incident ray makes with it, or, in other words, the angle of incidence is equal to the angle of reflection.[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 or normal to 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
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 mirror as 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 attained approximately by placing the lamp in front of a spherical mirror at any distance greater than half the radius of the curve surface, or accurately by 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 point half-way between the centre of curvature and the surface of the mirror, provided the surface of the mirror shall subtend 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 far in front of 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 the theoretical object to be attained is to make those flashes equally powerful at any distance, an effect which would be 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 line f F e, bounded by the curve at either end, would then be the parameter or latus 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
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 line a b perpendicular to the axis OX, and the position in this line, of a point p through which the curve passes, is easily found thus: Describe from F the focus as a centre with a radius equal to the perpendicular distance O d of the line a b from the directrix AB, a circle cutting the line a b in two points p and p′; 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
Lastly, from the equation to the curve, the length y of any ordinate may be computed, in terms of m its principal focal distance, and x its abscissa, by the simple expression,—
y = √4 m 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 necessarily possess 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 a theoretical defect 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 of each side 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 light
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 = GFPF or the sine of the divergence from each point = Radius of flame.Distance from focus to point of reflection.
Fig. 26.
Divergence of light
It is obvious that this quantity which varies inversely with 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 this minimum divergence; 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 which e 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 from e and e′ to his eye as parallel), would receive the first ray of light in the direction a D, as reflected at a, from a single point on the edge of the flame (where a tangent to the flame would pass through a); and conversely he would lose the last ray at D′, as reflected at a, 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 angles α and α′. 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 at b; while another ray from an opposite point reflected at b′ would be seen in the parallel direction b′ G′, thus indicating the boundary of a circular portion of the mirror b 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 edge e into the direction e H, and another from the opposite side of the flame to be reflected at its opposite edge e′, into the direction e′ 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 at e′ to the observer’s eye, a ray from a point in the margin of the flame (through which a tangent drawn from e′ 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 F e or F e′. After this the light would recede from the edges of the mirror in the same gradual manner, until it should vanish in the direction a D′, 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 to b, b′, e, e′, where they are diverted into the directions b B, b′ B′, e E, and e′ 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 Mr W. 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 luminous point mathematically true, would render the illumination of the whole horizon by means of a fixed light impossible; and it is only from the divergence caused by the size of the flame which is substituted for the point, 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 of one-half of the whole effective divergence of the mirror, may be equal to the quotient 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, should have 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 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 b = r²d 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 FI = PF²FO; and substituting the letters in the text, we get d ∶ r ∷ r ∶ b, and b = r²d.
Fig. 27.
Reflection of parabolic mirror
Fig. 28.
Details of lamp assembly
Fig. 29.
Details of lamp assembly
Fig. 30.
Details of lamp assembly
Fig. 31.
Oil cup
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.
Fig. 32.
Argand burner details
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 (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.
Fig. 33.
Argand burner details
Fig. 34.
Argand burner details
Fig. 35.
Argand burner details
Fig. 36.
Argand burner details
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. 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:
Fig. 37.
Working of oil outlet
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.
Fig. 38.
Oil cut-off
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.
Fig. 39.
Burner adjustment apparatus
Fig. 40.
Burner adjustment apparatus
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.
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 Distinctions of Catoptric Lights. 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.
Fig. 41.
Gauge for reflector alignment
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, Arrangement of Reflectors on the Frame. 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.
Fig. 42.
Elevation of revolving apparatus
Fig. 43.
Plan of revolving apparatus
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.
Reflector arrangement
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. 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 Sidéral. 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.
Fig. 45.
Fanal sidéral
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. 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.
Fig. 46.
Fanal à double face
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 b² (or FM² to F a²), 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.
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 Barlow′s Spherical Mirrors. 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.