Popular Science Monthly/Volume 24/March 1884/On Rainbows

by John Tyndall

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ON RAINBOWS.^[1]

By JOHN TYNDALL, F. R. S.

THE oldest historic reference to the rainbow is known to all: "I do set my bow in the cloud, and it shall be for a token of a covenant between me and the earth. . . . And the bow shall be in the cloud; and I shall look upon it, that I may remember the everlasting covenant between God and every living creature of all flesh that is upon the earth." To the sublime conceptions of the theologian succeeded the desire for exact knowledge characteristic of the man of science. Whatever its ultimate cause might have been, the proximate cause of the rainbow was physical, and the aim of science was to account for the bow on physical principles. Progress toward this consummation was very slow. Slowly the ancients mastered the principles of reflection. Still more slowly were the laws of refraction dug from the quarries in which Nature had imbedded them. I use this language because the laws were incorporate in Nature before they were discovered by man. Until the time of Alhazan, an Arabian mathematician, who lived at the beginning of the twelfth century, the views entertained regarding refraction were utterly vague and incorrect. After Alhazan came Roger Bacon and Vitellio,^[2] who made and recorded many observations and measurements on the subject of refraction. To them succeeded Kepler, who, taking the results tabulated by his predecessors, applied his amazing industry to extract from them their meaning—that is to say, to discover the physical principles which lay at their root. In this attempt he was less successful than in his astronomical labors. In 1604 Kepler published his "Supplement to Vitellio," in which he virtually acknowledged his defeat, by enunciating an approximate rule, instead of an all-satisfying natural law. The discovery of such a law, which constitutes one of the chief corner-stones of optical science, was made by Willebrord Snell, about 1621.^[3]

A ray of light may, for our purposes, be presented to the mind as a luminous straight line. Let such a ray be supposed to fall vertically upon a perfectly calm water-surface. The incidence, as it is called, is then perpendicular, and the ray goes through the water without deviation to the right or left. In other words, the ray in the air and the ray in the water form one continuous straight line. But the least deviation from the perpendicular causes the ray to be broken, or "refracted," at the point of incidence. What, then, is the law of refraction discovered by Snell? It is this, that no matter how the angle of incidence, and with it the angle of refraction, may vary, the relative magnitude of two lines, dependent on these angles, and called their sines, remains, for the same medium, perfectly unchanged. Measure, in other words, for various angles, each of these two lines with a scale, and divide the length of the longer one by that of the shorter; then, however the lines individually vary in length, the quotient yielded by this division remains absolutely the same. It is, in fact, what is called the index of refraction of the medium.

Science is an organic growth, and accurate measurements give coherence to the scientific organism. Were it not for the antecedent discovery of the law of sines, founded as it was on exact measurements, the rainbow could not have been explained. Again and again, moreover, the angular distance of the rainbow from the sun had been determined and found constant. In this divine remembrancer there was no variableness. A line drawn from the sun to the rainbow, and another drawn from the rainbow to the observer's eye, always inclosed an angle of 41°. Whence this steadfastness of position—this inflexible adherence to a particular angle? Newton gave to De Dominis^[4] the credit of the answer; but we really owe it to the genius of Descartes. He followed with his mind's eye the rays of light impinging on a rain-drop. He saw them in part reflected from the outside surface of the drop. He saw them refracted on entering the drop, reflected from its back, and again refracted on their emergence. Descartes was acquainted with the law of Snell, and, taking up his pen, he calculated, by means of that law, the whole course of the rays. He proved that the vast majority of them escaped from the drop as divergent rays, and, on this account, soon became so enfeebled as to produce no sensible effect upon the eye of an observer. At one particular angle, however—namely, the angle 41° aforesaid—they emerged in a practically parallel sheaf. In their union was strength, for it was this particular sheaf which carried the light of the "primary" rainbow to the eye.

There is a certain form of emotion called intellectual pleasure, which may be excited by poetry, literature, nature, or art. But I doubt whether among the pleasures of the intellect there is any more pure and concentrated than that experienced by the scientific man when a difficulty which has challenged the human mind for ages melts before his eyes, and recrystallizes as an illustration of natural law. This pleasure was doubtless experienced by Descartes when he succeeded in placing upon its true physical basis the most splendid meteor of our atmosphere. Descartes showed, moreover, that the "secondary bow" was produced when the rays of light underwent two reflections within the drop, and two refractions at the points of incidence and emergence.

It is said that Descartes behaved ungenerously to Snell—that, though acquainted with the unpublished papers of the learned Dutchman, he failed to acknowledge his indebtedness. On this I will not dwell, for I notice on the part of the public a tendency, at all events in some cases, to emphasize such short-comings. The temporary weakness of a great man is often taken as a sample of his whole character. The spot upon the sun usurps the place of his "surpassing glory." This is not unfrequent, but it is nevertheless unfair.

Descartes proved that, according to the principles of refraction, a circular band of light must appear in the heavens exactly where the rainbow is seen. But how are the colors of the bow to be accounted for? Here his penetrative mind came to the very verge of the solution, but the limits of knowledge at the time barred his further progress. He connected the colors of the rainbow with those produced by a prism; but then these latter needed explanation just as much as the colors of the bow itself. The solution, indeed, was not possible until the composite nature of white light had been demonstrated by Newton. Applying the law of Snell to the different colors of the spectrum, Newton proved that the primary bow must consist of a series of concentric circular bands, the largest of which is red, and the smallest violet; while in the secondary bow these colors must be reversed. The main secret of the rainbow, if I may use such language, was thus revealed.

I have said that each color of the rainbow is carried to the eye by a sheaf of approximately parallel rays. But what determines this parallelism? Here our real difficulties begin, but they are to be surmounted by attention. Let us endeavor to follow the course of the solar rays before and after they impinge upon a spherical drop of water. Take first of all the ray that passes through the center of the drop. This particular ray strikes the back of the drop as a perpendicular, its reflected portion returning along its own course. Take another ray close to this central one and parallel to it—for the sun's rays when they reach the earth are parallel. When this second ray enters the drop it is refracted; on reaching the back of the drop it is there reflected, being a second time refracted on its emergence from the drop. Here the incident and the emergent rays inclose a small angle with each other. Take again a third ray a little farther from the central one than the last. The drop will act upon it as it acted upon its neighbor, the incident and emergent rays inclosing in this instance a larger angle than before. As we retreat farther from the central ray the enlargement of this angle continues up to a certain point, where it reaches a maximum, after which further retreat from the central ray diminishes the angle. Now, a maximum resembles the ridge of a hill, or a water-shed, from which the land falls in a slope at each side. In the case before us the divergence of the rays when they quit the rain-drop would be represented by the steepness of the slope. On the top of the water-shed—that is to say, in the neighborhood of our maximum—is a kind of summit level, where the slope for some distance almost disappears. But the disappearance of the slope indicates, in the case of our rain-drop, the absence of divergence. Hence we find that at our maximum, and close to it, there issues from the drop a sheaf of rays which are nearly, if not quite, parallel to each other. These are the so-called "effective rays" of the rainbow.^[5]

Let me here point to a series of measurements which will illustrate the gradual augmentation of the deflection just referred to until it reaches its maximum, and its gradual diminution at the other side of the maximum. The measures correspond to a series of angles of incidence which augment by steps of ten degrees:

i		d	i		d
10°		10°	60°		42°28'
20°		19°36'	70°		39°48'
30°		28°20'	80°		31° 4'
40°		35°36'	90°		15
50°		40°40'

The figures in the column i express these angles, while under d we have in each case the accompanying deviation, or the angle inclosed by the incident and emergent rays. It will be seen that as the angle i increases, the deviation also increases up to 42° 28', after which, although the angle of incidence goes on augmenting, the deviation becomes less. The maximum 42° 28' corresponds to an incidence of 60°, but in reality at this point we have already passed, by a small quantity, the exact maximum, which occurs between 58° and 59°. Its amount is 42° 30'. This deviation corresponds to the red band of the rainbow. In a precisely similar manner the other colors rise to their maximum, and fall on passing beyond it; the maximum for the violet band being 40° 30'. The entire width of the primary rainbow is therefore 2°, part of this width being due to the angular magnitude of the sun.

We have thus revealed to us the geometric construction of the rainbow. But though the step here taken by Descartes and Newton was a great one, it left the theory of the bow incomplete. Within the rainbow proper, in certain conditions of the atmosphere, are seen a series of richly-colored zones, which were not explained by either Descartes or Newton. They are said to have been first described by Mariotte,^[6] and they long challenged explanation. At this point our difficulties thicken, but, as before, they are to be overcome by attention. It belongs to the very essence of a maximum, approached continuously on both sides, that on the two sides of it pairs of equal value may be found. The maximum density of water, for example, is 39° Fahr. Its density when 5° colder, and when 5° warmer, than this maximum is the same. So, also, with regard to the slopes of our water-shed. A series of pairs of points of the same elevation can be found upon the two sides of the ridge; and, in the case of the rainbow, on the two sides of the maximum deviation we have a succession of pairs of rays having the same deflection. Such rays travel along the same line, and add their forces together after they quit the drop. But light, thus re-enforced by the coalescence of non-divergent rays, ought to reach the eye. It does so; and were light what it was once supposed to be—a flight of minute particles sent by luminous bodies through space—then these pairs of equally deflected rays would diffuse brightness over a large portion of the area within the primary bow. But inasmuch as light consists of waves and not of particles, the principle of interference comes into play, in virtue of which waves can alternately re-enforce and destroy each other. Were the distance passed over, by the two corresponding rays within the drop, the same, they would emerge exactly as they entered. But in no case are the

distances the same. The consequence is that when the rays emerge from the drop they are in a condition either to support or to destroy each other. By such alternate re-enforcement and destruction, the colored zones are produced within the primary bow. They are called "supernumerary bows," and are seen not only within the primary but sometimes also outside the secondary bow. The condition requisite for their production is, that the drops which constitute the shower shall all be of nearly the same size. When the drops are of different sizes, we have a confused superposition of the different colors, an approximation to white light being the consequence. This second step in the explanation of the rainbow was taken by a man the quality of whose genius resembled that of Descartes or Newton, and who eighty-two years ago was appointed Professor of Natural Philosophy in the Royal Institution of Great Britain. I refer, of course, to the illustrious Thomas Young.^[7]

But our task is not, even now, complete. The finishing touch to the explanation of the rainbow was given by our last, eminent, Astronomer Royal, Sir George Airy. Bringing the knowledge possessed by the founders of the undulatory theory, and that gained by subsequent workers to bear upon the question, Sir George Airy showed that, though Young's general principles were unassailable, his calculations were sometimes wide of the mark. It was proved by Airy that the curve of maximum illumination in the rainbow does not quite coincide with the geometric curve of Descartes and Newton. He also extended our knowledge of the supernumerary bows, and corrected the positions which Young had assigned to them. Finally, Professor Miller, of Cambridge, and Dr. Galle, of Berlin, illustrated by careful measurements with the theodolite the agreement which exists between the theory of Airy and the facts of observation. Thus, from Descartes to Airy, the intellectual force expended in the elucidation of the rainbow, though broken up into distinct personalities, might be regarded as that of an individual artist engaged throughout this time in lovingly contemplating, revising, and perfecting his work.

We have thus cleared the ground for the series of experiments which constitute the subject of this discourse. During our brief residence in the Alps this year, we were favored with some weather of matchless perfection; but we had also our share of foggy and drizzly weather. On the night of the 22d of September, the atmosphere was especially dark and thick. At 9 p. m. I opened a door at the end of a passage and looked out into the gloom. Behind me hung a small lamp, by which the shadow of my body was cast upon the fog. Such a shadow I had often seen, but in the present case it was accompanied by an appearance which I had not previously seen. Swept through the darkness round the shadow, and far beyond, not only its boundary, but also beyond that of the illuminated fog, was a pale, white, luminous circle, complete except at the point where it was cut through by the shadow. As I walked out into the fog, this curious halo went in advance of me. Had not my demerits been so well known to me, I might have accepted the phenomenon as an evidence of canonization. Benvenuto Cellini saw something of the kind surrounding his shadow, and ascribed it forthwith to supernatural favor. I varied the position and intensity of the lamp, and found even a candle sufficient to render the luminous band visible. With two crossed laths I roughly measured the angle subtended by the radius of the circle, and found it to be practically the angle which had riveted the attention of Descartes—namely, 41°. This and other facts led me to suspect that the halo was a circular rainbow. A week subsequently, the air being in a similar misty condition, the luminous circle was well seen from another door, the lamp which produced it standing on a table behind me.

It is not, however, necessary to go to the Alps to witness this singular phenomenon. Amid the heather of Hind Head I have had erected a hut, to which I escape when my brain needs rest or my muscles lack vigor. The hut has two doors, one opening to the north and the other to the south, and in it we have been able to occupy ourselves pleasantly and profitably during the recent misty weather. Removing the shade from a small petroleum-lamp, and placing the lamp behind me, as I stood in either doorway, the luminous circles surrounding my shadow on different nights were very remarkable. Sometimes they were best to the north, and sometimes the reverse, the difference depending for the most part on the direction of the wind. On Christmas-night the atmosphere was particularly good-natured. It was filled with true fog, through which, however, descended palpably an extremely fine rain. Both to the north and to the south of the hut the luminous circles were on this occasion specially bright and well-defined. They were, as I have said, swept through the fog far beyond its illuminated area, and it was the darkness against which they were projected which enabled them to shed so much apparent light. The "effective rays," therefore, which entered the eye in this observation gave direction, but not distance, so that the circles appeared to come from a portion of the atmosphere which had nothing to do with their production. When the lamp was taken out into the fog, the illumination of the medium almost obliterated the halo. Once educated, the eye could trace it, but it was toned down almost to vanishing. There is some advantage, therefore, in possessing a hut, on a moor or on a mountain, having doors which limit the area of fog illuminated.

I have now to refer to another phenomenon which is but rarely seen, and which I had an opportunity of witnessing on Christmas-day. The mist and drizzle in the early morning had been very dense; a walk before breakfast caused my somewhat fluffy pilot dress to be covered with minute water-globules, which, against the dark background underneath, suggested the bloom of a plum. As the day advanced, the southeastern heaven became more luminous, and the pale disk of the sun was at length seen struggling through drifting clouds. At ten o'clock the sun had become fairly victorious, the heather was adorned by pendent drops, while certain branching grasses, laden with liquid pearls, presented, in the sunlight, an appearance of exquisite beauty. Walking across the common to the Portsmouth road, my wife and I, on reaching it, turned our faces sunward. The smoke-like fog had vanished, but its disappearance was accompanied, or perhaps caused, by the coalescence of its minuter particles into little globules, visible where they caught the light at a proper angle, but not otherwise. They followed every eddy of the air, upward, downward, and from side to side. Their extreme mobility was well calculated to suggest a notion prevalent on the Continent, that the particles of a fog, instead of being full droplets, are really little bladders or vesicles. Clouds are supposed to owe their power of floatation to this cause. This vesicular theory never struck root in England; nor has it, I apprehend, any foundation in fact.

As I stood in the midst of these eddying specks, so visible to the eye, yet so small and light as to be perfectly impalpable to the skin both of hands and face, I remarked, "These particles must surely yield a bow of some kind." Turning my back to the sun, I stooped down so as to keep well within the layer of particles, which I supposed to be a shallow one, and looking toward the "Devil's Punch-Bowl," saw the anticipated phenomenon. A bow without color spanned the Punch-Bowl, and, though white and pale, was well defined and exhibited an aspect of weird grandeur. Once or twice I fancied a faint ruddiness could be discerned on its outer boundary. The stooping was not necessary, and as we walked along the new Portsmouth road, with the Punch-Bowl to our left, the white arch marched along with us. At a certain point we ascended to the old Portsmouth road, whence, with a flat space of very dark heather in the foreground, we watched the bow. The sun had then become strong, and the sky above us blue, nothing which could in any proper sense be called rain existing at the time in the atmosphere. Suddenly my companion exclaimed, "I see the whole circle meeting at my feet!" At the same moment the circle became visible to me also. It was the darkness of our immediate foreground that enabled us to see the pale, luminous band projected against it. We walked round Hind Head Common with the bow almost always in view. Its crown sometimes disappeared, showing that the minute globules which produced it did not extend to any great height in the atmosphere. In such cases, two shining buttresses were left behind, which, had not the bow been previously seen, would have lacked all significance. In some of the combes, or valleys, where the floating particles had collected in greater numbers, the end of the bow plunging into the combe emitted a light of more than the usual brightness. During our walk the bow was broken and reformed several times, and, had it not been for our previous experience, both in the Alps and at Hind Head, it might well have escaped attention. What this white bow lost in beauty and intensity, as compared with the ordinary colored bow, was more than atoned for by its weirdness and its novelty to both observers.

The white rainbow (l'arc en ciel blanc) was first described by the Spaniard, Don Antonio de Ulloa, Lieutenant of the Company of Gentlemen Guards of the Marine. By order of the King of Spain, Don Jorge Juan and Ulloa made an expedition to South America, an account of which is given in two amply-illustrated quarto volumes to be found in the library of the Royal Institution. The bow was observed from the summit of the mountain Pambamarca, in Peru. The angle subtended by its radius was 33° 30', which is considerably less than the angle subtended by the radius of the ordinary bow. Between the phenomenon observed by us on Christmas-day, and that described by Ulloa, there are some points of difference. In his case fog of sufficient density existed to enable the shadows of him and his six companions to be seen, each, however, only by the person whose body cast the shadow, while around the head of each were observed those zones of color which characterize the "specter of the Brocken." In our case no shadows were to be seen, for there was no fog-screen on which they could be cast. This implies also the absence of the zones of color observed by Ulloa.

The white rainbow has been explained in various ways. A learned Frenchman, M. Bravais, who has written much on the optical phenomena of the atmosphere, and who can claim the additional recommendation of being a distinguished mountaineer, has sought to connect the bow with the vesicular theory to which I have just referred. This theory, however, is more than doubtful, and it is not necessary.^[8] The genius of Thomas Young throws light upon this subject as upon so many others. He showed that the whiteness of the bow was a direct consequence of the smallness of the drops which produce it. In fact, the wafted water-specks seen by us upon Hind Head^[9] were the very kind needed for the production of the phenomenon. But the observations of Ulloa place his white bow distinctly within the arc that would be occupied by the ordinary rainbow—that is to say, in the region of supernumeraries; and by the action of the supernumeraries upon each other Ulloa's bow was accounted for by Thomas Young. The smaller the drops the broader are the zones of the supernumerary bows, and Young proved by calculation that when the drops have a diameter of 1/3000 or 1/4000 of an inch, the bands overlap each other, and produce white light by their mixture. Unlike the geometric bow, the radius of the white bow varies within certain limits, which M. Bravais shows to be 33° 30' and 41° 46' respectively. In the latter case the white bow is the ordinary bow deprived of its color by the smallness of the drops. In all the other cases it is produced by the action of the supernumeraries.

The physical investigator desires not only to observe natural phenomena but to recreate them to bring them, that is, under the dominion of experiment. From observation we learn what Nature is willing to reveal. In experimenting we place her in the witness-box, cross-examine her, and extract from her knowledge in excess of that which would, or could, be spontaneously given. Accordingly, on my return from Switzerland last October, I sought to reproduce in the laboratory the effects observed among the mountains. My first object, therefore, was to obtain artificially a mixture of fog and drizzle like that observed from the door of our cottage. A strong cylindrical copper boiler, sixteen inches high and twelve inches in diameter, was nearly filled with water, and heated by gas-flames until steam of twenty pounds pressure was produced. A valve at the top of the boiler was then opened, when the steam issued violently into the atmosphere, carrying droplets of water mechanically along with it, and condensing above to droplets of a similar kind. A fair imitation of the Alpine atmosphere was thus produced. After a few tentative experiments, the luminous circle was brought into view, and, having once got hold of it, the next step was to enhance its intensity. Oil-lamps, the limelight, and the naked electric light were tried in succession, the source of rays being placed in one room, the boiler in another, while the observer stood, with his back to the light, between them. It is not, however, necessary to dwell upon these first experiments, surpassed as they were by the arrangements subsequently adopted. My mode of proceeding was this: The electric light being placed in a camera with a condensing lens in front, the position of the lens was so fixed as to produce a beam sufficiently broad to clasp the whole of my head, and leave an aureole of light around it. It being desirable to lessen as much as possible the foreign light entering the eye, the beam was received upon a distant black surface, and it was easy to move the head until its shadow occupied the center of the illuminated area. To secure the best effect it was found necessary to stand close to the boiler, so as to be immersed in the fog and drizzle. The fog, however, was soon discovered to be a mere nuisance. Instead of enhancing, it blurred the effect, and I therefore sought to abolish it. Allowing the steam to issue for a few seconds from the boiler, on closing the valve, the cloud rapidly melted away, leaving behind it a host of minute liquid spherules floating in the beam. A beautiful circular rainbow was instantly swept through the air in front of the observer. The primary bow was duly attended by its secondary, with the colors, as usual, reversed. The opening of the valve for a single second causes the bows to flash forth. Thus, twenty times in succession, puffs can be allowed to issue from the boiler, every puff being followed by this beautiful meteor. The bows produced by single puffs are evanescent, because the little globules rapidly disappear. Greater permanence is secured when the valve is left open for an interval sufficient to discharge a copious amount of drizzle into the air.^[10]

Many other appliances for producing a fine rain have been tried, but a reference to two of them will suffice. The rose of a watering-pot naturally suggests a means of producing a shower; and on the principle of the rose I had some spray-producers constructed. In each case the outer surface was convex, the thin convex metal plate being pierced by orifices too small to be seen by the naked eye. Small as they are, fillets of very sensible magnitude issue from the orifices, but at some distance below the spray-producer the fillets shake themselves asunder and form a fine rain. The small orifices are very liable to get clogged by the fine particles suspended in London water. In experiments with the rose, filtered water was, therefore, resorted to. A large vessel was mounted on the roof of the Royal Institution, from the bottom of which descended vertically a piece of compo-tubing, an inch in diameter and about twenty feet long. By means of proper screw fittings, a single rose, or, when it is desired to increase the magnitude or density of the shower, a group of two, three, or four roses, is attached to the end of the compo-tube. From these, on the turning on of a cock, the rain descends. The circular bows produced by such rain are far richer in color than those produced by the smaller globules of the condensed steam. To see the effect in all its beauty and completeness, it is necessary to stand well within the shower, not outside of it. A water-proof coat and cap are, therefore, needed, to which a pair of goloshes may be added with advantage. A person standing outside the beam may see bits of both primary and secondary in the places fixed by their respective angles; but the colors are washy and unimpressive, while within the shower, with the shadow of the head occupying its proper position on the screen, the brilliancy of the effect is extraordinary. The primary clothes itself in the richest tints, while the secondary, though less vivid, shows its colors in surprising strength and purity.

But the primary bow is accompanied by appearances calculated to attract and rivet attention almost more than the bow itself. I have already mentioned the existence of effective rays over and above those which go to form the geometric law. They fall within the primary, and, to use the words of Thomas Young, "would exhibit a continued diffusion of fainter light, but for the general law of interference which divides the light into concentric rings." One could almost wish for the opportunity of showing Young how literally his words are fulfilled, and how beautifully his theory is illustrated, by these artificial circular rainbows. For here the space within the primaries is swept by concentric supernumerary bands, colored like the rainbow, and growing gradually narrower as they retreat from the primary. These spurious bows as they are sometimes called,^[11] which constitute one of the most splendid illustrations of the principle of interference, are separated from each other by zones of darkness, where the light waves, on being added together, destroy each other. I have counted as many as eight of these beautiful bands, concentric with the true primary. The supernumeraries are formed next to the most refrangible color of the bow, and therefore occur within the primary circle. But, in the secondary bow, the violet, or most refrangible color, is on the outside; and, following the violet of the secondary, I have sometimes counted as many as five spurious bows. Some notion may be formed of the intensity of the primary, when the secondary is able to produce effects of this description.

An extremely handy spray-producer is that employed to moisten the air in the Houses of Parliament. A fillet of water, issuing under strong pressure from a small orifice, impinges on a little disk, placed at a distance of about one twentieth of an inch from the orifice. On striking the disk, the water spreads laterally, and breaks up into exceedingly fine spray. Here, also, I have used the spray-producer both singly and in groups, the latter arrangement being resorted to when showers of special density were required. In regard to primaries, secondaries, and supernumeraries, extremely brilliant effects have been obtained with this form of spray-producer. The quantity of water called upon being much less than that required by the rose, the fillet-and-disk instrument produces less flooding of the locality where the experiments are made. In this latter respect, the steam-spray is particularly handy. A puff of two seconds' duration suffices to bring out the bows, the subsequent shower being so light as to render the use of water-proof clothing unnecessary. In other cases, the inconvenience of flooding may be avoided to a great extent by turning on the spray for a short time only, and then cutting off the supply of water. The vision of the bow being, however, proportionate to the duration of the shower, will, when the shower is brief, be evanescent. Hence, when quiet and continued contemplation of all the phenomena is desired, the observer must make up his mind to brave the rain.^[12]

In one important particular the spray-producer last described commends itself to our attention. With it we can operate on substances more costly than water, and obtain rainbows from liquids of the most various refractive indices. To extend the field of experiment in this direction, the following arrangement has been devised: A strong cylindrical iron bottle, wholly or partly filled with the liquid to be experimented on, is tightly closed by a brass cap. Through the cap passes a metal tube, soldered air-tight where it crosses the cap, and ending: near the bottom of the iron bottle. To the free end of this tube is attached the spray-producer. A second tube passes also through the cap, but ends above the surface of the liquid. This second tube, which is long and flexible, is connected with a larger iron bottle, containing compressed air. Hoisting the small bottle to a convenient height, the tap of the larger bottle is carefully opened, the air passes through the flexible tube to the smaller bottle, exerts its pressure upon the surface of the liquid therein contained, drives it up the other tube, and causes it to impinge with any required degree of force against the disk of the spray-producer. From this it falls in a fine rain. A great many liquids have been tested by this arrangement, and very remarkable results have been obtained. I will confine myself here to a reference to two liquids, which commend themselves on account of their cheapness and of the brilliancy of their effects. Spirit of turpentine, forced from the iron bottle, and caused to fall in a fine shower, produces a circular bow of extraordinary intensity and depth of color. With paraffine-oil or petroleum a similar effect is obtained.

Spectrum analysis, as generally understood, occupies itself with atomic, or molecular, action, but physical spectrum analysis may be brought to bear upon our falling showers. I asked myself whether a composite shower—that is to say, one produced by the mingled spray of two or more liquids—could not be analyzed and made to declare its constituents by the production of the circular rainbows proper to the respective liquids. This was found to be the case. In the ordinary rainbow the narrowest color-band is produced by its most refrangible light. In general, the greater the refraction, the smaller will be the bow. Now, as spirit of turpentine and paraffine are both more refractive than water, I thought it probable that in a mixed shower of water and paraffine, or water and turpentine, the smaller and more luminous circle of the latter ought to be seen within the larger circle of the former. The result was exactly in accordance with this anticipation. Beginning with water, and producing its two bows, and then allowing the turpentine to shower down and mingle with the water, within the large and beautifully colored water-wheel, the more richly colored circle of the turpentine makes its appearance. Or, beginning with turpentine, and forming its concentrated iris; on turning on the water-spray, though to the eye the shower seems absolutely homogeneous, its true character is instantly declared by the flashing out of the larger concentric aqueous bow. The water primary is accompanied by its secondary close at hand. Associated, moreover, with all the bows, primary and secondary, are the supernumeraries which belong to them; and a more superb experimental illustration of optical principles it would be hardly possible to witness. It is not the less impressive because extracted from the simple combination of a beam of light and a shower of rain.

In the "Philosophical Transactions" for 1835, the late Colonel Sykes gave a vivid description of a circular solar rainbow, observed by him in India, during periods when fogs and mists were prevalent in the chasms of the Ghats of the Deccan:

It was during such periods that I had several opportunities of witnessing that singular phenomenon, the circular rainbow, which, from its rareness, is spoken of as a possible occurrence only. The stratum of fog from the Konkun on some occasions rose somewhat above the level of the top of a precipice forming the northwest scarp of the hill fort of Hurreechundurghur, from two to three thousand feet perpendicular, without coming over upon the table-land. I was placed at the edge of the precipice just without the limits of the fog, and with a cloudless sun at my back at a very low elevation. Under such a combination of favorable circumstances, the circular rainbow appeared quite perfect, of the most vivid colors, one half above the level on which I stood, the other half below it. Shadows in distinct outline of myself, my horse, and people appeared in the center of the circle as a picture, to which the bow formed a resplendent frame. My attendants were incredulous that the figures they saw under such extraordinary circumstances could be their own shadows, and they tossed their arms and legs about, and put their bodies into various postures, to be assured of the fact by the corresponding movements of the objects within the circle; and it was some little time ere the superstitious feeling with which the spectacle was viewed wore off. From our proximity to the fog, I believe the diameter of the circle at no time exceeded fifty or sixty feet. The brilliant circle was accompanied by the usual outer bow in fainter colors.

Mr. E. Colborne Baber, an accomplished and intrepid traveler, has recently enriched the "Transactions" of the Royal Geographical Society by a paper of rare merit, in which his travels in Western China are described. He made there the ascent of Mount O—an eminence of great celebrity. Its height is about eleven thousand feet above the sea, and it is flanked on one side by a cliff "a good deal more than a mile in height." From the edge of this cliff, which is guarded by posts and chains, you look into an abyss, and if fortune, or rather the mists, favor you, you see there a miracle, which is thus described by Mr. Baber:

Naturally enough it is with some trepidation that pilgrims approach this fearsome brink, but they are drawn to it by the hope of beholding the mysterious apparition known as the "Fo-Kuang," or "Glory of Buddha," which floats in mid-air, half-way down. So many eye-witnesses had told me of this wonder, that I could not doubt; but I gazed long and steadfastly into the gulf without success, and came away disappointed, but not incredulous. It was described to me as a circle of brilliant and many-colored radiance, broken on the outside with quick flashes and surrounding a central disk as bright as the sun, but more beautiful. Devout Buddhists assert that it is an emanation from the aureole of Buddha, and a visible sign of the holiness of Mount O.

Impossible as it may be deemed, the phenomenon does really exist. I suppose no better evidence could be desired for the attestation of a Buddhist miracle than that of a Baptist missionary, unless, indeed, it be, as in this case, that of two Baptist missionaries. Two gentlemen of that persuasion have ascended the mountain since my visit, and have seen the Glory of Buddha several times. They relate that it resembles a golden sun-like disk, inclosed in a ring of prismatic colors more closely blended than in the rainbow. . . . The missionaries inform me that it was about three o'clock in the afternoon, near the middle of August, when they saw the meteor, and that it was only visible when the precipice was more or less clothed in mist. It appeared to lie on the surface of the mist, and was always in the direction of a line drawn from the sun through their heads, as is certified by the fact that the shadow of their heads was seen on the meteor. They could get their heads out of the way, so to speak, by stooping down, but are not sure if they could do so by stepping aside. Each spectator, however, could see the shadows of the by-standers as well as his own projected on to the appearance. They did not observe any rays spreading from it. The central disk, they think, is a reflected image of the sun, and the inclosing ring is a rainbow. The ring was in thickness about one fourth of the diameter of the disk, and distant from it by about the same extent; but the recollection of one informant was that the ring touched the disk, without any intervening space. The shadow of a head, when thrown upon it, covered about one eighth of the whole diameter of the meteor. The rainbow ring was not quite complete in its lower part, but they attribute this to the interposition of the edge of the precipice. They see no reason why the appearance should not be visible at night when the moon is brilliant and appositely placed. They profess themselves to have been a good deal surprised, but not startled, by the spectacle. They would consider it remarkable rather than astonishing, and are disposed to call it a very impressive phenomenon.

It is to be regretted that Mr. Baber failed to see the "Glory," and that we in consequence miss his own description of it. There seems a slight inadvertence in the statement that the head could be got out of the way by stooping; for, as long as the "Glory" remained a circle, the shadow of the head must have occupied its center. Stepping aside would simply displace the bow, but not abolish the shadow.

Thus, starting from the first faint circle seen drawn through the thick darkness at Alp Lusgen, we have steadily followed and developed our phenomenon, and ended by rendering the "Glory of Buddha" a captive of the laboratory. The result might be taken as typical of larger things.

1. From author's advance sheets.
2. Whewell ("History of the Inductive Sciences," vol. i, p. 345) describes Vitellio as a Pole. His mother was a Pole; but Poggendorff ("Handwörterbuch d. Exacten Wissenschaften") claims Vitellio himself as a German, born in Thüringen. "Vitellio" is described as a corruption of Witelo.
3. Born at Leyden 1591; died 1626.
4. Archbishop of Spalatro, and Primate of Dalmatia. Fled to England about 1616; became a Protestant, and was made Dean of Windsor. Returned to Italy and resumed his Catholicism; but was handed over to the Inquisition, and died in prison (Poggendorff's "Biographical Dictionary").
5. There is, in fact, a bundle of rays near the maximum, which, when they enter the drop, are converged by refraction almost exactly to the same point at its back. If the convergence were quite exact, then the symmetry of the liquid sphere would cause the rays to quit the drop as they entered it—that is to say, perfectly parallel. But inasmuch as the convergence is not quite exact, the parallelism after emergence is only approximate. The emergent rays cut each other at extremely sharp angles, thus forming a "caustic" which has for its asymptote the ray of maximum deviation In the secondary bow we have to deal with a minimum, instead of a maximum, the crossing of the incident and emergent rays producing the observed reversal of the colors. (See Engel and Shellbach's diagrams of the rainbow.)
6. Prior of St. Martin-sous-Beaune, near Dijon, member of the French Academy of Sciences; died in Paris, May, 1684.
7. Young's works, edited by Peacock, vol. i, pp. 185, 293, 357.
8. The vesicular theory was combated very ably in France by the Abbe Raillard, who has also given an interesting analysis of the rainbow at the end of his translation of my "Notes on Light."
9. Had our refuge in the Alps been built on the southern side of the valley of the Rhone, so as to enable us to look with the sun behind us into the valley and across it, we should, I think, have frequently seen the white bow; whereas on the opposite mountain, slope, which faces the sun, we have never seen it.
10. It is perhaps worth noting here, that when the camera and lens are used the beam which sends its "effective rays" to the eye may not be more than a foot in width, while the circular bow engendered by these rays may be, to all appearance, fifteen or twenty feet in diameter. In such a beam, indeed, the drops which produce the bow must be very near the eye, for rays from the more distant drops would not reach the required angle. The apparent distance of the circular bow is often great, in comparison with that of the originating drops. Both distance and diameter may be made to undergo variations. In the rainbow we do not see a localized object, but receive a luminous impression, which is often transferred to a portion of the field of view far removed from the bow's origin.
11. A term, I confess, not to my liking.
12. The rays which form the artificial bow emerge, as might be expected, polarized from the drops.