of the ordinary succession of colours, reckoned from the outside, being red, orange, yellow, green, blue, indigo, and violet. Immediately in contact with the interior violet, succeeded the supernumerary stripes of different colours, consisting, most obviously, of green and purple or violet, in regular succession. The other colours of the spectrum were not observed. The whole phenomenon conveyed the idea of a splendid canopy of equal vertical arches, which seen from beneath, seemed to diminish in distinctness from the effect of the receding distance.

Another phenomenon of the same class, with a peculiarity which appeared to me to be of a very uncommon kind, may be of more importance to be described.

This consisted of two beautiful segments of primary and secondary rainbows, (called by the sailors" weather-galls," when, as in this case, they consist only of the portions next the horizon) with some supernumerary bows within the arch of the former; and likewise, which is the extraordinary part, another spectrum rising almost vertically from the base of each of the common arcs, at its apparent termination in the horizon of the sea, so as to form two figures nearly resembling the Greek ».

The segments a and b, Fig. 1. Pl. IV. represent the portions of the primary and secondary bows, and e the supernumerary bows, whilst c and d represent the two vertical spectra. Perhaps I err in defining them vertical spectra, because the apparent form was a portion of a circle, curved in the same direction (namely, towards the left) as the irides; but not having used any means to ascertain the exact form, I cannot speak with certainty, either as to the curvature, or to the direction in which it deviated, if it deviated at all, from the perpendicular. In other respects, there is no uncertainty, not even as regards the apparent form, a sketch of the appearance being carefully made at the time.

The colours of the primary vertical spectrum (c) were in the same order, and almost of similar brilliancy, as the rainbow with which it was connected; and the colour of the secondary vertical spectrum (d), as well as its width and general appearance, also corresponded with the colours and magnitude of its own bow.

This phenomenon was seen on the 3d of September 1821, at

sea, near the northern coast of Ireland, approaching the entrance of the North Channel. It occurred about half an hour before sunset. There was not a breath of wind at the time; and the sea was remarkably smooth and calm. The atmosphere was full of heavy rain clouds, except in the direction where the sun was, and these were discharging showers in various quarters.

Since this description was originally written (the above account being taken in substance from my journal kept at the time), a very simple explanation has occurred to me of this phenomenon, which, at the time of its appearance, seemed to partake so much of the nature of a prodigy.

The sea, on this occasion, it has been remarked, was quite smooth and calm; its surface, indeed, was like a mirror; for our situation, being almost "land-locked," happened to shut out whatever swell there might be in the main ocean, and likewise to afford time, during a day chiefly calm, for even the smaller waves, of the "wind-lipper," to subside. In consequence of these circumstances, the sea, at the close of the day, was without the slightest undulation. The sun, at the time when the rainbows appeared, was at a very low altitude. I assumed it in my notes at 3°; though being above half an hour before sun-set (6 P. M.), it must have been at least twice as great, probably betwixt 7° and 8°.

-Under such circumstances, there would be a reflection of the sun, from the surface of the water, almost half as strong as the rays proceeding direct from the sun itself; which power of rays was fully adequate to the production of a rainbow of nearly one-half the intensity of the common bow; and the direction of these rays being from a position, as much below the horizon, as the sun was at the time above it, the arches of the direct and reflected bows, would, of course, be differently situated, as arising from circles of equal diameter, whose centres were twice the altitude of the sun, or 15° apart. The reflected bow (as to the part above the horizon) would consequently be a segment larger than a semicircle, and precisely as much larger as

* The quantity of rays reflected by water, according to Sir Isaac Newton, when incident at an angle 74° inclined to the horizon, is about four-tenths of the whole quantity that reaches the surface.

the bow from the direct rays was less than a semicircle*. And all these circumstances are found to be realised in the phenomenon described.

Moreover, in proof that this was the real origin of the vertical spectra, I may mention the exact coincidence of the two bows on the line of the horizon-the similarity and order of the colours, and the peculiar position and curvature-with the whole of which particulars a bow produced by a reflected sun, would, under the circumstances, exactly correspond.

?

This is clearly shewn by the figures and diagrams. Fig. 1, - already referred to, is the appearance of the various arcs, as drawn and registered at the time when they were seen. Fig. 2. is the form and appearance, which, on the same scale of curvature, these arcs, according to theory, would assume, a, b, the primary and secondary bows being drawn from a centre 74° below the horizon (equal to the supposed altitude of the sun), and c, d, the bows of reflection from a centre 74° above the horizon. The resemblance, it is evident, is as near as could be desired. Had the arcs been complete, the form would have been according to the dotted lines.

From hence we derive an explanation of the cause of the inverted rainbow, described by some authors; a phenomenon, however, of rare occurrence, and requiring, on this principle, a variety of accommodating circumstances for its production. In respect to this phenomenon, many philosophers have either doubted its reality, or have considered it as an optical deception.

* The centre of the common rainbow being in a straight line continued from the sun, through the eye of the observer, as far as the base of the iris (when it appears to terminate at the horizon), that centre will evidently be just as much be low the horizon as the sun is above it. But the bow of reflection has its centre just as far above the horizon. For the angles of incidence and reflection being equal, the image of the sun, that gives rays to the bow of reflection, will be at an angle, just as much below the horizon as the sun is above it, and consequently the centre of its concentric bows will be exactly at the same altitude above the horizon as the sun is. Hence, whatever portion the bow of reflection exceeds a semicircle, in consequence of its centre being above the horizon, the direct bow will want of a semicircle, by its centre being equally below the horizon. Consequently, the chord of each arc at the horizon will be equal; and, therefore, if placed together, their feet or bases will correspond. And hence, the direct and reflected bows, as regards the portion above the horizon, and terminated by it, would, if one of them could be turned downward, exactly complete the circle.

Thus Dr Hutton, in his Philosophical and Mathematical Dic-` tionary, ascribes the appearance to a cloud happening to intercept the rays, and preventing them from shining on the upper part of the arch; in which case only the lower part appearing, the bow, he supposed, might seem as if turned upside down; "which," says he, " has probably been the case in several prodigies of this kind, related by authors.”—Article RAINBOW.

But the preceding facts and principles afford us, I conceive, a satisfactory solution of the phenomenon, in all cases where there is a smooth reflecting surface of water, suitably situated at the place of the inverted bow being seen; and I am not aware that it has been seen under other circumstances.

Suppose the sun's altitude to be 42° (the outer semi-diameter of the primary bow nearly), and the circumstances to be favourable for the production of the bow by the sun's rays reflected from a perfectly calm surface of water, then arches, if not circles, resembling figure 3, might occur, provided the quantity of reflected rays, at such an angle of incidence, were capable of producing the iris. Here c c, as in the other figures, represents the primary bow of reflection, having its centre 42 degrees above the horizon; d d the secondary bow of reflection, which, however, in this case, from the quantity of rays absorbed by the water, might not be visible; and b, a segment of the common secondary rainbow, the primary one not appearing above the horizon, on account of the greatness of the sun's altitude *.

The only doubt that I conceive likely to arise against this explanation of inverted rainbows appearing entirely above the horizon, is the small number of rays which are reflected from a surface of water, at the required angle of incidence, compared to

с

The relative position of the bows of reflected and direct rays, is simply illustrated by inscribing on paper the circles c and d complete, the same on both sides of the paper from the same centre. Then cut away all the blank paper without the outer circle d, and also the blank paper within the inner circle c, except a narrow slip, as a diameter ƒƒ (defined by dotted lines), and graduate this diameter as in the figure. If, then, the lower edge of the diagram be doubled up at the mark of 42°, a representation will be given of the reflected and direct bows, similar to fig. 3, when the sun's altitude is 42°. Or, if it be doubled up at 74°, it will represent fig. 2, or any other appearance of the combined phenomena, according to the altitude of the sun at the time. Hence when the sun is in the horizon, the bows of direct and reflected rays will cover one another and coincide.

the quantity absorbed. For, it would appear, according to Sir Issac Newton's experiments, that, at an angle of 42° of incidence (48° from the perpendicular), only from one-thirtieth to one-fortieth part of the light impinging is reflected from water. Is this proportion of light, then, sufficient for the production of the iris? There is good reason to suppose, I conceive, that even this proportion is abundantly adequate to the production of the phenomenon, because the light of the full-moon is occasionally sufficient for the purpose; yet that light, according to Dr Smith, is little more than a ninety-thousandth part of the light of the sun, or, according to M. Bouquer, not above a three-hundredthousandth part. In either case we see, that the light reflected from the sea, when the sun has an altitude of 42°, is some thousands of times greater than the quantity which is sufficient for the production of the lunar iris; consequently we may infer that an inverted iris from the reflected rays of the sun, may occur even when the sun has the greatest altitude to which it ever attains in any temperate or frigid climate

This being the case, there seems to be reasonable ground for supposing, that the reflection of the sun's rays from a perfectly calm surface of water, may have a share also in the production, of some of the various phenomena of haloes, such as are not otherwise explained,-a supposition which the resemblance that figures 2 and 3 bear to some of the prismatic circles, renders more than probable.

Tour to the South of France and the Pyrenees, in 1825. By G. A. WALKER ARNOTT, Esq. A. M. F.L.S. & R. S. E. &c. In a Letter to Professor JAMESON. (Continued from the preceding Volume, p. 275.)

I

HAVE taken notice of the Capouladoux Cyclamen, because by some it is considered as very different from the C. hederafolium. The Montpellier plant is certainly the same as that found in Corsica, and I believe not unfrequently along the shores of the Mediterranean. It flowers in spring. In this respect it agrees with that said to be found wild in Britain, but which has probably escaped from some garden. I have never seen the