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vigation of the Bonite, at periods so near each other, and in such a manner, that no perturbation can take place unobserved.

THE RAINBOW.—The explanation of the rainbow may be regarded as one of Descartes's most beautiful discoveries; but, still, even after the developements which Newton has furnished, it is yet incomplete. When we look attentively at this magnificent phenomenon, we perceive under the red of the interior arch several series of green and purple, forming narrow contiguous arches, well defined, and perfectly concentric to the principal arch. Of these supplementary arcs (for that is the name given to them,) the theory of Descartes and Newton takes no notice, and indeed it cannot even be applied to them.

The supplementary arcs appear to be an effect of luminous interfe

These interferences cannot be produced but by drops of water of a certain smallness. It is necessary also, for otherwise the phenomenon would have no brilliancy, that, besides this condition of magnitude, the drops, or at least the greater part of them, should be almost mathematically equal in their dimensions. If, therefore, the rainbows of equinoctial regions are never attended with supplementary arcs, it would be a proof that the drops of water which there issue from the clouds are of larger size, and more unequal dimensions, than in our climates. In our ignorance of the causes of rain, this fact would by no means be void of interest.

When the sun is low, the upper portion of the rainbow is, on the contrary, very much elevated. It is towards this culminating region that the supplementary arcs show themselves in greatest splendour. Descending from this, their colours become rapidly fainter. In the lower regions, near the horizon, and even considerably above it, no traces of them are ever seen, at least in Europe.

It follows, therefore, that rain-drops, during their vertical descent, lose the property which they at first possess; that they have no longer the conditions necessary for efficient interference, and that they increase in size.

Is it not curious, it may be asked in passing, to find in an optical phenomenon, in a peculiarity of the rainbow, a proof that in Europe the quantity of rain must be so much the less the higher we place the vessel in which it is to be received * !

The increase in the size of the drops, it can scarcely be 'doubted, is owing to a precipitation of humidity on their surface; this will be in proportion to the atmospheric strata through which they pass in their descent from the cold region of their origin; and which strata are warmer and warmer, as they approach the earth. It is then almost certain that, if supplementary rainbows are formed in equinoctial regions, as in Europe, they never reach the horizon; but a comparison of the angle of the height at which they cease to be seen with the angle of disappearance noticed in our climates, seems to offer a means of obtaining some meteorological results, which can be obtained by no other method at present known.

* In the Observatory at Paris, there are first. In the course of a year the resertwo vessels in which rain-water is collected; voir in the court received eight-hundredths one of them is on the terrace, the other in more water that that placed on the terrace. the court, 92 English feet lower than the

HALOS.-In high latitudes, off Cape Horn, for example, the sun and the moon often appear surrounded by two luminous circles, which meteorologists call halos. The radius of the smallest of these circles is about 22°,—that of the larger is almost exactly 46°. The first of these angular dimensions is within a little the minimum deviation which light undergoes while traversing a glass prism of 60°; the other would be given by two prisms of 60°, or by a single prism of 90°.

It seems, therefore, natural to seek for the cause of halos, as Mariotte has done, in the rays refracted by floating crystals of snow, which, as every one knows, usually present angles of 60° and 90°.

This theory, besides, has been rendered still more probable since the power has been acquired of distinguishing refracted from reflected light by means of chromatic polarization. It is, in fact, the colours of the first kind (refracted light) which produce the polarized rays of the halo. What, then, still remains to be known regarding this phenomenon ? It is the following:- According to theory, the horizontal diameter of a halo and the vertical diameter ought to have the same angular dimension; but we are assured that these diameters are sometimes strikingly unequal. Actual measurement alone can establish this fact; for if it has happened that a judgment of the inequality in question has been formed by the naked eye only, there are not wanting sufficient causes of illusion to explain how the most experienced physicien might be deceived. The reflecting circles of Borda are admirably adapted to the measurement of the angular distances at sea.

We may, therefore, without hesitation, recommend to the officers of the Bonite to apply the excellent instruments with which all of them are provided to determine the dimensions of all the halos that may appear to them to be elliptical. They will themselves perceive that the inner edge of the halo,--the only one which is distinctly defined,—is much better adapted for observation than the outer one; but they must never, with regard to the sun, neglect to indicate whether they take the centre or the edge as the term of comparison. We likewise regard it as indispensable, that, in each direction, the two rays diametrically opposite should be measured,—for certain observers have mentioned circular halos, in which, if they are to be believed, the sun did not occupy the centre of the

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WINDS. TRADE-WINDS.—Perhaps it will excite surprise to see the tradewinds announced as still affording a subject of important investigation; but it must be remarked, that the practice of navigators has often confined them to meagre notices; with such science cannot be satisfied. Thus it is not true, whatever may have been alleged, that to the north of the equator these winds constantly blow from the north-east; and that to the south of it they blow uniformly from the south-east. The phenomena are not the same in the two hemispheres. In each plane, moreover, they change with the seasons. Daily observations of the true direction, and, as far as practicable, of the strength of the eastern winds which prevail in equatorial regions, would therefore be a useful acquisition to meteorology.

The vicinity of continents, their western sides especially, modifies the trade-winds in their strength and direction. It sometimes even hap

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pens that they are displaced by a west wind. Wherever this change of the wind occurs, it is desirable to note the time, the bearing of the neighbouring coasts, their distance, and, where practicable, their general aspect. In order to show the utility of this last recommendation, it will be enough to say, that a sandy country, for example, will have a much speedier and more active influence, than one covered with forests, or any other kind of vegetation.

The sea which washes the western shore of Mexico, from Panama to the peninsula of California, between 8° and 22° north latitude, will afford an opportunity to the officers of the Bonite of observing a complete inversion of the trade-winds. They will find, as stated by Captain Basil Hall, a nearly permanent west wind, in a situation where it might be expected the east wind of the equinoctial regions would prevail. In these offings it would be curious to ascertain how far from the shore this anomaly extends-at what degree of longitude the trade-wind resumes, so to speak, its dominion.

According to the most generally adopted explanation of the tradewinds, there ought to exist, between the tropics, a more elevated wind, constantly blowing in an opposite direction to the one on the surface of the earth. Numerous proofs are already collected of the existence of this counter-current. Vigilant observations of elevated clouds, particularly of those called cirro-cumulus, would certainly furnish indications of great value to meteorology.

Finally, the periods, strength, and extent of the monsoons, form subjects of study, in 'which, notwithstanding a vast amount has been collected, there is still something to glean.

(To be continued. )

TRANSACTIONS OF THE ROYAL ASTRONOMICAL

SOCIETY.

In continuation of the plan we proposed (see p. 209) to adopt with respect to the labours of different learned societies, of giving, as occasion may arise, a more or less brief analysis of the papers published in the Transactions of those bodies, we now proceed to lay before our readers an account of the contents of the concluding section of the ninth volume of those of the Royal Astronomical Society. In our next number we propose to give a similar analysis of the Transactions of the Royal Society of Edinburgh.

This part contains ten papers, besides the Report of the Council, the Anniversary Address, and other miscellaneous information, chiefly relating to the management of the Society. I. On the Time of Rotation of Jupiter. By F. G. Airy, Esq., Astronomer

Royal, and President of the Society. Kepler inferred, from a presumed connexion between the time of the rotation and that of its first satellite, that Jupiter's time of rotation was less than 24 hours. Cassini was led from his own observations in 1664-5 to conclude that it was less than 14 hours. Subsequent observations in 1665 led him to the time of 9h 56m 0s. This is the period adopted by Laplace, and all subsequent writers.

In December, 1834, Professor Airy took, advantage of one of the two remarkably black and well-defined spots which appeared near the lower belt of the planet, to make a series of observations, with a view to the determination of the period of Jupiter's rotation with greater accuracy. These observations extend over the period from December 16th to March 19th following: and from them, by methods which he details, he finds that the true period corresponding to them is 9h 55m 21-3*, mean solar time.

This close approach (differing by only 38:7 seconds) to the period determined by Cassini, will seem remarkable enough to those who estimate by numerical differences the degree of approximation, without considering the unit by which those differences are measured: but to those who are accustomed to look upon an inquiry in all its details, and under careful mathematical discipline, it is obvious that this small quantity may be in reality a comparatively great one. It is so in the present case.

The time of the visibility is less than five hours; and the period of observation extending over 225 revolutions, from which Mr. Airy deduced his period, it would make 225 x 38.7 seconds, or 2h 25m 0·75, or about half the period of the visibility of the spot itself. The period then assigned by Cassini is, as the author remarks, incompatible with the observations recorded and discussed in his communication.

II. Continuation of Researches into the Value of Jupiter's Mass. By the

same.

It would be hardly possible to render the objects of this short paper intelligible to those who are unacquainted with the problem itself, and with the previous papers of the author on the subject. We propose, therefore, to enter into some degree of explanation of the general character and the nature of the difficulties encountered in it, in an early number, as well as such historical details as we think may be interesting to our readers. It is sufficient to state here, that Professor Airy finds the whole mass of the Jovial system 10ản•g of the sun's mass. The result of observations discussed in his former papers on the subject was nois•3.

III. On the Position of the Ecliptic, as inferred from Observations with the

Cambridge Transit and Mural Circle, made in the year 1834.

By the

same.

This determination is founded on 138 transits of the sun, in which both the preceding and following limbs were observed, and 143 polar distances, in which both the north and south limbs were observed. Professor Airy believes these determinations, in point of individual accuracy and general excellence, to be equal to any that have been used for the same purpose.

1. The author determines the place of the equinox to be intermediate between those assigned by Bessel and Pond, but a very little nearer to the former.

2. That the obliquity of the ecliptic assumed in the Nautical Almanac (namely, 23° 27' 39.26",) is too great by 0-357".

3. That the sun moves, independently of the effects of perturbations, in a small circle, whose distance from the north pole of the ecliptic is 90° 0:569".

This last is a startling conclusion. Mr. Airy is evidently embarrassed by it: but to our minds it appears clear that it must arise from either imperfection of method, or imperfection of instruments. not imagine the circumstances indicated by it to be the case of actual nature.

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IV. Description of the Mural Circle at the Armagh Observatory, and Erami

nation of its Divisions. By T. R. Robinson, D.D., &-c. This paper, which, in reference to the actual construction of mural instruments, consists almost entirely of practical details, is unsusceptible of material abridgement. The author comes to the conclusion that the present method of dividing large circles is insufficient for attaining the degree of accuracy which practical astronomers now require; and that to effect it satisfactorily, they must be divided on the engine, as Reichenbach divided his three-feet circles.

V. Report on the new Standard Scale of this Society (the Royal Astrono

mical]. Drawn up at the request of the Council, by Francis Baily,

Esq., F.R.S. Of this elaborate paper we shall give an analysis in a future number. VI. Two elementary Solutions of Kepler's Problem by the Angular Calculus,

By William Wallace, A.M., F.R.S.E., &c., Professor of Mathematics in

the University of Edinburgh. A planetary orbit being an ellipse, having the sun in one of its foci, Kepler discovered (by a discussion of the observations of Tycho Brahe) that the radius vector of a planet describes equal areas in equal times: but the truth of this law, as the result of any hypothesis respecting the force of gravitation, was first proved by Newton.

The equation to which it leads is in which z is the mean anomaly, x the true anomaly, and e the eccentricity of the elliptic orbit.

When x is given, z is readily found from a table of sines; but when z is given, and x required, (which is the form in which the problem always presents itself in astronomical research,) it becomes a matter of considerable difficulty, and oftentimes excessively troublesome. Various methods have been proposed,—of course, chiefly tentative, and necessarily inelegant combinations of geometry and trigonometry.

We shall give the conclusions of Professor Wallace, and refer our readers to the work itself for their investigations, as well as the examples by which he illustrates them.

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