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M. LEPISSIER, Elements of Europa.-Mr. POGSON, Ephemeris of Variable Stars for 1859.

Errata in the Art. Physical Astronomy (Encyclopædia Metropolitana) communicated by Captain Tennant.

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To be disposed of, an Iron Equatoreal Stand adapted for carrying a refractor of from 3 to 4 inches aperture. May be seen at the rooms of the Society.

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Ephemeris of the Variable Stars for 1859. By Norman Pogson, Esq., Director of the Hartwell Observatory.

(Communicated by Dr. Lee.)

In this ephemeris the initials in the sixth column represent the following names :-A., Argelander; Au., Auwers;
B., Baxendell; K., Krüger; P., Pogson; S., Schönfeld: W., Winnecke.

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The corrections to be applied to the observed times of minima of the short-period variables, before comparing with the ephemeris may be found by the formulæ on page 27 of vol. xvii. of the Monthly Notices.

With very few exceptions, the same elements have been employed in preparing this as in the last year's ephemeris. When no authority is stated, the times of maxima must only be regarded as indications as to when a search will prove most beneficial for the determination of the elements of variation of such star. If invisible, a mere record of such being the case will, by contradicting the assumed elements, remove an erroneous prediction from the next ephemeris, and thereby possess great interest and value. For the short-period variables (all of which except a Tauri are from Prof. Argelander's elements), those minima only are tabulated which occur when the sun is considerably below, and the star at least ten degrees above, the horizon.

I have again to acknowledge my obligation to Mr. Baxendell for having obligingly communicated the ephemerides of a Tauri, 13 Lyra, R and S Herculis, based upon elements derived from his own observations.

The unavoidable delay in the preparation of this little. annual contribution is a matter of much regret, but one which, I am happy to say, is not likely to happen again. Change of residence, and other pressing interruptions, all conspired to derange my plans, and throw me behind in their execution. The variable stars are, however, marked out as special objects of observation and investigation in Dr. Lee's Observatory, and I shall therefore hope to have the ephemeris for 1860 in print before the close of the present year.

Hartwell Observatory, April 11, 1859.

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Professor ADAMS, on the Secular Variation of the Eccentricity and Inclination of the Moon's Orbit.

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"It is curious that the coefficients of e2 and 2, in this expression, are equal and of contrary signs, although they are found by totally distinct processes. The effect of the terms in e2 and on the magnitude of the secular acceleration is, as I anticipated, very insignificant. The term in e' increases the coefficient of the square of the number of centuries by o"-036, and that in diminishes the same coefficient by o" 097; so that, on the whole, the coefficient 5"70, which I previously found, must be diminished by o" 06, or reduced to 5"-64. This value I believe to be within one-tenth of a second of the true theoretical value of the coefficient of the secular acceleration. Whether ancient observations admit of such a small value of the acceleration is a different question.

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acceleration to 5"7, only about one-half of the value hitherto received. M. Delaunay has recently verified my coefficient of m4; and he informs me that he shall very soon have carried the approximation to the eighth order in m, and included the terms depending on e2 and 2.

"In my memoir above referred to I mentioned that other elements of the moon's orbit suffer secular changes which had been overlooked.

"I find the following expressions for the secular variation of the eccentricity and inclination of the moon's orbit, adopting Plana's definitions of e and y:

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"Since I sent my result respecting the secular variations of the eccentricity and inclination of the moon's orbit to the Society the other day, I have found the leading terms of the secular acceleration of the mean motion which depend on the eccentricity and inclination of the orbit. The result is one of remarkable simplicity, considering the nature of the calculations which have led to it; and I should be glad if you would let it appear in the Monthly Notices as soon as you conveniently can, as a supplement or a note to my former communication. The result is,

On the Apparent Projection of Stars upon the Moon's Disk in Occultations. By G. B. Airy, Esq., Astronomer Royal.

It is well known that on occasions of the occultation of a star by the moon the star has been frequently observed to advance apparently upon the moon's disk, and after remaining visible in this manner for a very short time has then vanished instantaneously. In the paper above entitled, the author inquires into the origin of this curious phenomenon.

Nearly thirty years ago the author himself saw the phenomenon of projection in great perfection. The singularity of the phenomenon made a strong impression on his mind, and induced him frequently to consider the possibility of explaining it on recognised optical principles. The only remark which appeared to lead towards a conjectural explanation was one by Sir James South, that in many instances a red star was the subject of projection. It seemed then not impossible that, if the light of the moon and the light of the star differed materially in refrangibility, the rays of the star (supposed the less refrangible), though actually touching the moon's body at the instant of occultation, might be so much less bent than the rays of the moon by the action of the earth's atmosphere, that at that instant the star would actually be seen lower than the moon's limb. If, then, the occultation took place at the moon's upper limb, there would be projection of the star on the moon's disk. If it took place at the lower limb, the star would disappear at a small distance external to the limb. If the rays of the star were more refrangible than those of the moon, these appearances would be reversed. Here, then, was indicated a distinct criterion upon which the fate of the hypothesis must depend. It became necessary only to ascertain whether, in the instances of recorded projection, the star was uniformly higher or uniformly lower, as referred to the zenith of the place of observation, than the moon's centre. If either of these laws held uniformly, the hypothesis would be plausible; if neither law was sufficiently maintained, the hypothesis would be certainly false.

In order to test the hypothesis by this criterion, it was necessary to compute, to a considerable degree of approximation, the apparent zenith distances of the moon and star for all the occultations on the occasion of which the phenomenon was observed. The author has accordingly collected together and subjected to computation all the recorded observations bearing upon the question which were accessible. This laborious

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ASTRONOMER ROYAL: Apparent Projection of Stars upon the Moon's Disk in Occultations.

operation was carefully executed by Mr. Ellis, one of the assistants at the Royal Observatory. The author has divided the observations into four distinct classes. The results of the calculation are shown not to favour the conjecture which gave rise to them.

The author then proceeds to point out a circumstance which appears to him to throw light upon the phenomenon. It is contained in an account of the disappearance of Aldebaran at the moon's bright limb on October 23, 1831, as observed by Mr. George Innes at Aberdeen. (Ast. Nach. vol. x. p. 211.) Mr. Innes states that when Aldebaran came within about six seconds of the moon's limb, it passed through the remaining distance with great rapidity, its apparent velocity becoming five or six times as great as before. It appeared to hang on the moon's limb for about five seconds of time, and then suddenly disappeared. In other words, the disk of the moon appeared suddenly to swell or to extend itself into what was previously the dark space. The author does not doubt that the statement made by Mr. Innes involves a severely accurate account of the appearances which might have been observed in other cases if the observers had been equally cool and accurate. He accordingly proceeds to consider whether the apparent swelling of the moon's disk can be explained on recognised optical and physiological principles.

The opinion which the author entertains of the origin of the phenomenon is founded on the undulatory theory of light. According to that theory the image of a luminous point in a telescope (whether of a star or a portion of the moon's illuminated surface) is not a point. The bright rings which appear to surround the image of a star as seen in good telescope, afford an apt illustration of the actual distribution of light in such cases. The author thus expresses his views on the subject:

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"It is to be conceived that every luminous point of the moon's disk is accompanied with a similar system of rings, and therefore that the aggregate of light produced by the aggregate of all the luminous points of the moon's disk, is not a luminous image bounded by a sharp outline at what we consider the geometrical outline of the image, but that the geometrical outline is fringed by a band of illumination, produced by the interlacing and superposition (not interference) of all the systems of rings. The integral which determines the brightness is so unmanageable that I am unable at present to assign the numerical values of the brightness at different distances from the geometrical outline (though there would be no difficulty in finding them by the troublesome method of quadratures); but as the light from the different sources is actually superposed and aggregated, it is certain that there must be a considerable quantity of light external to the geometrical limb. And when, with a very fine telescope, we see the moon's limb very sharply defined, and apparently surrounded by immediate darkness, we do in reality see it erroneously. Probably some operation of the mind, under the conviction that the outline of light ought to fall in a given curve, acts on the animal faculty of sensation so as to incapacitate the visual organs from perceiving the fainter light beyond that curve.

"But in the excitement and intentness of observing an occultation, the state of the sensational organisation is probably much changed. And as the presumed time of the phenomenon comes nearer and nearer, the eye probably becomes more and more sensible to the faint diffused light, and the visible boundary of light extends further and further into the darkness. And this presents that appearance of rapidly increasing velocity of approach which is so graphically described by Mr. Innes.

"In numerous instances, when the boundary of the moon's light has swelled till it touches the star, it swells no further, and the star' hangs' on the moon's limb. It seems perfectly conceivable that the mental contemplation of the relation of the

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positions of the moon and star which is implied in the phenomenon that is to be observed, may frequently so far act on the sensibilities that when that relation (namely, contact) is once gained, the mental effort does not make the sense more acute than is necessary, and may even somewhat relax as the denser light of the moon approaches the star.

"The explanation which I have offered of these curious phenomena does in reality bring them under the general category of irradiation. But it is a kind of irradiation which has not, so far as I know, been noticed in other instances, an irradiation which sometimes exists and sometimes (under the same astronomical circumstances) does not exist, which at the same place is seen by one observer and not by another, which sometimes remains apparently constant for at least several seconds of time, and sometimes varies from instant to instant. It is probable that there is irradiation of a similar kind when the wire of a meridional instrument is placed on the moon's limb; but critical observations are yet wanting."

Results of a Comparison of the Lunar Tables of Burckhardt
and Hansen, with recent Meridional and Extra-Meridional
Observations of the Moon, made at the Royal Observatory,
Greenwich; with accompanying Remarks by the Astronomer
Royal.

"In the last autumn a correspondence took place between Mr. Hind, Superintendent of the Nautical Almanac, and myself, on the subject of comparing Professor Hansen's new lunar tables with the observations of the moon made at the Greenwich Observatory. Mr. Hind entered most warmly into the matter; and, with a zeal for which astronomers cannot be too grateful, at once undertook to superintend, in the Nautical Almanac Office, the laborious operations for computing the moon's place from Hansen's tables, provided the funds for supporting the necessary expenses should be supplied by the Government. The Lords Commissioners of the Admiralty without hesitation granted the necessary sums, and the calculations were soon commenced on the scheme which had been arranged.

"In explanation of the plan of comparison, it is to be remarked that the Greenwich observations of the moon consist of two series, one made with the meridional transit-circle, and the other made with the extra-meridional altazimuth. The meridional observations are, nearly without exception, confined to those parts of the moon's orbit in which her transit takes place between 6 and 18h mean solar time. The extra-meridional observations extend over almost all parts of the orbit, but the mean solar hour of the actual observation with the altazimuth is usually between 6h and 18h, and though, from the nature of the observations (which are not made simultaneously on the two elements) it is not possible, as in the meridional results, to state precisely the hour and minute to which the inferred tabular errors apply, yet the hour can be very nearly stated, and that hour will not be very far distant from midnight.

"The Greenwich observations exhibit the apparent errors of the places of the Nautical Almanac (Burckhardt's) as compared with every day's observations of the moon. These apparent errors are corrected (so far as applies to the present purpose) for the faults of the Nautical Almanac parallax (Burckhardt's) in a table at the end of the introduction to the Greenwich Observations, 1856. As great pains have been taken to use a correct value also of the semi-diameter, the final results of that table may be received as exhibiting, with the utmost accuracy, the errors of Burckhardt's longitude and latitude deduced from observations made on the moon with two first-class instruments, at

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