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Three Hundred and second Meeting.

January 4, 1848. — MONTHLY MEETING.

The PRESIDENT in the chair.

Mr. Everett read a letter from M. Leverrier, acknowledging his election as a Corresponding Member of the Academy.

Mr. Everett also submitted to the Academy a paper received from M. Leverrier, containing a succinct abstract of the first of two memoirs lately read by him to the Academy of Sciences at Paris, on the subject of periodical comets. It was the intention of M. Leverrier that this communication should reach the Academy in advance of the publication of the Compte Rendu for the 25th of October, in which the abstract of the first memoir appears in extenso. Owing to the great length of the passage of the vessel by which M. Leverrier's communication was transmitted, this expectation was disappointed. As the Compte Rendu, however, of course possesses but a limited circulation in this country, a translation of this interesting paper was read by Mr. Everett to the Academy.

After alluding to the stability of the orbits of the planets, caused by their moderate eccentricity, small inclination, and the great preponderance of the central force, M. Leverrier ob

serves, that

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" It is not so with respect to the comets. Those of them, which move in planes but little inclined to the ecliptic, cut very near the orbits of one or more of the planets. It may accordingly happen, that they will pass in the neighbourhood of the planets themselves, and that the disturbing force, thus rendered preponderant, may turn them from their course. Thus the comet, which, left to itself, would have continued to move in a parabola, may by the action of Jupiter be brought for ever, or only for a limited period, into an ellipse of moderate extent. The same cause which shall have compelled the comet to describe this ellipse may be able hereafter again to control its movement, and to force it for ever from our planetary system, by throwing it into a hyperbolic curve."

M. Leverrier then adverts to the discovery of a comet by Messier in 1770, which was afterwards known as Lexell's, in consequence of its being discovered by that astronomer to move in an elliptical orbit of five years and a half period. To the objection made against this theory, that it had not before been seen, Lexell replied, that it might be a new comet, drawn into an elliptical orbit by the action of Jupiter, and that it would approach that planet again in 1779, which might then, perhaps, throw it off from our system, to return no more. In point of fact, astronomers have looked in vain for the return of Lexell's comet !

In the month of November, 1843, M. Faye saw a comet, whose observed movement could not be reduced to a parabolic curve. Dr. Goldschmidt discovered that it described an ellipse of a period of seven years and a half. The objection to this theory, that it ought to have been seen before, was answered, as in the case of Lexell's comet, by reference to the action of Jupiter.

As the region of the heavens where this approach to Jupiter took place was nearly the same for both comets, M. Leverrier was led to admit the possibility, that the comets of 1770 and 1843 might be the same, although their orbits were altogether different.

In 1844, M. de Vico, at Rome, discovered a comet, which was shown by M. Faye to move in an orbit of five years

and a half. The possibility that this was Lexell's comet of course conflicted with M. Leverrier's first impressions, just mentioned, but increased the probability that Lexell's comet might be recovered in one or the other of the recent discoveries.

“ The only difficulty," says M. Leverrier," was, that the calculations became immensely laborious, and I was obliged to devote to them several years, including the last (1846). Although my researches are brought to a close, however great my desire to submit them to the Academy, the necessity of passing some days in collecting the documents relative to the comet of De Vico will oblige me to confine my. self at present to that of M. Faye.”

The elements of the comet of 1770, being different from those of the comets of 1843 and 1844, M. Leverrier first undertook to follow the former into the neighbourhood of Jupiter and the other regions which it would have traversed up to the years 1843 and 1844, and to ascertain, in this way, if the comet of 1770 might not place itself upon the orbits of one or the other of those discovered by M. Faye or M. Vico.

On approaching the subject more nearly, M. Leverrier found that the calculations of Laplace, in the Mécanique Céleste, as to the direction given by Jupiter to the comet of 1770, could not be depended on. Slight changes in the elements of the orbit give routes so different to the aphelion, that it remains uncertain whether it passed within or beyond the orbit of Jupiter, through the system of the satellites or outside of them. M. Leverrier was accordingly obliged to commence by studying the movement of the comet of 1770, leaving to it all the latitude which resulted from the observations made at the time. In pursuing this course,

“I established,” says M. Leverrier, “ the following points :

"1. That it was impossible that the comet should have been arrested within the system of Jupiter, without falling into the planet itself; an event very improbable, it is true, without being absolutely inadmissible.

“2. I showed that Jupiter might have forced the comet to pass off in an hyperbola round the sun. In this case, we could not expect to see it again, as it would continually move on to a greater distance from our system, to enter into other spheres of attraction.

“3. It is possible that the comet, after having escaped the action of Jupiter, might have pursued its course in ellipses of very long period. But it is much more probable that it continued to move in ellipses whose moderate period must permit us often to witness its return. I have formed a complete table of all the possible ellipses, which will serve henceforth as the basis of our further inquiries.”

The first inquiry will, then, be, whether the elements of the new comet (that of Faye), as calculated from the observations, present themselves among the systems of this table. If so, the problem is solved.

Should this not be the case, it will be necessary to inquire if the new comet may not have experienced perturbations since 1779, which would account for the present want of coincidence in the elements with those of Lexell's comet in the table. If no such considerable deviation from a regular course can be admitted as probable, the hypothesis of identity with the comet of 1770 must be given up.

But if the new comet has experienced considerable perturbations since 1779, these must be calculated before we can pronounce against the suspected identity. As the observations made at one appearance cannot be depended upon as a sufficient foundation for fixing its position for a period of more than sixty years, it became necessary to pursue the same course, in reference to the new comet, which had been followed in regard to Lexell's, and “ to determine all the positions which it could have occupied in 1779, and the elements of all the orbits in which it could have moved conformably with the recent observations.”

The great complexity and difficulty of the problem undertaken by M. Leverrier are now apparent.

He proceeds to solve it by examining the positions and elements of the comet of Faye, in the reverse order of time, during several successive periods, viz. : 1. from 1843 to 1839; 2. from 1839 to 1819; 3. from 1819 to 1814; 4. from 1814 to 1797; 5. from 1797 to 1792.

The paper of M. Leverrier, as transmitted to the American Academy, being itself an abstract of the memoir read to the Academy of Sciences at Paris, hardly admits, in this portion of it, a further condensation, which could not be made without impairing the clearness of the discussion. At the close of the examination of these successive periods, M. Leverrier arrives at the definite conclusion, that the periodical comets of Faye and Lexell are two different bodies."

In concluding the memoir, M. Leverrier briefly considers the question, At what time did the action of Jupiter give to the comet its present orbit? Or rather, What is the least remote time at which this phenomenon may have taken place? He establishes this least remote period at the year 1747. It is possible that the comet in question may have received, on its approach to Jupiter in that year, the impulse which placed it in its present orbit, and that it was consequently discovered by M. Faye on its thirteenth return.

Professor Peirce read some correspondence between Dr. Gerling of Marburg and Lieutenant Gillis, communicated by the latter, and offered the following resolutions, which were adopted.

Resolved, That, in the opinion of this Academy, the enterprise for determining the solar parallax, in the method proposed in the correspondence between Lieutenant Gillis and Dr. Gerling, is worthy to be promoted by the government of the United States, by sending an expedition to Chiloë, both on account of the great uncertainty which attends the adopted value of this fundamental basis of astronomical measurement, and the probability that this attempt will prove successful, and thus redound to the honor of the country by which it is undertaken.

Resolved, That a copy of the above resolution be transmitted by the Corresponding Secretary to Lieutenant Gillis, with a request that he will communicate it to the public authorities who may have this subject under consideration."

Professor Peirce also reported some of Mr. George P. Bond's observations upon the nebula in Andromeda.

Mr. Paine stated the results of his meteorological observations upon the present extraordinarily mild winter.

Three hundred and fourth Meeting.

January 26, 1848. — QUARTERLY MEETING. The PRESIDENT in the chair.

The Corresponding Secretary read letters of acceptance from the Hon. Abbott Lawrence and Professor Edward H. Courtenay, who were chosen Fellows at the last quarterly meeting.

Mr. Everett read a communication from Professor Nichol, directing attention to certain deficiencies in the meteorological records as printed in the Academy's Memoirs; whereupon,

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