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path, and if missing now in the heavens may have been the planet. This comparison was made by Mr. Walker on the 2d of February, a cloudy night. He immediately, by letter of that date, notified the Superintendent of the Observatory, Lieutenant Maury, of his expectation that on examination of that region on the next clear night No. 8 would be missing.

“On the 4th of February, Professor Hubbard examined the region and verified the expectation of Mr. Walker. The star was in fact missing. Here, then, was a presumption in favor of their identity. Mr. Walker believed his limits sufficiently extensive to comprise the Neptunian region of May 8th and 10th, 1795. The planet was of the size 7, 8 magnitude, seldom omitted by Lalande. No star except No. 8 fulfilled all the conditions. There is, however, a (:) placed by Lalande after the observation of the star No. 8, which indicates that the declination is doubtful £ 5. Mr. Walker's attention was first called to this circumstance by Professor Peirce.

The entries in the Histoire Céleste are as follows:

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Wire II.

Zen. Dis.

Mid. Wire. h. m. 8.

h.

m.

8.

Mag. Wire I.
7,8
14 11 23.5

6Ô 16 : (now missing.)
2 - 6
14 12 3.4

59 33 59 8

14 11 50.5 : 59 54 40 If then the two (:) only indicate a doubt of 5', there is no contradiction of the possible identity of the star 7,8 mag. and the planet. If, however, the two (:) may be so construed as to make the 1st and 3d star the same in declination as they are in right ascension, then no star is missing, and the heavens are now as in Lalande's time. The difference of magnitudes 7,8 and 8 militates against this supposition, that stars 1 and 3 are the same.

“Mr. Walker concludes by remarking, that he has stated all the circumstances known to him favorable or unfavorable to the supposition of identity of the star and planet. The decision of the question must be the work of time. In order to establish the priority in determining these elements, if the identity should be confirmed, he had computed his Elements III. upon this hypothesis of identity. The three sets of elements are here given, referred to the mean equinox of January 1st, 1847, and to mean time Greenwich."

.

Elements if the mis. sing star was Neptune.

I.

Elements of Neptune. Circular Hypothesis Elliptic Hypothesis Elliptic Hypothesis

II.

III. Longitude of perihelion,

unknown unknown 00 12' 25.51 “ ascend. node, 2 1290 48' 23".16 1290 48' 234.16131° 17' 357.80 Inclination,

i 1° 45' 19'.88 10 45' 19".88 10 54' 53.83 Long. of epoch, Jan. 1, 1847, 4 unknown unknown 328° 7' 56''.64 True heliocentric long.

on orbit, Sept. 28, 1617{ 326° 59' 41".50 3260 59' 34".743260 59'34".74 Eccentricity,

0.

unknown 0.0088407 Radius vector, Sept. 28, 1847, 7 29.93995 30.00506 30.02596 True sid. orb. mot.,

21".65857 21".65789 21".64553 Mean distance,

29.93995 30.200585 30.25042 Mean daily sidereal motion, 21":65857 21".37881 21".32600 Period in tropical years,

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7 1634.8259 1654.97030 166.381:34

Professor Peirce remarked, that the orbits given by Mr. Walker differ so widely from the predictions, that he has been induced to make a careful reëxamination of the observations. He has not only himself verified Mr. Walker's distance of 30, and the consequent angular motion; but Mr. George P. Bond, of the Cambridge Observatory, has also, at his request, verified this distance and motion from the Cambridge observations alone. From these data, without any hypothesis in regard to the character of the orbit, he has arrived at the conclusion, that THE PLANET NEPTUNE IS NOT THE PLANET TO WHICH GEOMETRICAL ANALYSIS HAD DIRECTED THE TELESCOPE ; that its orbit is not contained within the limits of space which have been explored by geometers searching for the source of the disturbances of Uranus; and that its discovery by Galle must be regarded as a happy accident.

“Mr. Adams, in his Explanation of the Observed Irregularities of Uranus, considered two hypothetical orbits, in one of which the mean distance is 38.4, or just double that of Uranus, and in the other it is 37.6; while M. Le Verrier, in bis Researches into the Motions of the Planet Herschel, called Uranus, after deriving some rough approximations from the consideration of the mean distance 38.4, proceeds to the accurate examination of the three distances 39.1, 37.6, and 36.2.

The extension of the investigations to any other mean distances can be made only by assuming a continuous law to pervade the subject of inquiry, and that there is no important change in the character of the resulting perturbations. Guided by this principle, well established, and legitimate, if confined within proper limits, M. Le Verrier narrowed with consummate skill the field of research, and arrived at two fun. damental propositions, namely,

1st. That the mean distance of the planet cannot be less than 35, or more than 37.9. The corresponding limits of the time of sidereal revolution are about 207 and 233 years.

2d. “That there is only one region in which the disturbing planet can be placed, in order to account for the motions of Uranus ; that the mean longitude of this planet must have been, on January 1st, 1800, between 243" and 2520.”

“Neither of these propositions is of itself necessarily opposed to the observations which have been made upon Neptune, but the two combined are decidedly inconsistent with observation. It is impossible to find an orbit, which, satisfying the observed distance and motion, is subject at the same time to both of these propositions, or even approximately subject to them. If, for instance, a mean longitude and time of revolution are adopted according with the first, the corresponding mean longitude in 1800 must have been at least 400 distant from the limits of the second proposition. And again, if the planet is assumed to have had in 1800 a mean longitude near the limits of the second proposition, the corresponding time of revolution with which its motions satisfy the present observations cannot exceed 170 years, and must therefore be about 40 years less than the limits of the first proposition. Neptune cannot, then, be the planet of M. Le Verrier's theory, and cannot account for the observed perturbations of Uranus under the form of the inequalities involved in his analysis.

" It is not, however, a necessary conclusion that Neptune will not account for the perturbations of Uranus, for its probable mean distance of about 30 is so much less than the limits of the previous researches, that no inference from them can be safely extended to it. An important change, indeed, in the character of the perturbations takes place near the distance 35.3; so that the continuous law by which such inferences are justified is abruptly broken at this point, and it was hence an oversight in M. Le Verrier to extend his inner limit to the distance 35. A planet at the distance 35.3 would revolve about the

Sun in 210 years, which is exactly two and a half times the period of the revolution of Uranus. Now, if the times of revolution of two planets were exactly as 2 to 5, the effects of their mutual influence would be peculiar and complicated, and even a near approach to this ratio gives rise to those remarkable irregularities of motion which are exhibited in Jupiter and Saturn, and which greatly perplexed geometers until they were traced to their origin by Laplace. This distance of 35.3, then, is a complete barrier to any logical deduction, and the investigations with regard to the outer space cannot be extended to the interior.

" The observed distance 30, which is probably not very far from the mean distance, belongs to a region which is even more interesting in reference to Uranus than that of 35.3. The time of revolution which corresponds to the mean distance 30.4 is 168 years, being exactly double the year of Uranus, and the influence of a mass revolving in this time would give rise to very singular and marked irregularities in the motions of this planet. The effect of a near approach to this ratio in the mean motions is partially developed by Laplace, in his theory of the motions of the three inner satellites of Jupiter. The whole perturbation arising from this source may be divided into two portions or inequalities, one of which, having the same period with the time of revolution of the inner planet, is masked to a great extent behind the ordinary elliptic motions, while the other has a very long period, and is exhibited for a great length of time under the form of a uniform increase or diminution of the mean motion of the disturbed planet. But it is highly probable that the case of Neptune and Uranus is not merely that of a near approach to the ratio of 2 to 1 in their times of rev olution, but that this ratio is exactly preserved by those planets ; for it may be shown, as was shown by Laplace for the ratio two fifths, that a sufficiently near approach to it must, on account of the mutual action of the planets, result in the permanent establishment of this remarkable ratio. Thus, if

v=the mean longitude of Uranus,

v' = that of Neptune, V = 20' — v; and if D expresses the differential coefficient relatively to the time, a near approach to the ratio of 2 to 1 gives the equations,

Dév =p sin. (2 v'—0+ A)=p sin. (V+A),
D'o' =q sin. (2 v'—0+A)=q sin. (V + A);

in which p, q, and A are known functions of the masses and different elements of the orbits. These equations give at once

D'V=2 D'v' - Dy=(29-p) sin. (V+A), which, multiplied by 2 D V and integrated, becomes

DV=V (H’— (4q-2p) cos. (V+A)], in which

H=2 n' -n; if

n = the mean motion of Uranus,
and n'=that of Neptune.
It follows from the value of DV, that if

H’ < 49—2p,
V+ A cannot increase indefinitely, and that, therefore, the term

(2 n - nt, upon which its indefinite increase depends, must vanish, or in other words

2 n' - n=0, and V + A must oscillate in value either about zero when

2p-49 is positive, or about 1800 when 2p-49 is negative. The probability of the occurrence of this ratio depends, it will be seen, upon the magnitudes of p and q, which are always of opposite signs. It is evident, from inspecting the computations of Mr. Walker, that Neptune's period of revolution is not less than in his second hypothesis of 166 years ; and Professor Peirce infers from the investigations which he has already made, that a period of 166 years, which involves only a slight additional eccentricity, is already a sufficiently near approximation to establish the exact permanency of the period of 168 years. As soon, then, as there may be observations sufficient to prove that Neptune revolves in more than 166), and in less than 1694 years, the conclusion is inevitable, that its year is precisely twice as long as that of Uranus."

Professor Peirce communicated, from Mr. Bond, of the Cambridge Observatory, the following

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