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until the mass and orbit of this planet have been determined with accuracy. Mr. Sears C. Walker, of Washington, is actively engaged in computing the orbit of Neptune, and has sent an account of his results in a letter, from which the following is an extract.
“Washington, D. C., May 3d, 1847. “ After computing my Elements IV. of the planet Neptune, I compared with an ephemeris derived from them one hundred and thirteen American and three hundred and sixty-six European observations, being the entire series extant to this date.
“From this collection of observations I have derived thirteen nor. mal places, which gave me thirteen conditional equations for correct. ing Elements IV., which were a slight modification of Elements II. of my former letter.
" In computing the conditional equations I used the method sketched out in my former letter. As this application of the method of me. chanical quadratures to the formation of conditional equations for cor. recting an approximate orbit is new, I will give a brief statement of it. The conditional equation is,
0 = ax +by+cz + du tev + &c. + n. Where
a= (t — 1946 years, 340 days).
Numerical term ...n=
= (computed – observed) true orbital longitude. Also, no = the assumed true daily sidereal angular motion for a=0.
wi= the assumed true orbital longitude for a = 0.
ro = the assumed radius vector . . . for a = 0. x, y, and z = Ano, 4o, and aro= the required corrections for a=0.
w'(a) = value of w, from normal place, for date t, using r=ro.
for date t.
K’= (ro + z)” (no + x) = Neptune's daily area. n(a) = K’ (r(a))-: = value of n for date t for conserva
tion of areas. A“, B(), &c. = the part of the coefficients of u, v, introduced by the
quadratures. “These coefficients were computed from Laplace's formula (Mec. Cel., Vol. V.), viz. : Jamondt=+in(0) + ( + n(?) + &c. tnia-1 + 4 min)
- the lonia-1) — anos)
- &c. “The solution of the thirteen equations of condition by least squares gave for Elements V.,Longitude of the Perihelion, n= 1° 45' 32".90 m. eq. Jan. 1, 1841. Ascending Node, . . . 8= 129° 51' 134.53 Inclination, . . . . .i 1° 45' 38".10 Eccentricity, .... e=0.00505292 Mean distance, ... a= 30.145119 Epoch, Jan. 1st, 1847, · M= 326° 2' 1".34 ..... for mean noon at Mean daily sidereal motion, u = 21".437843
[Greenwich. Period in tropical years, T= 165.51330.
“ The ephemeris from Elements V. in order to agree with the thirteen normal places requires the following corrections of the geocentric longitude and latitude.
“ I do not recollect a closer agreement of an orbit with actual observation. Accordingly I regard Elements V. as the present disturbed elements of Neptune.
“You will notice that the values of e and a came out nearly the same as those of Elements III., required by the hypothesis of identity of the planet and missing star of the Histoire Céleste, May 10th, 1795. The node and inclination are so connected together at present that (very nearly) ten times the increase of the latter applied to the former leaves the geocentric place unchanged.
“Let us make the hypothetical Elements VI. by applying to (V.) the corrections 18=+85.50, and Ai=+84".8, and let us suppose that the term ; 38 (nt) has increased 0".03422 in the last fifty-two years; then Elements VI. will represent the last nine months' observations, and place the star and planet together May 10th, 1795.
“I am engaged in computing the constant coefficients for the pertur. bations of Neptune on your hypothesis of (2 n VI. — n ".) = 0, or in other words of the applicability of the Laplacian libration first pointed out by yourself. As far as I am at present informed, the near approach of this expression to 0 was first noticed by ourselves, on the occasion of your visit to Washington, on the 25th of February last.
“A glance at the configurations of the planets for the last two or three years would serve to indicate that while Saturn and Uranus are still increasing the term į so (n t), Jupiter has produced a tide (if I may use the phrase) which has not yet subsided, and which, added to the action of the other two, may have increased the disturbed daily motion 0".32 above the pure elliptic value. In this case, your period is established.
“Both hypotheses, that of the identity of the star and planet, and of the libration of Neptune's year round the double of that of Uranus, are now rendered so probable by conclusions from direct observations, that nothing but a rigorous computation of the perturbations of Neptune can throw any farther light on the subject at present. I shall look with anxiety for the publication of your researches on this subject. “Yours truly,
“Sears C. WALKER.” After reading this letter, Professor Peirce remarked that Mr. Walker's discovery of the identity of Neptune and the star of Lalande was indisputably confirmed by an examination which Mr. Mauvais of the Paris Observatory had made into the orig
inal manuscripts of Lalande, at the request of Leverrier. He had found that the doubtful marks of the printed copy were not contained in the original record; and that there was an observation of the planet of May 8, 1795, which was not published. More than fifty years ago, then, Lalande had in his possession observations enough of Neptune to have discovered it; and he could not have failed to make this discovery if he had taken reasonable pains to satisfy himself as to the discrepant character of the observations by a new comparison with the stars.
Professor Peirce stated that he had compared the observation of May 8, 1795, with Mr. Walker's orbit, and found it to be perfectly consistent with the slight changes which are required to satisfy the observation of May 10, 1795. Mr. Walker's orbit cannot, therefore, differ much from the exact orbit, and there can be no important error in adopting it as the basis of further research. The period is very near the double period of Uranus, but yet it seems to differ too much from this double period to admit of the establishment of a libration about that period. The principal effect of Neptune upon Uranus must, in case of the failure of this double period, be exhibited in the manifestation of an equation of the centre different from that which belongs to the proper elliptic motion, so that Uranus will have two equations of the centre, one of which will belong to its ellipse, and the other to the attraction of Neptune.
James D. Dana, Esq., Corresponding Member of the Academy, presented (through the Corresponding Secretary) a paper comprising brief characters of the Crustaceæ collected in the United States Exploring Expedition under Captain Wilkes, as follows:
Conspectus Crustaceorum, in orbis terrarum circumnavigatione, C.
Wilkes e classe Reipublicæ Fæderatæ duce, collectorum auctore J. D. Dana.*
* Conspectus narrationis uberioris auctore auctoritate publicà edendæ.
Pars I. — CRUSTACEA COPEPODA (CYCLOPACEA*).
Familia I. CYCLOPIDÆ. Oculi duo simplices tantum. Palpi mandibulorum maxillarumque
breves aut obsoleti. Sacculi ovigeri duo.
Genus I. CYCLOPS. Antennæ maris anticæ subcheliformes aut articulo geniculante instructæ.
1. Cyclops BRASILIENSIS. — C. cephalo-thorace posticè obtuso, abdominem longitudine superante; antennis anticis in utroque sexu elongatis (cephalo-thorace longioribus), articulis primo secundoque majoribus et setis oblongis apice instructis, setis antennarum aliis brevibus ; anntennis maris 7-articulatis, articulis tribus basalibus crassissimis, reliquis teretibus, feminæ, 14-articulatis, teretibus ; stylis caudalibus
* Cyclopaceorum organa sunt:
Cephalo-thorar 4-7-articulatus. Abdomen 1 - 6-articulatum, carapace non tectum.
Frons sæpissimè rostrata, rostro aut simplice, aut furcato, aut transversim emarginato, aut appendicibus instructo.
Oculi duo simplices, pigmento aut connati aut disjuncti; quoque quibusdam, oculi duo coaliti sub capite insistentes ; aliis, oculi lenticulis duobus grandibus, uno oblato, uno prolato, constructi.
Antenna anticæ 4-28-articulatæ, aut simplices, aut appendiculatæ ; postica, 2-5-articulatæ et sæpe ramum ferentes, aliis apice setigere, aliis subcheliformes.
Mandibulæ apice dentatæ, sæpius palpigeræ.
Marillæ duæ setose ; sæpe palpigeræ, palpo sive parvulo et vix discernendo, sive setas diffusas ferente.
Mazillipedes duo, aliis parvi et parcius setigeri, aliis crassiores et valde setigeri, setis spinulosis.
Pedes antici duo simplices, aut obsolescentes, aut elongati, aliis setigeri setis non spinulosis, aliis subcheliformes.
Pedes biremes decem; octo anteriores sæpius natatorii, sed duo antici interdum subprehensiles ; duo posteriores plurimum obsoleti aut parvuli; in quibusdam masculinis pergrandes et uno ainbove prehensiles.
Abdomini pertinentes ad basin sæpissimè pedes spurii, sive obsolescentes, sive oblongi et setis armati; ad extremum, styli caudales duo, unusquisque 4-6 setis plerumque plumosis instructus.
Ad segmentum cephalo-thoracis septem-articulati primum, antennæ quatuor pertinent; ad secundum, mandibula, maxillæ, et maxillipedes; ad tertium, pedes quatuor antici; (cephalo-thorace quadri-articulato, hæc tota ad segmentum anticum pertinent ;) ad segmenta sequentia, singulatim, duo pedes biremes.