The daily union. [volume] (Washington [D.C.]) 1845-1857, 1846-11-07
ASTRONOMY.
M. r. MAURY,


On , planet oheh produces the irregularities Observed
IN lhs m0pemini Of Uranus Determinations Of Us
mass, orbit and is actual position, BY NJ u j. lie
Vfrtier.
had the honor at the meeting Of the FIRST Of June
last, 20 communicate to the Academy, the principal
results Of on investigation, which had undertaken
the theory OF Uranus. bad proved that 1t was
not possible 10 represent the observations OF this
planet by the aystem Of universal gravliauOn, in
suppUsing that il exposed only 10 the united
actions Of the SUM- and known planets. On the con-
trary, all the observed irregularities explain them
selves n their mnutest details, by the influence OF
new planet, which w0uld be situated beyond IRA.
nus, aud which would pass through Discriminate
orbit. In this FIRST undertaking, could with
precision pronounce on several points, and par
iieusdy the actual position Of the new planet 10
which had assigned 325 degrees Of heliocentric
longitude on the first Of January, le47 The other
elements, particularly the mass, the knowledge OF
which would have afforded much interest as regards
the Visibility, and the time Of the periodical reyou-
ton, were let as TOO uncertain. have announced
that would employ myself in removing these i'm
peections and that with the view Of actual search
for the planet, would end ayor 10 attain this end
soon as possible. But have met with great DIFF
fculues, and the dine which have needed TO sur
mount them, has brought 10 the moment Of the
opposition Of the planet, which is just about TO oc-
cur Happily The researches which astronomers,
with powerful telescopes, will make TO discover the
three months, and have been assured that this
tune shall he well employed ....
Whilst was entirely in the dark ms TO what part
Of the zodiac should look for this planet, and
as had, IN consequence, to extend my researches
To all The regions OF the echptic was obliged mot
TO render the discussions Unfortunately to confine
myself certain number Of well chosen obserya-
uons OF Uranus. In my present work, Ito give
more precision TO my results,) | make use
of all the ancient observations Of Uranus, to
the number Of nineteen, taken by Flam-
sized, Bradley, Mayer, and -Lemonnier; and
employ the large number Of two hundred and six
ty-two observations, suitably chosen from among
those takenb at Paris and Greenwich, from the
year 1871 until l545; both those taken in oppos-
ton and in the quaratures. Each longitude deduced
from the observations, compared with the longitude
given at the time by theory, furnishes an
equation &c condition between the corrections of
the elements Of the orbit Of Uranus, between the
mass, and the elements Of the orbit Of the disturbing
planet. These equations thus contain nine I'M
known quantities, and il is necessary that should
enter into some details to explain the manner IN
which these variables there combined. The
corrections of the clements of the orbit of Uranus
appear in linear fam, and can therefore occasion
no difficulty. ei ~. a4..a. I'd.
Let US consider among the elements of the sup
posed planet its mass its eccentricity and the lon
gtude Of its perhelien; and let substitute for
these three vuriabes the three following: LIST, the
mass; ID, the product of the mass by the eccen-
trcity, and by the sine Of the longitude of the per-
iheion; Sd, the product of the mass by the eccen-
tricity, and by the cosine of the Longitude of the
perhelion The equations will be of the first de-
gree in respect to these new variables, it have
regard only the secular inequalities, TO the peri
odca inequalities independent Of the eccontricities,
and to the periodical inequalities dependent on the
first power of the eccentricities. This advantage
would be lost II 1t were necessary to take account OF
the inequalities of the second order; and if it be per-
milted 20 neglect them in first approximation, it
becomes impossible in precise work 10 omit the
inequalities ola second order, on which depends
the argument Of the mean longitude Of Uranus, di-
unfinished by three times the longitude of the
supposed planet. | have avoided the difficulties
which would have arisen from the introduction Of
this inequality in the ordinary formula, by ari-
fee founded the length Of the period; that the
equations of condition have been defntively of the
first degree in respect to the mass and the other
two yariables, which the eccentrclties and the
longitude of the perhelion depend.
The coefcients Of these three forces are the funo
tons Of the semi-najor axis Of the disturbing
planets orbit and of the longitude Of the epoch Of
this planet but these functions IN their most gen
era form, very complicated that it would
be impossible to discuss them at this moment; and
while the mass, the eccentrcities, and the periheon
longitude may be deduced directly from the equa-
tons, the mean longitude and semi-axis maj re-
quire a recourse to successive approximations.
Guided by peculiar considerations and by several
experiments, i admitted in my first solution, that
the major axis of the orbit of the planet in question
was double the major axis of the orbit Of Uranus.
have since proved that with this hypothesis, and
by suitable determination Of the other elements,
we could satisfy the equations of the problem. This
was an inverse solution.
In the work itself the most exact value of the
major axis is (ike that Of the other elements) de-
duced directly from equations, and the case, is the
same with regard to the limits within which it may
be varied, without ceaslng to represent the obser-
vations of Uranus.
have said that the functions of the major axis
and CT the longitude of the epoch which enter into
the equations Of condition. being complicated, il
was necessary in respect to these two varables to
have recourse to successive approximations. My
preceding researches had acquainted me with the
fact, that the fraction $50 might be taken for APP
proximate value of the ratio Of the major axis Of
Uranus to that Of the disturbing planet subsequent
experiments satisfied me that the friction @ 81 would
be still more exact As to the mean longitude, ac-
cording to the same researches, il must have been
equal 10 nearly 352 degrees. BY means Of these
data, 1 had so arranged it that tho coefficents
which functions of the major axis of the orbit
and Of the longitude of the epoch should not include
any other varables, but the corrections necessary
to the approximate values which we have just given
70 these elements. Also, these corrections small
enough to allow us to develop according 70 their
powers and their products, the functions that con
tain Them and TO conhne ourselves to the terms OF the
first and second order in the limits in which are IN
cluded the variables. We see, then, regards the
form Of the equations that they are Of the first de
gree in respect to the corrections Of the elements Of
the orbit Of Umnusj that they are also ofthe FIRST de-
gree in respect TO the three elements which give the
mass the eccentricy, and the longitude ofhe perhe-
lion ofth supposed planets lastly, that the coecen,s
Of these three vsrables functions OF the second
order IN respect to the corrections Of the two other
elements. pass to the resolution Of the equations
after remarkng that, If two Of the clements have
Obliged me to have recourse to the method Of sue
cessve approximations, rs in my former researches
we cannot possess more simple means of deter.
mining the orbits Of planets than by direct obser.
walton Of these bodies.
II is not necessary to treat separately Of each Of
the equations thus formed. The SLOW movement d
both Uranus and the disturbing planet permits us d
unite several Of them in manner to form mear
equations, Of which the constants will probably u
the more exact, since they result from the employ
ment Of a greater number Of observations. The
equations Of distinct condition, which have used
have been formed IN the following manner
First equation-0ne observation made by Flan1
= anI ~