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

4 Second equation--Four observations made IN
i I7l2 and Ills, by Flamsteed.
4 Third equation-Two observations made IN 1850
II by Lemonnier.
Fourth equation--Two observations made in
Il 1883 and 1856, by Bradley and Mayer
4 Fifth equation-one observation made IN lIo4,
by Lemonnier.
Sixth equaton--Eight observations made In l7oo
and 1863, by Lemonnler
II by LemonnleT. -
And lastly, the observations taken in 1881, until
the year l845 being suitably combined have inr-
nished me with twenty six equations, which, united
to ths preceding have carried the number OF denni-
tive equations 10 thirty -three.
After several Intellectual attempts 10 oouln rom
the preceding equations, not only the most pro6a-
BILE value of the unknown quantities which they
contain but also the linfhs within which these UNI
known quantities must be comprised, so that the
theory might represent the obsersatlons was leu
10 the conclusion that il indispensable, as IN my
first solution, 10 commence by eliminating six OF the
unknown quantities, which the equations furnish
very clearly 10 functions Of three Othersj namely,
the four unknown quantities on which depend the
orbit Of Uranus, and the two unknown quantities
which determine the ecceDtrieity and periheion OF
the disturbing planet, when It's mass Is known Inc
three other yarables, the mass, the corrections OF
the major axis and of the longitude OF the epoeh Of
the supposed planet, must be reserved Tor suose-
quent discussion. .a.
| have employed Tor the nrst elimination OF tne
six unknown quantities the method Of least squares.
| have done this, acknowledge, with great regret
for the circumstance that three Of the coecents
functions of the second order in respect TO two vara
bles, renders the Of this method excessively to
dious and troublesome. did not decide to have
| recourse TO IL, until was convinced that no more
simple plan could give me satisfactory result. |
have naturally taken into account the number Of
| observations on which is based each Of the equs-
tons and also the relative correctness OF these OBJ
| seryauons. ....-
| The value Of the six unknown quantities thus
determined in functions OF the others, contain the
required mass in the first degree. Con6ning myself
10 the terms Of the second order, ! have developed
the functions Of the corrections Of the major axis
/ and Of the longitude of the epoch which they in
cUde, in respect TO the powers OF these variabes
Lasly substituting the results thus obtained IN the
first members OF the equation OF condition, and pre-
serving always the same degree Of approximation
have formed the expressions OF the mean errors
Of the theory, IN respect TO the observations IN func
TONS Of the mass and Of the corrections Of the major
axis, and Of the longitude of the epoch. These ex-
pressons are Indispensable 10 FIX the limits within
which must be comprised each Of the elements in
the first place, let determine the precise orbit to
which they should lead. ..
These are the elements at which | have arrived
the ongitudes are reckoned from the equinox OF
the LIST of January l547 the distances referred
to the distance Of the earth from the sun; and
lastly, the mass of the has been taken as unity
Semi-axis major OF the orbit 36 l54
Duration of the sideral revolution 2l7 3s7 years.
Eccentricty O.lO76l
Longitude Of perihslon 2S4o As
Mean longitude on LIST January
I947 3l8.47
MI
''''' $500
In can be seen that in supposing, in my first
work that the male axis of the orbit Of the planet
in question double that of the orbit of Uranus,
had made an hypothesis very near the truth.
We deduce from the preceding elements the fol-
lowing position Of the planet on the LIST January,
I547:
True helioccntric Longitude 1860. 3g
Distance from the sun 1906
This true longitude differs but little from 325 de-
grees a value that resulted from my first researches
The actual determination is founded data more
ample and precise. They place the new star
nearly 30 degrees east of the star Dela) Capricorn
The opposition Of the planet took place the
10Th of last August We thus are actually at
a moment very favorable for its discovery. The
advantage which results from its great angu-
lar distance from the sun, will 20 constantly
and rapidly diminishing; nevertheless, as the length
Of the day in climate decreases very rapidly we
shall be for long time in very favorable position
for the search which will be undertaken. The ma
ture and success Of this search will depend on the
degree OF the stars brightness. Let stop for a
moment at this question. Let us examine what are
actually at the moment Of the opposition the appa-
diameter, and the relative brightness of the new
planet
Ii is known that at a distance equal TO nineteen
times the distance ofthe earth from the SUM- the disc
of Uranus appears under an angle of A.. The mass
of this planet is known. Ii is about twice and a
half smaller than that Of the new planet. These
data, joined to the preceding, would suffice to calcu-
late the apparent diameter of the new star, if we
knew the ratio offs density to that of Uranus. In
general, the density of planets diminis, proper
ton they more distant from the sun. We
would make, then, as respects the diameter, an UNI
favorable Hypothesis as 10 the visibility Of the sup
posed STAR in admitting that its density is equal to
Uranus We shall find that, at the moment of the
opposition, the new planet oughtto be perceived I'M
der an angle of ga This diameter is quite suffi-
cient for good telescopes to distinguish it from the
spurious diameters ofsars) produced by various ab
erraons provided the brightness of the disc be suf.
hcient.
In supposng the rejecting power of the surface of
the planet to be the same with that of the surface
Of Uranus, its actual specific brightness will be
nearly one-third the specific brightness possessed
by Uranus at its mean distance from the sun.
These physical conditions appear to promise me,
that not only the planet can be through good
| telescopes but that it will be distinguished by the
size of its disc, and that its appearance will differ
from that Of star. This is an important point
If the star which is to be discovered should be con-
founded, as to appearance, with the fixed stars it
will be necessary-to distinguish it among them--to
observe all the small stars situated in the region
of the heavens to be explored and to detect one Of
| them proper motion. This work will be long
and troublesome. But it, on the contrary, the
planets disc has sensible breadth, that will pre-
vent it from being COMPOUNDED with stars; if
one can substitute, for the rigorous determination
Of the position of all these luminous points, sim
pie study of their physical appearance, the search
will then advance more rapidly.
The elements attributed above to the disturbing
planet are those with which we can best represent
the observations Of Uranus. refer, for the degree
of exactness which thus be attained to the
table at the end of this analysis and which presents
the comparison of the new theory with the results
| of the observations.
| 1t will be seen that The precision is as great as
any one could desire, and superior to that
given by theory, for most Of the known planets.
While do not take into account the influence of
the neo planet, the of the theory of Uranus
are enormous, and ten times greater than any which
| should be tolerated.
| pass to the determination of the limits within
IF