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

elements arbitrary, propose 10 mark out the area
in which II Will be necessary 10 place TINS pians.n
order 70 satisfy the observations on Uranus ms
area WILL not be regular in shape; Il WIN DC pody-
gon with curvilinear sides; pentagon generally Inc
reason Of this particular circumstances will easily be
understood II we reflect that the ancient oDserva-
| tions OF Uranus, which play important part IN
these discussions are not found except al very long
intervals, and that they differ very mueh rom one
another
| Let US imagine that we are about to move our
planet from its most probable position ~ gwen d.
recon, without varying the length Of its revolution
All the observations will continue TO be represented
as far as certain distance from the original place
where we shall be obliged TO stop, because one of
these Internationally one gsnerally-will not
| permit us to proceed any further. Suppose,
Just by way of fixing the ideas, that this is
the first observation Of Fiamsteed, inasmuch as
il will be this FIRST observation which limits the
deviation OF the planet IN respect 10 the original
place, and in direction differing from the first.
| The limit which we thus obtain will be a con-
tinuous curve. Blu; il we take another observation,
(that, for example, made in 1855 by Mayer,) and
substitute II for the preceding, because this requires
more accuracy than that, the curved limit will
change its form at the point where il intersects the
first and II will go on diminishing in area. This
area will be as Il have announced) poygon OF
euryiinear sides. .. .".
We can also trace the euryilinear polygons within
which will be included planet which would re-
quire TO effect its revolution not more than 300
years, but more properly 222 years, pa years, and
| so on to 233 years. We cannot admit longer rev.
ouuOn. La like manner, we may suppose that the
period OF a revolution decreases successfully 10 2lS
and 2l0 years, and so on to POT years The size Of
the polygons thus formed vii, in general, diminish
in proportion as the period approaches lis extreme
values; and when we suppose this period equal TO
one OF It's limits tho polygon will be reduced to
point This will be the only position that can be
occupied by the planet. .
Let US now return TO the most general problem
Let consider the period of revolution variable as
the other elements. The planet may be sought for
then in any Of the curvlinear poygons which we
trace. After having suitably matiplied the number
of these polygons, one may eircumscribe them by a
curve which forms the desired area
have now only 10 make known the loDgltudes Of
the extreme tangents drawn to this
The longitude Of the tangent drawn to the west is,
10 round numbers, 22l degrees. The most precise
position assigned to the star being $3.50 80, il is evil
dent that 1t Will be necessary to explore backward
from this position a distance Of 5 degrees and half
The greatest limit is far from being thus
abridged, but 1t does not appear TO me that 1t
can be accepted with any great certainty in all It's
extent; for, in proportion as the longitude u in
creased, we perceive, starting from a certain point
the eccentricity Of the sought-for star constantly
increasing and acquiring values which appear little
10 hurmonze with the order Of the system Of large
planets, a system in which the new planet Is lncu-
ued as wen from us posluon as from the size Oh ilh
mass. However one may carry the actual position
Of the planet up to 335 degrees ofheeocentc longi
tude, without causing the value Of eccentricity to
increase to more than one-eghth; but If we wish to
admit greater eccentricity equal to one-ffth 1t
will be necessary to extend the researches to PAS de-
greos Of longitude.
These positions, removed from the most probable
place, appear to me, repeat ruther far from the
truth. We cannot admit them without admitting,
also, considerable eccentrlcity and being careful
to satisfy the observations with moderate degree
of exactness il appears to me, then, that the expora
ton will be best conducted in the following
One should set ost from the point situated in 1860
80 Of longitude and explore left Of this point the
region about the elliptic, which is comprised be-
tween 32l and 1876 degrees of heeocentric longi-
tudes. II far the explorations should be in vain,
one can fall back upon greater longitudes.
In the discussion, Of which | have given merely.
the principal results, the of the planet is inclu
ded between l-liJO0 and l-4700. Thus, in every
admissible Hypothesis it is superior to the mass Of
Uranus.
COmpa' iSon Of the theory toih The observations.
POSITION. EXCESS OF POSITION.
Dates OF OBJ Calculations above Dates.