The enquirer. [volume] (Richmond, Va.) 1804-1815, 1815-05-20

conclusion, viz. The coincidence of lines due
east and west. with parallels of latitude.
The writer in Tie Courier, (who, from the
signature J. w. is understood To be MIR. John
Wood, President OF the Petersburg Acade-
my,) has replied 10 Mr.. Wallace, so TAR as
Mr.. Wallace's remarks applied to him, and
to that part ofthe Citizens proposition, which
he supported and in his communication OF
the 25th April, he has very ingeniousy and
concisely shewn the absurdity of Mr.. Wal
iace's Theory. But as neither of those gen
tlemen has explained the subject, according
to the view of the Citizen, it becomes his dli-
~ to demonstrate what be advanced to
the public. Therefore, in order to correct
misrepresentation to refute the charge of
changing the words of the Treaty; and to
establish the truth of what the Citizen adj
vanced, Mr.. Richie is requested to re-publish
from the original communication, the two fol-
lowing passages with the subsequent remarks
and demonstration.
l. " In the 5th article of the Treaty, it is
stated, that the above line shall proceed from
point, III the middle of Connecticut River
on the 45th degree of north latitude, due west
on the same latitude. Now, it IS impossible
that the line should proceed both due west,
and on the 45th parallel of lati,Ndc.
:" III our Commissioners had admitted as
the northern boundary of Louisiana. n line
due west from the northwest corner of the
Lake OF the Woods, instead of a parallel of
latitude, passing through the same point, we
should have lost land enough for large
state"
1t is evident from the above, that there
was not Change of the words line due
west, tor - right line due west" It's al
so evident, that what was advanced BY the
Cit'zen on this subject, was one proposition
consisting of two parts, viz. 1st. That line
west COn(l npt he el ateH
parallel of latitude, from given point in the
same; but 2tily, that it would lie between the
parallel and Equator.
The writer in the Courier (or Mr.. John
Wood) admits the 1st part of the Prop. but
denies the 2d. MIR. Wallace admits neither;
out IN attempting to demonstrate the contra
ry, wiz the coincidepce of east & west lines,
with parallels oflatitude,) makes use of pre-
mss and reasoning, which support BOTH
This diff renee of opinion, between two emf
nent Mathematicians, (for it appears, from
Mr.. Wallace s references, that he is IN an of
great mathematical reading, and Mr.. Wood,
whose profundity iii the Mathematics is un-
questionable, may justly re considered the
Descartes of the age) This difference of D
pmiQn, between these great men, say, will
JUSTIFY the Citizen in giving the public de
monstr Ition of what he advanced.
1. According to the definition of east and
=
made by the intersection of this circle, with
the Horizon. Hence. at the time OF the r
quinoxes the sun rises in the east & sets in the
west OF every place between the Equator &
poles, as well as of every place on the Equa-
tor.
II two compasses be set in the plane of
the same meridian. one ON the Equator, the
other at place of north and south latitude,
the right lines from their centres to that of
Ill wi me- 81, al &
SraVitatlon) at an angle equal to the latitude
OF the place, and being produced, will, (by
the 10Th prop. OF the LIST Book of Euclid) meet
the surface OF the lower Hemisphere, in the
same meridian, the first on the Equator, the
othcr IN the nadir of the given place of north
or south latitude
s: ne east and west line Of every place,
oeiFg IN the same plane, with the right line
pa55nS from that place through the centre of
the earth to the naiir, it is evident that the
east or west line of any place of north or south
latitude, will, 10y the 1st and I'd of this de-
nonstration. the 9th def. of the 18th Book of
cucl'd. and the 81 prop. of Spherics) when
produced both ways, recede from the nearest
Pole--and, consequently, from tle parallel Of
latitude, and approach the Equator until it
meets 1t In the Horizon, at the distance of 9O'
rom the place, and at an angle equal to the
latitude at the place thence produced. it
wards the other pole, until it completes
great Circle. in the nadir of the given place.
bisecting the Equator, by the list of Sphe-
rlcs) in the east and west points of the said
place.
q. The parable, Of latitude, passing through
any place north or south of the Equator,
beng small circle, produced from the, same
point, from which the east and west line of the
: piece is produced in different direction,
(Which is evident from the definition of a par
allei, and the Sd. art. of this demonstration) it
follows that the. parallel Of latitude and the
east ana west line are two circles lying out of
each other and touching III one and the Civ
en- point and that they can touch each othe
ut no other point, is demonstrated by Euclid
himself, III the 18Th prop. of his I'd Book. -
Ana since 10 two points in the east and west
me- can Coincide with any two points in the
parallel OF latitude and since a line must
he between two points, it is evident that line
due east or west cannot coincide with ore. pa-
rahelt to the Equator. Therefore, the Citizen
was perfectly correct in asserting that ~ a
line due west, from point on tue 45th par
allel OF north latitude, could not b. delineatrd
on shat parallel" And by the Sd art. of this
! demonstration, il is evident that "if the
northern boundary of Louisiana, should be es-
t;tblished due west, Instead of On the d ralIeI
| OF latitude OF the same place, we should lose
| land enough for lacge state"