Virginia Argus. [volume] (Richmond, Va.) 1796-1816, 1815-04-15
THE BOUNDARY LINE.
Messrs. Gales C Seaton.

Messrs. Gales C Seaton,
Having lately accidentally cast nv eve
over curisus piece in your paper of April
4th copied from the Petersburg Courier, res
iative to the boundary line lately agreed on
by the American ard British commissioners
at Ghent, where i9iicious zyriter in the.
Rcainond Enquirer remarks and pretends
to prove, very correctly, that the line which
commences At lat. 45 ueg Cannot be extend
Ell due west, and in that parallel of Lar.
and further says, that in any parable, of la
titude, north or south, an east and west
line will approach one of the poles and re-
cede from the equator Now, I affirm
without fear of contradiction, because I al
iirm 1t on the evidence OF mathematical de-
monstration, that Doth the above assertions
OF This learned mathematician, however ;u.
6ftfons and eo,rect he may be, are utterly
false and tina; those gentlemen who form
Gu me treaty have made no mistake or
pidnder against the most rigorous mathc-
maticat principles, in the enunation of these
words IN the 5ih article -" thence by
line due west on said latitude flat As deg.)
until 1t strikes the river Iroquois or Gaia
raguay, however great the astonisamen,
of this writer may De. As this is a subiec.
which not only concNras the commissioners
OF both nations, tut ths-public in genera,
ana the practical eurveYof in particular. The
following remarks may not be undererving
attention.
That a due east or west line IL any ma !.
rallel Of latitude is a true rhun,b line - g.
Vident to any one that has the sl;rbtes,
knowledge of the nature of rhum line. be-
cause it cuts all the meridians at right an
sies' and therefore at equal angles, as is
clearly demonstrated in periodical work.
Puoisht' by the late George Buron, New
YORK, page Is. arr. 8, and is evident from
prop. 10 B 8, OF Euclld's Elements. The
''e mus traced CUT IL certainly curve line,
DIS every line on the surface of the earth
must De, but II is the curve of a lesser Cir
Gle, the center OF which is different from the
Center OF the sphere (allowing the earth a
spaere) and therefore not spjral. IL i,
true, that II any two points be taken in a
parallel OF latitude, and the surveyor &C.
cording to common practice takes sight
with his INSTRUMENT (the plane of which is
parallel 10 the plane of the horizon) from
one OF those points to a staff or object erect
ed perpendicuiarly to the plane of the no.
rizon IN the other point, aud thea traces his
me ny continuation of suciI perpendicu,
lar OBJECTS, the line thus traced out will be
the curve OF great circle, whose center
VIII De the same as that OF the sphere, as is
evident and this curve continued will cut
me equator in two opposite points, but
WIZ net pass through either pole. If east
OF west bearings be taken to those perpen-
dicuiar objects, set up at any convenient
distances in the same parallel. the short.st
lines connecting these objects will be arch
IS CT great circlas. But if the staff or ob
Jects be set up in the plane of the lesser Cir
Gle or parallel, so as to make angles with
the horizontal plane equal the Complement
OF the latitude, and declining towards the
equator, and the sights of the instruments
DC placed. or the telescope by a single con.
t,lVance be made to play in the plane of
those objects, which plane will be the same
as that OF the lesser circle or parallel, and
tnen sights be taken to the respective oh.
Jects so placed, other objects may be set
up IN the same plane, by working the tel
escope until the different parts Of the OBJ
Jects coincide, and thus series of objects so
placed will trace out the parallel required
other methods might be pointed out of trac.
ing parallel of latitude, but the dispu te is
not about the practicabiIity but the posi-
oiiity OF its being traced however, as the
tracing of it is attended with some difficult.
w. the above new and simple method NAV
De OF no small use TO practical surveyors, as
H VIII answer Whatever be the figure of the
earth.
Now the bearing of each Of the objects SO
placed will, evidently, be east or west. as
the whole continued parallel is evidently
so but to ascertain the bearing OF any one
from The other, the distances must be "a
ken at very small intervals, otherwise i,
would be the angle of position, and no, the
bearing that would be measured by the i'm
strument, and it Is well known that the an .
gle OF position is essentially different from
the bearing, as is clearly shewn in page,
III, l36 &c. OF late Treatise on the
Giooes and Astronomy by j. Wallace,
The Method above given of tracing a pa
rallel OF latitude 5y having two points in the
parallel gwen by astronomical observation,
IS independent OF the bearing of any of the
objects and therefore liable to no error.
The mistake Of the judicions zOrifer in thu
Enquirer, evidently arose from his chang.
ing the words in the treaty, "a line due
vest for right line due west Had the