# University of Virginia Library

#### 4473. LATITUDE AND LONGITUDE, Without chronometer

[288] .—If two persons, at
different points of the same hemisphere (as
Greenwich and Washington, for example), observe
the same celestial phenomenon, at the
same instant of time, the difference of the times
marked by their respective clocks is the difference
of their longitudes, or the distance of their
meridians.* To catch with precision the same
instant of time for these simultaneous observations,
the moon's motion in her orbit is the best
element; her change of place (about a half
second of space in a second of time) is rapid
enough to be ascertained by a good instrument
with sufficient precision for the object. But
suppose the observer at Washington, or in a
desert, to be without a timekeeper; the equatorial
is the instrument to be used in that case.
Again, we have supposed a contemporaneous
observer at Greenwich. But his functions May
be supplied by the nautical almanac, adapted to
that place, and enabling us to calculate for
any instant of time the meridian distances there
of the heavenly bodies necessary to be observed
for this purpose. The observer at Washington,
choosing the time when their position is suitable,
is to adjust his equatorial to his meridian,
to his latitude, and to the plane of his
horizon; or if he is in a desert where neither
meridian nor latitude is yet ascertained, the
advantages of this noble instrument are that
it enables him to find both in the course of a
few hours. Thus prepared, let him ascertain by
observation the right ascension of the moon
from that of a known star, or their horary distance;
and, at the same instant, her horary
distance from his meridian. Her right ascension
at the instant thus ascertained, enter with
that of the nautical almanac, and calculate, by
its tables, what was her horary distance from
the meridian of Greenwich at the instant she
had attained that point of right ascension, or
that horary distance from the same star. The
addition of these meridian distances, if the
moon was between the two meridians, or the
subtraction of the lesser from the greater, if
she was on the same side of both, is the difference
of their longitudes. This general theory
admits different cases, of which the observer
may avail himself, according to the particular
position of the heavenly bodies at the moment
of observation. Case 1st. When the moon is
on his meridian, or on that of Greenwich. Second.
When the star is on either meridian.
Third. When the moon and star are on the same
side of his meridian. Fourth. When they are
on different sides. For instantaneousness of
observation, the equatorial has great advantage
over the circle, or sextant; for being truly placed
in the meridian beforehand, the telescope May
be directed sufficiently in advance of the moon's
motion, for time to note its place on the equatorial
circle, before she attains that point.
Then observe, until her limb touches the crosshairs;
and in that instant direct the telescope
to the star; that completes the observation, and
the place of the star may be read at leisure.
The apparatus for correcting the effects of refraction
and parallax, which is fixed on the
eye-tube of the telescope, saves time by rendering
the notation of altitudes unnecessary,
and dispenses with the use of either a time-keeper
or portable pendulum. I have observed
that, if placed in a desert where neither
meridian nor latitude is yet ascertained the
equatorial enables the observer to find both in
a few hours. For the latitude, adjust by the
cross-levels the azimuth plane of the instrument

477

to the horizon of the place. Bring down the
equatorial plane to an exact parallelism with it,
its pole then becoming vertical. By the nut
and pinion commanding it, and by that of the
semi-circle of declination, direct the telescope
to the sun. Follow its path with the telescope
by the combined use of these two pinions, and
when it has attained its greatest altitude, calculate
the latitude as when taken by a sextant.
For finding the meridian, set the azimuth circle
to the horizon, elevate the equatorial circle to
the complement of the latitude, and fix it by
the clamp and tightening screw of the two
brass segments of arches below. By the declination
semicircle set the telescope to the
sun's declination of the moment. Turn the instrument
towards the meridian by guess, and by
the combined movement of the equatorial and
azimuth circles direct the telescope to the sun,
then by the pinion of the equatorial alone, follow
the path of the sun with the telescope. If
it swerves from that path, turn the azimuth
circle until it shall follow the sun accurately.
A distant stake or tree should mark the meridian,
to guard against its loss by any accidental
jostle of the instrument. The 12 o'clock line
will then be in the true meridian, and the axis
of the equatorial circle will be parallel with that
of the earth. The instrument is then in its true
position for the observations of the night.—
To——. Washington ed. vii, 226.
(M. 1821)

See Lewis and Clark Expedition.

[288]

Jefferson called this paper “A method of finding
the longitude of a place at land, without a time-keeper ”.—Editor.