HOW TO FIND OUR SITUATION ON THE EARTH.
DETERMINATION OF LATITUDE.—In order that we may precisely define our
situation upon the terrestrial sphere, we have seen that two
measurements are necessary, namely, latitude and longitude. The first of
these indicates the angular distance from the Equator, and the latter
the angular distance east or west of an arbitrary initial meridian. It
is necessary for us then to learn something of how these important
co-ordinates can be determined.
In considering the apparent movements of the heavenly bodies in
different latitudes, we have already seen that at places on the earth’s
Equator the north celestial pole is on the horizon, while at the North
Pole it is in the zenith, and in other latitudes is elevated at
different angles. If one sails from England to the Cape, for example,
the Pole Star is seen to gradually get lower and lower in the sky,
until, on crossing the Equator, it descends below the northern horizon
and is no longer visible. Sailing northward, as to Norway, the Pole Star
is seen to get higher in the sky.
Now, although the Pole Star is not exactly at the north celestial pole,
it is a convenient guide to the eye as to the location of that very
important mathematical point, and what we learn from its behaviour as
our latitude is changed is that the altitude of the Pole above the
horizon is equal to the latitude of the place of observation.
One of the methods employed for finding the latitude of a place is
accordingly to determine the altitude of the Pole. This can be obtained
by an instrumental measurement of the altitude of the Pole Star, from
which, if the time of observation be known, the altitude of the true
Pole, which occupies the centre of the small diurnal circle traversed by
the star, can be computed. Tables which save an immense amount of labour
in the calculations involved are given in the “Nautical Almanac,” and in
“Whitaker’s Almanac.”
Another method of finding the elevation of the Pole is to take advantage
of the fact, that at intervals of twelve sidereal hours the Pole Star
passes the meridian alternately above and below the Pole. If, then, one
finds the altitudes at the upper and lower transits, and corrects them
for refraction, the average of the readings is a measure of the altitude
of the true Pole, and therefore of the latitude. Other stars which are
circumpolar may be employed for the same purpose, and this method has
the great advantage that a knowledge of the correct time, or of the
exact position of the star observed, is superfluous. The disadvantage is
that the correction for refraction, especially in low latitudes, cannot
be made with the necessary degree of accuracy. It must be remembered
that an error of only 1′ in latitude implies a mistake of a mile
measured on the earth’s surface.
Other methods, however, are available. As we go southwards, not only
does the Pole Star become lower in the sky, other stars in the southern
part of the sky become higher at the same rate that the Pole Star
descends. Other stars can therefore be utilised, and in order that
refraction may affect the observations as little as possible, stars of
known declination near the zenith are observed. Suppose an observer,
situated at O (Fig. 34) on the earth’s surface, observing a star S on
his meridian, O Z will represent his zenith, and O E, parallel to the
Equator, will be the direction in which he will see the celestial
equator where it crosses his meridian. The declination of the star,
represented by the angle S O E, has been previously determined with
great accuracy, and the angle S O Z, the zenith distance of the star, is
the angle which he measures. In the case illustrated by the diagram, the
difference between the declination and the zenith distance will give the
angle Z O E, which is evidently equal to the latitude O C Q. To get rid
of the ever troublesome refraction of our atmosphere, stars which pass
as nearly as possible through the zenith are selected for observation,
and stars both to north and south are observed.
[Illustration:
FIG. 34.—_Determination of Latitude._
]
Another way of determining the latitude, which is very commonly
employed, is known as Talcott’s method. The observations are made with
the aid of a zenith telescope. The latitude being approximately known,
two stars are selected which transit nearly at the same time and nearly
at the same distance from the zenith, one to the north and the other to
the south. That which transits first is brought to the centre of the
field of view, which is marked by a spider thread. The instrument is
then reversed in its bearings so that it points at the same angle on the
opposite side of the zenith. When the second star comes into the field,
the telescope is kept fixed, and a moveable spider thread is made to
coincide with the star passing through the field. The distance between
the spider threads furnishes a measure of the difference in zenith
distances. Half the sum of the declinations added to half the difference
of zenith distances gives the latitude when this method is employed.
Various other methods have been devised for the precise determination of
latitude, but the foregoing will sufficiently serve to illustrate the
processes followed when the observations are made on land.
Before the invention of astronomical instruments, latitude was
approximately measured by the lengths of shadows. At the summer
solstice, at noon, the shadow of a vertical stick is at its shortest,
while at the winter solstice it is longest. By measuring these lengths,
a diagram can be made showing the altitude of the sun at noon on each
occasion. Midway between these will be the altitude of the celestial
equator where it crosses the meridian. Since the altitude of the Pole is
equal to the latitude, the altitude of the Equator, subtracted from 90°,
thus gives the latitude.
[Illustration:
FIG. 35.—_Ancient Mode of measuring Latitude._
]
It will be noted that this _gnomon_ experiment also furnishes a measure
of the obliquity of the ecliptic. The gnomon was in use by the ancient
Chinese, and it is also believed that the Egyptian obelisks which are
now embellishing various cities were originally erected for the same
purpose.
DETERMINATION OF LONGITUDE.—As we have imagined an observer travelling
in a north or south direction in connection with the measurement of
latitude, let us consider what will happen to an observer who travels
only in longitude—that is, east or west. At the starting-point, he will
see the Pole at a certain altitude, and the stars will perform their
diurnal revolutions at a certain inclination to the horizon depending
upon his latitude. If he travels towards the east, the Pole will remain
at the same angle above the horizon, and he will detect no difference in
the apparent movements of the stars. What then is there to indicate that
he has changed his place at all? The answer is simple; he will find that
the sun and stars cross the meridian earlier, and if he be 15° east of
his first station they will transit an hour sooner, because it takes the
earth an hour to turn through that angle. If he travel westward in the
same way, the earth must turn through a greater angle to bring him back
to the same star, so that the stars will appear to cross the meridian
later.
The determination of longitude is accordingly based upon a measurement
of the difference in the times of transit of sun or stars at the place
of observation, and the place from which longitude is reckoned.
Let us take Greenwich as the start-point for our longitudes, and suppose
we are in Dublin. The sun, or a star, will cross the meridian of Dublin
at a certain interval after it has passed that of Greenwich, and if we
measure this interval, the angle turned through by the earth in that
time will determine the longitude. With a transit instrument one can
readily tell the exact moment when the star crosses the meridian of
Dublin, but how is one to know the exact moment at which the star
crossed the meridian of Greenwich without going there?
Looking at the question in another way, let us remember that the clocks
in Dublin register local time, that is time reckoned from the passage of
the sun over the meridian of Dublin, while the Greenwich clock indicates
times based on the transit of the sun over the Greenwich meridian.
Evidently the difference of these times is the difference of longitude,
and our question becomes, how to find the time at Greenwich when
stationed at the observatory in Dublin.
In all modern work, the telegraph is employed whenever it is available,
the two stations being directly connected. An observer at Greenwich is
thus enabled to transmit a signal to the observer in Dublin at the exact
moment a star passes through the centre of his transit instrument, and
the latter observer then notes the interval which elapses before the
same star passes the central line of his own instrument. If the signals
were transmitted instantaneously, the interval elapsed from the
reception of the signal to the observed transit of the same star would
give the longitude as reckoned in time.
Practically, what is done is for each observer to determine his local
sidereal time very accurately, with the aid of his transit instrument,
and in this way to find the error of his clock. It is then only
necessary to compare the two clocks, and this is done in the following
way: the clock at Greenwich has an attachment by which an electrical
contact is made every second, and this is switched in to the telegraphic
circuit, so that the Dublin observer receives a signal every second so
long as the clock is connected. These signals are automatically recorded
by a chronograph, together with similar signals from the Dublin clock,
and the times to which each of them corresponds is easily identified.
Immediately afterwards the Dublin clock is switched into the circuit,
and records its beats on the chronograph sheet at Greenwich, alongside
those sent by the Greenwich clock. In this way the differences between
the clocks can be very accurately measured, and the longitude can then
be reckoned in degrees and minutes by allowing 15° for each hour. Before
the invention of the telegraph, less accurate methods were of necessity
employed. Among others the entrance of the moon into the earth’s shadow
during an eclipse was noted by an observer desiring to know his
longitude. As we have already seen, this occurrence is independent of
the observer’s position on the earth, so that if he records the local
time of the observation and compares with the calculated Greenwich time
of the commencement of the eclipse, he can find his longitude.
Similarly, the eclipses of the satellites of Jupiter may be utilised to
signal Greenwich time to an observer situated elsewhere. Unfortunately,
the shadows are too ill-defined at the edges to permit very accurate
determinations in this way.
METHODS EMPLOYED AT SEA.—One of the most important applications of
astronomy to the needs of everyday life is in enabling the navigator on
the open ocean to determine the situation of his ship. Without the help
supplied by astronomical predictions the sea would be truly trackless,
and commerce by sea would be almost impossible.
A sextant and two or three good chronometers, together with a copy of
the current “Nautical Almanac,” furnish the means of ascertaining the
geographical position of a ship. With the aid of the sextant, the sun’s
greatest angular distance above the sea horizon—that is, its meridian
altitude—is measured, and from the known declination of the sun at the
time, the latitude is deduced in exactly the same way as in the case of
an observation of a star (p. 124).
The sextant also enables the observer, by measuring the sun’s altitude
in the early morning or evening, to determine the local time, as already
explained (p. 83). Greenwich time is kept by the chronometers, and the
difference between this and the local time is a measure of the
longitude. More than one chronometer is carried by a ship, for fear that
a single one might fail, through accident or other causes, to give
correct readings. The rate of each has been previously very accurately
gauged, and by taking the average indications, Greenwich time is known
with considerable accuracy.
Should the chronometers fail, or any doubt be thrown upon their
accuracy, there is another method by which the Greenwich time, and
thence the longitude, can be ascertained. This is the _lunar method_, in
which the heavens become the equivalent of the dial of a clock, while
the moon, with its rapid easterly movement, plays the part of the hands.
In the words of Dr. Lardner, this is “a chronometer of unerring
precision; a chronometer which can never go down, nor fall into
disrepair; a chronometer which is exempt from the accidents of the deep;
which is undisturbed by the agitation of the vessel; which will at all
times be present and available to him wherever he may wander over the
trackless and unexplored regions of the ocean.”
From the known movements of the moon, its position with regard to the
sun, planets, or conspicuous stars, at definite Greenwich times, can be
calculated in advance, and “lunar distances” are accordingly tabulated
in our nautical almanacs. We find, for instance, that the apparent
distances of the moon from the star Regulus, as they would appear from
the earth’s centre, were as follows on Jan. 1, 1896:—
6 P.M. G.M.T. 35° 50′ 22″
9 P.M. „ 34° 3′ 23″
12 P.M. „ 32° 16′ 12″
To utilise these predictions for the purpose in hand, the observer would
measure with the sextant the apparent distance of the moon from Regulus
at a known local time, and he would then compute what the apparent
distance would have been if his observation had been made from the
earth’s centre. From the tabulated distances, he would then be able to
find the Greenwich time at which his observation was made; and, as we
have seen, the difference between this and local time is a measure of
the longitude.