CHAPTER IX.
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.