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making bodies appear lower in the heavens; whereas, a ray of light passing through the atmosphere becomes refracted and bent downwards, and the body from which the ray proceeds, appears above its true place in the heavens. The space through which a body is raised by refraction (and which is different for different altitudes), is given in tables computed for various altitudes; this correction must, of course, be subtracted from the apparent observed altitudes.
2dly. By the greatest and least altitudes of the sun above the horizon in the course of a year.
The path in which the sun's apparent yearly motion in the heavens takes place (called the ecliptic) is, at one point of it, about 23° 28' on the north side of the equator; and, at the exactly opposite point, it is the same number of degrees and minutes on the south side of the equator. These two points of the ecliptic are the farthest off from the equator, and are exactly 90° distant from the two points where the ecliptic and equator cut each other, which are called the equinoctial points. The sun is in the former point on or about the 24th of June, and in the latter on or about the 24th of December. To all persons, therefore, living between the north pole and latitude 23° 28', it will, on the 24th day of June, when it comes on the meridian, be the highest above the horizon, or have its greatest altitude, compared with its altitude on every other day in the year; and, in like manner, it will, on the 24th of December, have its least meridional altitude. Let S (fig. 6.) be.its position in the former, and S' in the latter, of these two cases. Then, as is the point in the equator from which S and S are both distant 23° 28', ES and ES' are equal. The altitudes of the sun's centre in both positions are to be observed with an instrument, which observation, when corrected for parallax and refraction, will give HS and H S', the greatest and least meridional altitudes of the sun in the course of the year. Now, HÆ=HSÆS, and HE is also =H S'+ÆS' or Æ S, and therefore 2 HÆ=HS+HS'; and HÆ, the height of the equator above the horizon, or the co-latitude of the place, is equal to the sum of the greatest and least meridional altitudes of the sun in the course of the year. As, however, it seldom happens in practice that the sun, when it comes upon the
meridian of the observer, is exactly at that point of its path where it is farthest from the equator, but has either already passed that point, or has not yet quite reached it, certain corrections upon the observed altitudes become necessary, in order to allow for this circumstance.
3dly. By the observed altitude, or the observed zenith distance of a star or other heavenly body, when on the meridian.
This method of finding the latitude is that which is generally employed for common geographical purposes. It is the most simple in practice, as depending only upon one observation, and is also, on this account, the most immediate in its result. It is also adapted for nautical purposes, the only difference between the modes of conducting the operation on land and at sea being in the instruments employed for making the observations, and also that, at sea, the heavenly body selected for observation is either the sun or moon, because, from the motion of the vessel, it is difficult to obtain a correct observation of the meridian altitude of any body having so small an apparent magnitude as a star. A few remarks will be made in a subsequent page, explanatory of some of the peculiarities of the modes of finding the latitude at sea: we shall, therefore, in the present instance, confine ourselves to the supposition, that the observer who is about to adopt this method of ascertaining his latitude, is on land.
Suppose (fig. 6.) S or S' to be the star or other heavenly body which is selected, S being a heavenly body above the equator, S' being a heavenly body below it; the observation is to be made when the body is on the meridian. Let ZS H represent a portion of the meridian in the heavens, and Ee Qq represent the equator: SH or S'H is then ascertained from observation, if the altitude be taken; or SZ or S' Z, if the zenith distance be taken; which it is more usual to take, as, from the inequalities of the earth's surface, it is difficult to obtain on land a true horizontal boundary. These observations must be corrected for parallax and refraction, if the body be either the sun or moon; and for refraction only, if it be a fixed star. Now, the object being to ascertain either AH, the height of the equator above the horizon (which has been already shown to be equal to the co-latitude), or
Z, the zenith distance of the equator,
(which is the latitude,) it is evident that if the distance of the observed heavenly body from the equator-that is, SÆ or or S'E, be known, the co-latitude will be found by subtracting SA, or adding S'E to the observed altitude; and the latitude will be found by adding SÆ in the one case, and subtracting S'E in the other, according as the body observed is above or below the equator. Now, SE or S'E, which is the distance of a heavenly body from the equator, measured upon a meridian in the heavens, is called its declination, and is either north or south declination, according as the body is nearer and farther off the north pole than the equator. This declination is either computed by the observer by certain astronomical calculations, or it is taken out of astronomical tables. The Nautical Almanack gives the declination of the sun and moon for every day in the year. From the foregoing explanation of this method, the following general rule is derived for finding the latitude by means of meridian altitudes, or zenith distances of heavenly bodies. If the heavenly body have a north declination, add the declination to its observed zenith distance (corrected), or subtract it from its observed altitude (corrected), and the latitude in the first case, and the co-latitude in the other, will be obtained. If the body have a south declination, the same result will be obtained by subtracting the declination from the zenith distance, and adding it to the altitude.
4th. By the zenith distances of stars which pass the meridian near to the observer's zenith.
When this method is adopted, the observations are generally made at two places having different latitudes; and the latitude of one of the places is supposed to be previously known. It is immaterial whether both places are or not situated upon the same meridian; the star must be one which passes near the zenith of both places. The observations are generally made at both places on the same day; if they happen to be made on different days, various corrections become requisite, which it is as well, if possible, to avoid.
The instrument employed on this occasion is one called a zenith sector, by which small zenith distances can be measured with great exactness. Let Z, Z', (fig. 7.) be the zeniths of any two places, Q the equator; and suppose that the latitude of the place whose
zenith is Z (that is, Z Æ,) is known, the object is to find the latitude of the place of which Z' is the zenith (that is, Z' Æ). The zenith distances of the star S, when it comes on the meridians of both places, must be observed. These observations will give us Z S and Z' S. Then if S is to the south of both zeniths, as in the figure, or to the north of both, Z' S Z S, or the difference between the observed zenith distances, will give ZZ'; if S be to the north of one zenith, and to the south of the other, then Z S+Z'S, or the sum of the zenith distances, will give ZZ'. Now ZZ' is the difference of the latitudes of the two places, as is evident by an inspection of the figure; and therefore ZÆ being known, we get the latitude Z'E= ZE+ZZ. This method was used in the trigonometrical survey of England, and gives the latitude with great accuracy.
5th. The remaining method is by making several successive observations upon the same star at several and successive altitudes above the horizon, when it is near the observer's meridian. The various altitudes thus obtained are made the basis of a computation by which the star's actual meridional altitude is obtained. This is called reducing the observed altitudes to the meridian. It is a process too intricate to be introduced in this place. The star's meridional altitude is thus obtained with great exactness. The latitude is then very easily ascertained by the application of the third method. This mode of computing the latitude, by which it may be obtained to within the fraction of a second, is that which was employed by the French astronomers in their last
operation of measuring an are of the meridian.
At sea none of the preceding methods, except the third, are ever employed; the first and fourth are founded upon observations made with instruments requiring some nice adjustments by means of the plumb line and the spirit level, in order that the instrument may be placed exactly in the plane of the meridian and in a horizontal position-these adjustments cannot be made at sea, owing to the unsteady motion of the vessel: the fourth method is moreover not applicable to all places; the second method would clearly be useless, since at sea an immediate result is required; and the fifth is too complex in its calculations to be fitted for nautical purposes. The instrument used at sea is Hadley's sextant, by which any angles whatever may be measured, and it does not require any previous adjustments, being held in the hand of the observer. The horizon being well defined at sea, the altitudes of heavenly bodies are taken. The observations are taken when the sun or other body is near the meridian, and are continued until it is found that its altitude has attained its greatest quantity and begins to decrease: at its greatest altitude the body is on the meridian of the observer at Š (fig. 6.); the complement of the latitude is, therefore, obtained, as in the third method, by adding or subtracting the distance of the observed body from the equator, according as it is below or above it, or has a south or north declination. The sun or moon is commonly the object observed, and the Nautical Almanack gives the declination of these bodies for every day in the The corrections for parallax year. and refraction must be made upon the observed altitudes. Besides these corrections, another is rendered necessary, in consequence of the observer being elevated above the surface of the sea. This elevation causes a correspondent depression or sinking of the horizon, and gives a greater apparent altitude to the observed body than it really has. This correction is called the dip.
But as it frequently happens that, at the time when the sun or moon is on the meridian, clouds prevent the observing of its meridional altitude, the latitude may then be obtained by observing two altitudes out of the meridian at different times, and noting the interval of time which elapses between the times of observation. ZP (fig. 6.), or the
co-latitude, is then computed by the resolution of three spherical triangles, á mere mathematical process, which we need not stop to investigate.
Longitude-Mode of Measuring Time
HAVING by one
of the foregoing
methods ascertained the parallel of latitude in which any particular place is situated, the next inquiry is directed to the finding of the longitude, or the position which a place occupies in the parallel with respect to what is called the first meridian. In this country the meridian of the observatory at Greenwich is generally taken for the first meridian. Various are the methods which have been proposed for finding the longitudes of places; in every point of view the subject is one of very considerable interest, not only on account of its great importance in commerce and science, but also because the attempts which have for so many years been made, in order to determine the longitude with the same accuracy with which the latitude of places is found, have hitherto been unsuccessful. Since the time of Queen Anne it has been regarded as an object of great national importance; and a board, called the Board of Longitude, consisting of various official and scientific persons, was then established for the purpose of encouraging and directting attempts to determine it.
All the methods for finding the longitudes depend upon the manner in which time is measured; and in order to attain a clear notion of them, it will be proper to explain at some length how a measure of time is obtained.
Properly considered, time is, in itself, without parts, and indivisible; the flow or lapse of time is, however, capable of being measured by means of events happening in time, and which, when compared one with another, are of different continuance, taking up more or less time in their completion. Time and space are in one respect similar; space is in its nature indivisible, it does not contain within itself any marks or circumstances of division; but by means of bodies which are situated within it, we are able to consider space as though it were divided into parts. What bodies
are, in this respect, to space, that precisely are events to time; they afford us the means of measurement. This is done by the comparison of those events one with another in respect of their duration; but in order to do this with accuracy, it is necessary to possess some standard event which always takes up exactly the same time, and to which we may refer as affording, by comparison with it, a measure of the duration of all other events: without this we should be at a loss to ascertain exactly how much time is taken up by any other event, and be left to the uncertainty of only probable conjecture. In this particular there is also a similarity between time and space; for, in measuring space, the object has been, even in remote periods of history, to fix upon a certain standard. Thus our king Henry the First commanded that the standard of measure of length should be of the exact length of his own arm, which is our present yard measure. But with him perished the standard by which the measure called a yard might afterwards be compared, corrected, and ascertained afresh. It is clear that something which was liable neither to decay nor variation was requisite to form a proper standard of measure; and accordingly by the recent Act of Parliament for weights and measures, and which proceeds upon more scientific principles, such a standard has been established in the length of a pendulum beating seconds of mean time in the latitude of London. On observing the various occurrences or events in nature, with a view to fix upon some one event, as a standard for the measure of time, it was discovered that the motion of the earth round its axis possessed all the qualifications requisite for such a purpose. This event is invariably of exactly the same continuance, and it is the only one in nature with which we are acquainted, that is so. The time spent in one revolution of the earth round its axis forms, therefore, an exact and perfect standard measure, by reference to which the time taken up by all other events may be ascertained, The beginning and the end of the revolution, and consequently the duration of it, is determined by means of the fixed stars: these stars have no motion of their own; so that their apparent daily motion is caused by the daily motion of the earth on its axis. Hence, if a fixed star be upon the meridian of a place, this motion of the earth, which is in a direc⚫
tion from West to East, gives to the star an apparent motion towards the West; and when the star next appears upon the same meridian, having moved through 360°, an entire revolution of the earth has been accomplished. The time spent in performing this revolution is the standard measure of time, and it is called a sidereal or star day, because it is by the appearance and re-appearance of the same star in the same place in the heavens that the completion of the revolution is ascertained. This standard being once established, it may be divided into smaller portions of time at pleasure. Portions of time measured by a reference to this standard are called sidereal time. Astronomical clocks are made to show sidereal time.
But it was requisite, for the sake of convenience, to obtain some other standard of measure of time, having reference to the sun, by which the common affairs of life are regulated. Now the same motion of the earth about its axis, which has already been noticed with respect to the fixed stars, gives to the sun also an apparent daily motion from the east towards the west. When the sun is upon the meridian of a place it is apparent noon at that place, or, in popular language, the hour of twelve in the day. After this hour, the sun, leaving the meridian, appears gradually to travel towards the west. This westerly motion continues below the horizon until it has brought the sun to a point where it rises again, and proceeding in its daily course, again reaches the same meridian on which it appeared at the hour of apparent noon on the former day. The time which has passed between these two successive appearances of the sun on the meridian of any place is called a solar day. A solar day is longer than a sidereal day; for if upon any day the sun and a fixed star be observed to be upon the meridian of a place together, the star will, on the following day, return to the meridian a few minutes before the sun. This difference in the times of the sun and a fixed star leaving and returning to a particular meridian, is caused by the sun's apparent yearly motion in the ecliptic, which being in a direction from west to east, and opposite to that daily motion which brings it to the meridian, makes the star, which has only the daily motion, from east to west, to appear on with the meridian before the sun. The daily average amount of this yearly motion of the sun in an easterly
direction away from a meridian, is 59' 8" (nearly one degree)
We have called this 59' 8" the daily average amount of the sun's yearly motion, because, during some parts of the year, it is more than 59′ 8′′, and at others less. Hence it follows, that the intervals of time, which in the course of a year elapse between the sun's successively leaving and returning to the same meridian, are of different lengths. An apparent solar day, therefore, or the time between two actual successive passages of the sun over the same meridian, could not be adopted as a standard measure of time, because it is a varying, fluctuating quantity; and it is essential to a standard measure of time, that it should be a fixed quantity. This gives rise to an artificial solar day, called a mean solar day; the length of which is the mean or average length of all the various apparent solar days in the course of a year; and the difference in length between a mean solar day and the apparent solar day for the time being, is called the equation of time.
When time is reckoned with reference to the apparent solar day, it is called apparent time; when with reference to the mean solar day, it is called mean time. A common sun-dial shows the hour of apparent time. Time-keepers or chronometers, common watches and clocks, are made to show the hour of mean time. Both the apparent solar day, and the mean solar day, are divided into 24 hours; and are, for astronomical and scientific purposes, reckoned from noon to noon. The mean day is always of the same length, and although it is longer than the sidereal day, yet the quantity by which it is greater (viz. the time required for the earth by its motion on its axis to move through 59' 8" of space) is always the same.
Hence, the uniformity and equal length of mean days, and of seconds of mean time, really depend upon, and must at last be referred to the uniform and equal motion of the earth upon its axis, which consequently is the standard, by reference to which, the measure of time afforded by the pendulum beating seconds of mean time is ascertained, and may be corrected. It is not uninteresting to observe, that to the equable and invariable motion of the earth about its axis, we are indebted, not only for a standard measure of time, but also for all our standard measures of length, capacity, and weight; since, by the recent Act of
Parliament, before referred to, all of them are referred to the length of a pendulum beating seconds of mean time in the latitude of London.
At four times in the year, and only four, that is, on or about the 15th day of April, and the 1st of September; and on or about the 15th of June, and the 24th of December,-mean time and apparent time agree; or, which is the same thing, on these four days the sun is actually upon the meridian of some particular place, and the shadow of the style of a dial at that place is upon the hour of twelve, at the very moment that a correct time-keeper, or watch measuring mean time, and adjusted for this particular place, shows the hour of 12. Throughout the rest of the year, apparent time and mean time are different. The exact amount of this difference is easily calculated for every day: it is called the equation of time; because, by either adding it to, or subtracting it from, the time of the apparent solar day, the result will be, the time of the mean solar day. The equation of time is given for every day in the year in the Nautical Almanack, with directions, showing whether it is to be added to or subtracted from the apparent time, in order to get at the mean time.
Various Methods of Finding the Longitude.
IN the application of the above-mentioned principles for reckoning the time of the day, consists the simplest method of finding the longitude of a place, or its situation in a given parallel of latitude with respect to the first meridian, the
meridian of Greenwich.
As in the 24 hours into which an apparent solar day is divided, the sun returns to a meridian which it has left, it may be said to describe, in that time, 360 degrees of longitude; which, dividing the whole 360° by 24, and supposing the motion to be uniform, is at the rate of 15° of longitude for every hour of apparent time; so that if we find the sun to be upon the meridian of Greenwich, or it is 12 o'clock apparent time at Greenwich, it will, in one hour after of apparent time, be 15° to the west of Greenwich, in 2 hours 30° west, in 6 hours 90°, in 12 hours 180°, and so on, at which several times in succession the