The indications of a chronometer at any given instant require a correction for the accumulated error to that instant; and this can be found if the error at any given time, together with the daily rate, are known.

262. WINDING.-Chronometers are ordinarily constructed to run for 56 hours without rewinding, and an indicator on the face always shows how many hours have elapsed since the last winding. To insure a uniform rate, they must be wound regularly every day, and, in order to avoid the serious consequences of their running down, the navigator should take some means to guard against neglecting this duty through a fault of memory. To wind, turn the chronometer gently on its side, enter the key in its hole and push it home, steadying the instrument with the hand, and wind to the left, the last half turn being made so as to bring up gently against the stop. After winding, cover the keyhole and return the instrument to its natural position. Chronometers should always be wound in the same order to prevent omissions, and the precaution taken to inspect the indicators, as a further assurance of the proper performance of the operation.

After winding each day, the comparisons should be made, and, with the readings of the maximum-and-minimum thermometer and other necessary data, recorded in a book kept for the purpose.

The maximum-and-minimum thermometer is one so arranged that its highest and lowest readings are marked by small steel indices that remain in place until reset. Every chronometer box should be provided with such an instrument, as a knowledge of the temperature to which chronometers have been subjected is essential in any analysis of the rate. To draw down the indices for the purpose of resetting, a magnet is used. This magnet should be kept at all times at a distance from the chronometers.

263. COMPARISON OF CHRONOMETERS.-The instrument believed to be the best is regarded as the Standard, and each other is compared with it. It is usual to designate the Standard as A, and the others as B, C, etc. Chronometers are made to beat half seconds, and any two may be compared by following the beat of one with the ear and of the other with the eye.

To make a comparison, say of A and B, open the boxes of these two instruments and close all others. Get the cadence and, commencing when A has just completed the beat of some even 5-second division of the dial, count "half-one-half-two-halfthree-half-four-half-five," glancing at B in time to note the position of its second hand at the last count; the seconds indicated by A will be five greater than the number at the beginning of the count. The hours and minutes are also recorded for each chronometer, and the subtraction made. A good check upon the accuracy is afforded by repeating the operation, taking the tick from B.

Where necessary for exact work, it is possible to estimate the fraction between beats, and thus make the comparison to tenths of a second; but the nearest half second is sufficiently exact for the purposes of ordinary navigation at sea. 264. The following form represents a convenient method of recording comparisons:

STAND. A, No. 777.

CHRO. B, No. 1509.

CHRO. C, No. 1802.

York for

San Juan,

265. The second difference in the form is the difference between the comparisons of the same instruments for two successive days. When a vessel is equipped with only one chronometer there is nothing to indicate any irregularity that it may develop at sea-and even the best instruments may undergo changes from no apparent cause. When there are two chronometers, the second difference, which is equal to the algebraic difference between their daily rates, remains uniform as long as the rates remain uniform, but changes if one of the rates undergoes a change; in such a case, there is no means of knowing which chronometer has departed from its expected performance, and the navigator must proceed with caution, giving due faith to the indications of each. If, however, there are three chronometers, an irregularity on the part of one is at once located by a comparison of the second differences. Thus, if the predicted rates of the chronometers were such as to give for the second difference of A-B,+ 18.5, and of A-C, -0.5, suppose on a certain day those differences were +48.5 and -0.5, respectively; it would at once be suspected that the irregularity was in B, and that that chronometer had lost 3° on its normal rate during the preceding day. Suppose, however, the second differences were +45.5 and +2.5; it would then be apparent that A had gained 3.

266. TEMPERATURE CURVES.-Notwithstanding the care taken to eliminate the effect of a change of temperature upon the rate of a chronometer, it is rare that an absolutely perfect compensation is attained, and it may therefore be assumed that the rates of all chronometers vary somewhat with the temperature. Where the voyage of a vessel is a long one and marked changes of climate are encountered, the accumulated error from the use of an incorrect rate may be very material, amounting to several minutes' difference of longitude. Careful navigators will therefore take every means to guard against such an error. By the employment of a temperature curve in connection with the chronometer rate the most satisfactory results are arrived at.

267. There should be furnished with each chronometer a statement showing its daily rate under various conditions of temperature; and this may be supplemented by the observations of the navigator during the time that the chronometer remains on board ship. With all available data a temperature curve should be constructed which will indicate graphically the performance of the instrument. It is most convenient to employ for this purpose a piece of " profile paper," on which parallel lines are ruled at equal intervals at right angles to each other. Let each horizontal line represent, say, a degree of temperature, numbered at the left edge, from the bottom up; draw a vertical line in red ink to represent the zero rate, and let all rates to the right be plus, or gaining, and those to the left minus, or losing; let the intervals between vertical lines represent intervals of rate (as one-tenth of a second) numbered at the top from the zero rate; then on this scale plot the rate corresponding to each temperature; when there are several observations covering one height of the thermometer, the mean may be used. Through all the plotted points draw a fair curve, and the intersection of this curve with each temperature line gives the mean rate at that temperatnre. The mean temperature given by the maximum and minimum thermometer shows the rate to be used on any day.

268. HACK OR COMPARING WATCH.-In order to avoid derangement, the chronometers should never be removed from the permanent box in which they are kept on shipboard. When it is desired to mark a certain instant of time, as for an astronomical observation or for obtaining the chronometer error by signal, the time is marked by a "hack" (an inferior chronometer used for this purpose only), or by a comparing watch. Careful comparisons are taken-preferably both before and afterwards-and the chronometer time at the required instant is thus deduced. The correction represented by the chronometer time minus the watch time (twelve hours being added to the former when necessary to make the subtraction possible) is referred to as C-W.

Suppose, for example, the chronometer and watch are compared and their indications are as follows:

If then a sight is taken when the watch shows 3h 01m 275, we have.

It may occur that the values of C-W, as obtained from comparisons before and after marking the desired time, will vary; in that case the value to be used will be the mean of the two, if the time marked is about midway between comparisons, but if much nearer to one comparison than the other, allowance should be made accordingly.

Thus suppose, in the case previously given, a second comparison had been taken after the sight as follows: Chro. t., 6h 12m 458

W. T.,

-3 21 59.5

C-W, 2 50 45.5

The sight having been taken at about the middle of the interval, the C-W to be used would be the mean of the two, or 2h 50m 458.0.

Let us assume, however, that the second comparison showed the following:

Then, the sight having been taken when only about one-third of the interval had elapsed between the first and second comparisons, it would be assumed that only one-third of the total change in the C-W had occurred up to the time of sight, and the value to be used would be 2h 50m 45o.0.

269. It is considered a good practice always to subtract watch time from chronometer time, whatever the relative values, and thus to employ C-W invariably as an additive correction. It is equally correct to take the other difference, W-C, and make it subtractive; it may sometimes occur that a few figures will thus be saved, but a chance for error arises from the possibility of inadvertently using the wrong sign, which is almost impossible by the other method. Thus, the following example may be taken:

11h 42m 35"

10h 57m 388 - 11 42 35

W.

CHAPTER IX.

TIME AND THE NAUTICAL ALMANAC.

270. The subjects of Time and the Nautical Almanac are two of the most important ones to be mastered in the study of Nautical Astronomy, as they enter into every operation for the astronomical determination of a ship's position. They will be treated in conjunction, as the two are interdependent.

METHODS OF RECKONING TIME.

271. The instant at which any point of the celestial sphere is on the meridian of an observer is termed the transit, culmination, or meridian passage of that point; when on that half of the meridian which contains the zenith, it is designated as superior or upper transit; when on the half containing the nadir, as inferior or lower transit.

272. Three different kinds of time are employed in astronomy-(a) apparent or solar time, (b) mean time, and (c) sidereal time. These depend upon the hour angle from the meridian of the points to which they respectively refer. The point of reference for apparent or solar time is the Center of the Sun; for mean time, an imaginary point called the Mean Sun; and for sidereal time, the Vernal Equinox, also called the First Point of Aries.

The unit of time is the Day, which is the period between two successive transits over the same branch of the meridian of the point of reference. The day is divided into 24 equal parts, called Hours; each hour is divided into 60 equal parts, called Minutes, and each minute into 60 equal parts, called Seconds.

273. APPARENT OR SOLAR TIME.-The hour angle of the center of the sun affords a measure of Apparent or Solar Time. An Apparent or Solar Day is the interval of time between two successive transits over the same meridian of the center of the sun. It is Apparent Noon when the sun's hour circle coincides with the celestial meridian. This is the most natural and direct measure of time, and the unit of time adopted by the navigator at sea is the apparent solar day. Apparent noon is the time when the latitude can be most readily determined, and the ordinary method of determining the longitude by the sun involves a calculation to deduce the apparent time first.

Since, however, the intervals between the successive returns of the sun to the same meridian are not equal, apparent time can not be taken as a standard. The apparent day varies in length from two causes: first, the sun does not move in the equator, the great circle perpendicular to the axis of rotation of the earth, but in the ecliptic; and, secondly, the sun's motion in the ecliptic is not uniform. Sometimes the sun describes an arc of 57' of the ecliptic, and sometimes an arc of 61' in a day. At the points where the ecliptic and equinoctial intersect, the direction of the sun's apparent motion is inclined at an angle of 23° 27' to the equator, while at the solstices it moves in a direction parallel to the equator.

274. MEAN TIME.-To avoid the irregularity of time caused by the want of uniformity in the sun's motion, a fictitious sun, called the Mean Sun, is supposed to move in the equinoctial with a uniform velocity that equals the mean velocity of the true sun in the ecliptic. This mean sun is regarded as being in coincidence with the true sun at the vernal equinox, or First Point of Aries.

Mean Time is the hour angle of the mean sun. A Mean Day is the interval between two successive transits of the mean sun over the meridian. Mean Noon is the instant when the mean sun's hour circle coincides with the meridian."

Mean time lapses uniformly; at certain times it agrees with apparent time, while sometimes it is behind, and at other times in advance of it. It is this time that is measured by the clocks in ordinary use, and to this the chronometers used by navigators are regulated.

275. The difference between apparent and mean time is called the Equation of Time; by this quantity, the conversion from one to the other of these times may be made. Its magnitude and the direction of its application may be found for any moment from the Nautical Almanac.

276. SIDEREAL TIME.-Sidereal Time is the hour angle of the First Point of Aries. This point, which is identical with the vernal equinox, is the origin of all coordinates of right ascension. Since the position of the point is fixed in the celestial sphere and does not, like the sun, moon, and planets, have actual or apparent motion therein, it shares in this respect the properties of the fixed stars. It may therefore be said that intervals of sidereal time are those which are measured by the stars.

A Sidereal Day is the interval between two successive transits of the First Point of Aries across the same meridian. Sidereal Noon is the instant at which the hour circle of the First Point of Aries coincides with the meridian. In order to interconvert sidereal and mean times an element is tabulated in the Nautical Almanac. This is the Sidereal Time of Mean Noon, which is also the Right Ascension of the Mean Sun. 277. CIVIL AND ASTRONOMICAL TIME.-The Civil Day commences at midnight and comprises the twenty-four hours until the following midnight. The hours are counted from 0 to 12, from midnight to noon; then, again, from 0 to 12, from noon to midnight. Thus the civil day is divided into two periods of twelve hours each, the first of which is marked a. m. (ante meridian), while the last is marked p. m. (post meridian).

The Astronomical or Solar Day commences at noon of the civil day of the same date. It comprises twenty-four hours, reckoned from 0 to 24, from noon of one day to noon of the next. Astronomical time (apparent or mean) is the hour angle of the sun (true or mean) measured to the westward throughout its entire circuit from the time of its upper transit on one day to the same instant of the next.

The civil day, therefore, begins twelve hours before the astronomical day, and a clear understanding of this fact is all that is required for interconverting these times. For example:

January 9, 2 a. m., civil time, is January 8, 14h, astronomical time.

January 9, 2 p. m., civil time, is January 9, 2h, astronomical time.

278. HOUR ANGLE.-The hour angle of a heavenly body is the angle at the pole of the celestial concave between the declination circle of the heavenly body and the celestial meridian. It is measured by the arc of the celestial equator between the declination circle and the celestial meridian.

In figure 35 let P be the pole of the celestial sphere, of which VMQ is the equator, PQ the celestial meridian, and PM, PS, PV the declination circles of the mean sun, a heavenly body, and the First Point of Aries, respectively.

Then QPM, or its arc QM, is the hour angle of the mean sun, or the mean time; QPS, or QS, the hour angle of the heavenly body; QPV, or QV, the hour angle of the First Point

M

FIG. 35.

of Aries, or the sidereal time; VPQ, or VQ, the right ascension of the meridian; VPS, or VS, the right ascension of the heavenly body; and VPM, or VM, the right ascension of the mean sun.

279. TIME AT DIFFERENT MERIDIANS.-The hour angle of the true sun at any meridian is called the local apparent time; that of the mean sun, the local mean time; that of the First Point of Aries, the local sidereal time. The hour angles of the same body and points from Greenwich are respectively the Greenwich apparent, mean, and sidereal times. The difference between the local time at any meridian and the Greenwich time is equal to the longitude of that place from Greenwich expressed in time; the conversion from time to arc may be effected by a simple mathematical calculation or by the use of Table 7.

In comparing corresponding times of different meridians the most easterly