advantageously be used for ascertaining with sufficient approximation the local time, latitude, and direction of the meridian. To point the telescope to a star when culminating, and supposing the finder to read zenith-distances, we have for a star SS of the zenith Z =LFD-r, where the upper sign refers to southern and the N lower sign to northern stars with respect to the zenith; the refraction, r, may generally be neglected. The indexerror of the finder may readily be removed by pointing to a known star and keeping it between the horizontal threads when transiting, for which position the finder is to be made to show the correct setting. The chronometertime of the transit of a slow-moving (polar) star is next computed, the telescope pointed to it, and the star bisected with the middle thread at the computed time of culmination, making use of the slow azimuth-motion of the Y, or, if need be, by shifting the frame of the instrument. The axis having been leveled, we next set for and observe two close zenith-stars, one north, the other south of it, and with clamp east and clamp west, from which we obtain a very close approximation of the chronometer-correction on sidereal time. The process of bisecting a circumpolar star may then be repeated, using the azimuth-screw only for this adjustment, after which the telescope will generally be found sufficiently near in the plane of the meridian to admit of commencing the regular series of observations. Art. 198. Method of observation.-Generally, a series of observations commences with transits of stars selected to furnish instrumental corrections, then follow transits of so-called time-stars; and the night's work is concluded by again observing stars of the character first named. The deviation from horizontality of the transit-axis is determined by level-readings, for each star, if possible, and the inequality of pivots is to be allowed for. The value of a division of the striding-level is ascertained by any of the methods explained in connection with the zenith-telescope, and the effect of temperature is to be allowed for, if sensible. The collimation is ascertained by observing one-half of the number of stars with clamp east or west; then reversing the telescope and observing the remaining half, clamp west or east; or we may specially observe for collimation, noting the transits of a close circumpolar star over one-half of the threads, then reversing the telescope and noting the remaining transits over the same threads now presented in the reverse order; it is well to note the state of the level during each transit. The deviation in azimuth is obtained from observations of stars differing considerably in declination (sometimes called high and low stars), but little in right ascension, or from observations of two close circumpolar stars, one culminating above the other below the pole, and having a difference of right ascension not differing much from twelve hours. It is not safe to rely on the stability of the instrument and the constancy of the rate of the chronometer by observing the same star at upper and lower culminations immediately following. Knowing the reading of the azimuth-screw for any two states of the instrument in which the azimuthal deviation has been determined, the value of one division of its micrometer-head becomes also known. It is desirable that the sum of the azimuthal corrections for the circumzenith-stars nearly balance, and that for any two zenith-stars the mean of the tangents of their declinations equals the tangent of the latitude; the deduced chronometer-correction will then be free of any error in azimuth. If more than one observer engages in the same series of observations, their personal equation must be ascertained. Art. 199. Fig. 56 represents a modified form of the portable transit, the "broken-backed" or prismatic instrument, which is rapidly coming into favor owing to the great facility with which it can be used. It is either a zenith telescope, or a transit instrument, and possesses the excellent feature of permitting the striding-level to rest at all times on its axis. The explanation already given of the straight transit will suffice for an understanding of this instrument with a study of the figure. Art. 200. Table 48 gives a list of stars selected for the determination of time with the portable transit. Other lists of stars are to be found in the American and British Nautical Almanacs, the Connaissance des Temps, the Berlin Star List, and others. 5. THE CHRONOMETER. Art. 201. The chronometer is simply a correct time-measurer and differs from an ordinary watch by having the force of its main-spring rendered uniform by means of a variable lever. Owing to the fact that on a sea voyage a chronometer is exposed to many changes of temperature by changing climate, &c., it is furnished with an expan sion balance, formed of a combination of metals of different expansive qualities, such as brass and steel, which produces the required compensation. Against accidental causes of irregularity the chronometer can be guarded by proper treatment, by regular and systematic winding, by being stowed in boxes lined with soft cushions, and by being hung in gimbals. Since, however, it is not possible to make a perfect instrument, one which will be uninfluenced by the disturbing causes incident to a sea voyage, it becomes the duty of the Navigator to determine the error and to keep watch upon the variable rate of the instrument. Art. 202. The error of the chronometer on mean time at any place is the difference between the time indicated by the chronometer and the mean time at that place. The amount the chronometer gains or loses daily is the daily rate. 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 is known for any given time together with the daily rate. The methods of finding these quantities will be given hereafter. Art. 203. Stowage and transportation.-Chronometers should be stowed on board ship as near the centre of motion as possible, in boxes with as many divisions as there are instruments to be provided for; the sides and bottoms of the divisions should be cushions stuffed with horse-hair, so that each chronometer may be tightly wedged in. This precaution is to overcome, as far as possible, the effects of vibration and concussion. They should be stowed with the XII and VI marks in parallel lines, not only for convenience of comparison, but that they may all be similarly affected by the local magnetic attraction of the ship's iron. Their lids should be removed and a fearnaught cover substituted, with a flap for each instrument, thus avoiding shocks from accidental falling of lids and affording a convenient method of regulating temperature. The flaps also facilitate the operation of comparing, for by keeping all covered but the standard and the one being compared with it the sound is deadened. Since the principal cause of deviation of chronometers is change of temperature, regard should be had in selecting a place for them, that it should be of as nearly as possible uniform temperature. When transporting by hand the chronometer should be clamped, for if left free to move in the gimbals it will be more liable to bad results from the violent oscillations. If permitted to run down, the balance-wheel should be lightly wedged with bits of cork. Árt. 204. Winding.-Chronometers are made to run either eight days or forty-eight hours, and should be wound every seventh day, or, in the case of the latter, daily, which will allow twenty-four hours if through any cause the winding should not be done at the specified time. Although chronometers are wound with a given number of half-turns (which number should be displayed over each instrument), after completing this accurate number the winding should be continued gently until the key is felt to butt. In winding box-chronometers, the chronometer is taken firmly in the left hand and inverted carefully in its gimbals, the key inserted, and turned with the right hand, being careful to ease back the slide which covered the Keyhole, and returning the instrument to its natural position. The chronometers should be wound consecutively and always in the same order to prevent omissions, and a farther precaution taken to inspect the indicators to see if all have been wound. Art. 205. Comparison.-Some one instrument is selected as the standard, the best, as near as can be judged, and with this all others are compared daily after winding. Box-chronometers are made to beat half. seconds, and in comparisons it will be found that the beats of two instruments are nearly synchronous, and this fraction of a beat must be estimated by the ear, which can be done without difficulty within a half beat, or a quarter of a second; but considerable practice is necessary to estimate within o°. I with certainty. A record should be made and retained of the comparisons, which will furnish a graphic history of the perform- The error and daily rate are — if the chronometer is fast and gaining; + if slow and losing. The second differences expressed in the last column are the daily rates in case the standard Z does not change. When taking observations the chronometers should not be taken from the box, but a hack-watch or pocketchronometer used to note the times; careful comparisons taken before and after the observation in order to reduce the time noted to the corresponding chronometer time. Art. 207. The practical benefit of a system of daily comparisons is that a guard may be kept on the steadiness of the rates of the instruments. For instance, take the case of the chronometer marked A; the record gives the daily values of ZA. If the daily rates happened to be the same, Z - A would remain a constant quantity; if, as is the general rule, the rates were different, Z-A would vary by a quantity equal to the algebraic difference of their rates; if the rates remained uniform the second difference would remain constant; therefore, if the second difference should not remain uniform it would show the rate of Z, of A, or of both was changing, and in case there is a third chronometer it may be useful in pointing out which one of the other two was going astray. Having three chronometers, the record gives daily Z - A and Z-B, whence from those two quantities there may be found A-B or B-A. Hence, if the second difference of the daily value of A— B remained constant while Z - A was irregular, it is fair to presume that the rate of chronometer Z was altering. The same course of reasoning may be carried out for any number of instruments. Of course, with but three instruments, a direct comparison can be readily made between A and B; but, in case of a larger number, this system is almost absolutely essential. It must be noted that, for the purposes of comparison, it is best to consider the standard Z fast of all other chronometers, no matter what may be the actual indications; and also that all the chronometers may be treated in a uniform manner, considered either all fast or all slow of local mean time, regard then being had for the algebraic signs of the quantities. Art. 208. Each chronometer should be accompanied with a record from the Observatory showing the daily rates for mean temperatures for each 10°, say, from 40 to 100° Fah.; then, with a maximum and minimum thermometer in the chronometer-case, the actual temperature of the preceding day is recorded as soon as the case is opened for winding in the morning. Then, referring to the tabulated record of observed daily rates according to temperature, the rate for the preceding day is found by inspection, and, applying this according to its sign to the sum of the accumulated daily rates up to the previous day, there will be found the whole amount of the accumulated rate on the given day, to be applied as a correction to the primary error. Although the rates may differ with lapse of time, &c., it is more than likely that the differences of rates for corresponding temperatures will remain the same or nearly so. The proper methods of determining chronometer errors and rates, and for carrying "traveling" rates, will be given hereafter. 6. THE NAUTICAL ALMANAC. Art. 209. The first part of the "American Ephemeris and Nautical Almanac" is especially prepared for the use of Navigators, and therefore adapted to the meridian of Greenwich. It contains the Ephemeris of the Sun and Moon; the distances of the Moon from the centres of the Sun and the four most conspicuous planets, and from certain fixed stars; the Ephemeris of the planets Venus, Mars, Jupiter, and Saturn; and the mean places of a large number of the principal fixed stars. In a supplement it gives tables for finding the latitude of a place by altitudes of the Pole Star, the same as Table 28. Art. 210. TIME.-Astronomers make use of several different kinds of time, dependent upon certain defined points, the Centre of the Sun, an imaginary point called the Mean Sun, and the First Point of Aries, or the Vernal Equinox. Art. 211. TRANSIT.-The instant when any point of the celestial sphere is on the meridian of the observer, either that half containing the zenith or that containing the nadir is called the transit of that point, also the meridian passage, or the culmination. When on the half of the meridian containing the zenith, it is designated as the upper transit; when on the half containing the nadir, the lower transit. Art. 212. Diurnal time is the hour-angle of those points which are chosen to define it, and the unit of time is the period between two successive transits over the same branch of the meridian. This unit is called a Day. It is divided into 24 equal parts called Hours, which are subdivided into Minutes and Seconds. Art. 213. Solar time is measured by the daily motion of the Sun, and is designated as Apparent time. Apparent time is the hour-angle of the centre of the actual sun. An apparent solar day is the interval of time between two successive transits of the sun's hour-circle over the same meridian. Apparent noon is 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 easily and readily determined, and the ordinary method of determining the longitude involves a calculation to deduce the apparent time first. Art. 214. But, since the intervals between the successive returns of the sun to the same meridian are not equal, apparent time cannot be taken as a standard. The apparent day varies in length from two causes: 1st, the sun does not move in the equator, that great circle perpendicular to the axis of rotation of the heavens, but in the ecliptic; 2d, that the sun's motion in the ecliptic is not uniform. At times the sun describes an arc of 57′ of the ecliptic; at other times, an arc of 61' in a day. At the points where the ecliptic and equinoctial intersect the inclination is 23° 27', and at the solstices they are parallel. Art. 215. 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 equator with a uniform velocity, which is the mean velocity of the true sun in the ecliptic; in other words, its motion in right ascension is strictly uniform. In order to establish a connection between the two suns, it is necessary to imagine a subsidiary sun starting with the true sun and moving uniformly in the ecliptic with the average motion of the true sun, returning with it to the perigee. When this subsidiary sun crosses the first point of Aries, the mean sun is supposed to be with it at that point, and thence to commence its uniform motion in the equinoctial. Art. 216. 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 is perfectly equable in its increase, and at certain times agrees with apparent time; then again it is in advance, at other times behind it. Mean time lapsing uniformly, is measured by the clocks in ordinary use, and the chronometers used by Navigators are regulated to it. Art. 217. The difference between apparent and mean time is called the Equation of time. By means of it apparent time is changed to mean time or the reverse. Thus, if the apparent time be given, the corresponding mean time wi'l be found by adding or subtracting the equation of time according to the precept at the head of the column in which it is found on Page I of the Nautical Almanac. If the mean time be given, the apparent time is found by applying the equation of time as directed by the precept on Page II. Art. 218. Sidereal time is measured by the daily motion of the stars; or, as it is used by Astronomers, by the daily motion of that point of the equator which is the origin of the co-ordinate's right ascension and declination, the vernal equinox; hence, Sidereal time is the hour-angle of the First Point of Aries. A sidereal day is the interval between two successive transits of the First Point of Aries across the same me ridian. Sidereal noon is the instant the hour circle of the First Point of Aries coincides with the celestial meridian. In order to connect sidereal time with mean time an element is calculated and tabulated in the Nautical Almanac, the Sidereal Time of Mean Noon, which is also the Right Ascension of the Mean Sun. Art. 219. Civil Time.-The civil day, according to the customs of society, commences at midnight and comprises twenty-four hours until the following midnight. The hours are counted from o 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 Meridiem), the last is marked P. M. (Post Meridiem). Art. 220. The astronomical or solar day commences at noon of the civil day of the same date. It com. prises 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 (apparent or mean) reckoned on the equator westward throughout its entire circumference from oh to 24h. The civil day begins twelve hours before the astronomical day, and an understanding of this is the only guide necessary for converting one kind of time to the other. For instance, Civil time January 9, 2 a. m., is Astronomical time January 8d 14b. Civil time January 9, 2 p. m., is Astronomical time January 9d 2h. Art. 221.—Time at different meridians.-The hour-angle of the sun at any meridian is called the local (solar) time. The hour angle of the sun at the same instant is the corresponding Greenwich time. The difference between the local time at any meridian and the Greenwich time is equal to the longitude of that place from Greenwich (that being, as before stated, the prime meridian for American Navigators), expressed in time. This may be readily reduced to arc by observing that Art. 222. The difference between the local times of any two meridians is equal to the difference of longitude of those meridians. Both local and Greenwich times, or Tm and TG, in the above formula, are supposed to be reckoned westward always from their respective meridians and from oh to 24h; in other words, TG and Tm are the astronomical times which should be used in all astronomical computations. The formula Lo. TGTm is true for any kind of time, solar or sidereal; or, in general terms, TG and Im are the hour angles of any point of the sphere at the two meridians whose difference of longitude is Lo. S may be the sun (true or mean) or the vernal equinox. Since nearly every computation made by the Navigator is dependent upon some data from the Nautical Almanac, the first operation necessary is to deduce from the local time the corresponding Greenwich date, either exact or approximate, and the Greenwich time should invariably be expressed astronomically. The formula is TGTm + Lo., remembering that west longitudes are positive, east longitudes are negative. Hence the following RULE. Having expressed the local time astronomically, add the longitude if west, subtract it if east; the result is the corresponding Greenwich time. |