Ex. 2. 1876, September 30th, 10h 15m mean time at Greenwich: find the Equation of time to be applied to app. time in working the chronometer. Eq. of Time, page II, N.A. Diff. for 1h, page I, N.A. Sept. 30th, at noon, 08.805 Corr. for 10th +8.3 101 Ex. 3. 1876, December 23rd, 22h 56m, mean time at Greenwich: find equation of time to be applied to apparent time. In this example the equation of time is taken for the nearest noon to Greenwich date, viz., Dec. 24th. To obtain the correction we go back 1 hour, and since the equation of time is increasing at noon, Dec. 24th, it was less at one hour earlier, therefore the correction is subtractire. Ex. 4. 1876, August 31st, 5h 42m 158, mean time at Greenwich: find equation of time to be applied to apparent time. In this case the correction is subtractive, and exceeds in amount the equation of time at noon, therefore the equation of time is taken from the correction, and the remainder is the reduced equation of time to be subtracted from A.T., according to the precept for the day following the given day-a change of precept occuring between Aug. 31st and Aug. 32nd (Sept. 1st.)-which change is shown by means of a black line drawn between the Equations for the two named days. Ex. 5. 1876, June 13th, 22h 25m 218 mean time at Greenwich; find equation of time to be applied to apparent time, in working the chronometer. In this case also, the correction is subtractive, and exceeds the Equation itself, therefore, the equation is subtracted from the correction and a change of precept is made i.e., the equation of time at noon being subtractive, after it has been subtracted from the correction; to the remainder prefix the precept add to A.T. By using the Eq. T. of time corresponding to the nearest Greenwich noon, viz., that for June 14th the work vill stand thus: The Eq. Time would be less at 1b-6 before noon than what it is at noon, the correction is therefore subtracted from the noon Eq. of Time. EXAMPLES FOR PRACTICE. In each of the following examples it is required to find the equation of time corresponding to the given Greenwich date: 278. The Altitude of a celestial body is the angular distance of the body from the horizon. It is measured by the arc of a circle of Azimuth (which is hence generally called a circle of altitude) passing through the plane of the body, or by the corresponding angle at the centre of the sphere. 279. The corrections necessary to reduce an altitude observed from the sea-horizon with a quadrant or sextant, &c., to the true altitude, consist of the index correction, the dip, the correction of altitude, or the joint effect of refraction and parallax, and, in certain cases, of the semi-diameter. The altitudes of heavenly bodies are observed from the deck of a ship at sea, with the sextant, for the purpose of finding latitude, longitude, &c. Such an altitude is called the "observed altitude." There are certain instrumental and circumstantial sources of error by which this is affected:-(a) The sextant (supposed otherwise to be in adjustment) may have an index error: (6) The eye of the observer being elevated above the surface of the sea, the horizon will appear to be depressed, and the consequent altitude in reality too great: and (e) One of the limbs of the body may be observed instead of its centre. When the correction for these errors and method of observing are applied-" the index correction," "correction' for dip, and "semi-diameter,"-the observed is reduced to the apparent altitude. But, again, for the sake of comparison and computation, all observations must be transformed into what they would have been, had the bodies been viewed through a uniform medium, and from one common centre-the centre of the earth. The altitude supposed to be so taken is called the "true altitude;" it may be deduced from the apparent altitude by applying the corrections called "corrections for refraction" (Table V, Norie, or XXXI, Raper), and "correction for parallax" (Table VI, Norie, or XXXIV, Raper), which, however, are sometimes given in tables combined under the names "correction of altitude" (Table XVIII, Norie). (a) "Correction for refraction;" when a body is viewed through the atmosphere, refraction will cause the apparent to be greater than the true altitude; hence the correction for refraction is subtractive in finding the true from the apparent altitude. (b) "Correction for parallax;" the position of the observer on the surface, especially for near bodies, will cause the apparent to be less than the true altitude; hence the correction for parallax is additive in finding the true from the apparent altitude. 1o. TO CORRECT THE SUN'S ALTITUDE. RULE LXXXVII. Correct the observed altitude of the sun for index error, if any. 20. Subtract the dip answering to height of eye (Table V, Norie, and Table XXX, Raper); the remainder is the apparent altitude of the limb observed. 3°. Subtract the refraction (Table IV, Norie, and XXXI Raper), add the parallax (Table VI, Norie, XXXIV, Raper); or take out the "correction in altitude of sun" (Table XVIII, Norie), and subtract it; the remainder is the true altitude of the observed limb. 4°. Take from page II of the month in the Nautical Almanac the sun's semidiameter, adding it when the sun's lower limb (L.L.) is observed; the result thus obtained is the true altitude of the sun's centre. Table 9, Norie, and Table 38, Raper, contain the gross correction of altitude, or the corrections for dip, refraction, sun's semi-diameter, and parallax-exclusive of index error, which are son etimes used in solving questions in nautical astronomy when great precision is not necessary. EXAMPLES. Ex. 1. 1876, January 6th, the observed altitude sun's L.L. 39° 8' 30", index correction +33", height of eye 19 feet: required the true altitude. Ex. 2. 1876, June 18th, the observed altitude sun's L.L. 71° 19′ 20′′, index correction +346, height of eye 18 feet: required the true altitude. Ex. 3. 1876, October 8th, the observed altitude sun's L.L. 19° 50' 10", index correction +50, height of eye 16 feet. Ex. 4. 1876, August 8th, observed altitude sun's U.L. 12° 52′ 30′′, index correction + TO FIND THE LATITUDE BY A MERIDIAN ALTITUDE OF THE SUN. RULE LXXXVIII. 1o. With the ship's date and longitude in time, find the Greenwich date apparent time (Rule LXXXI, 5°, page 222). 2o. Take the sun's declination from Nautical Almanac (page I of the month, and correct it for the Greenwich date (Rule LXXXIII, page 225). Instead of proceeding according to 1^ and 2o the declination may be found thus:—(1) Taku the sun's declination from the Nautical Almanac, for apparent noon, page I; and also the corresponding hourly difference. (2) Multiply the hourly diff. by long. in time, expressed in hours and decimals of an hour. (3) When the declination is increasing the correction is to be added in West, but subtracted in East longitude; but when the declination is decreasing subtract in West but add in East longitude. See Rule LXXXIV, page 229. 3°. Correct the observed altitude for index error, dip, semi-diameter, and refrac tion and parallax, and thus get the true altitude (Rule LXXXVII, page 236); subtract true altitude from 90°: the result will be the true zenith distance.* 4°. Call the zenith distance N., when the observer is North of sun, or when the sun bears South; call zenith distance S., when the observer is South of sun, or u hen it bears North. 5°. Add together the declination and zenith distance, when they have ti same name (see examples 1 and 3); but take the difference if their nameɛ b unlike (see examples 2, 5, and 6); the latitude is N. or S., as the greater is. 6o. When the declination is 0°, the zenith distance is the latitude, and of the s name as the zenith distance (see example 7); and when the zenith distance is the declination is the latitude, which is of the same name as the declination ( example 4). Ex. I. EXAMPLES. 1876, January 15th, in longitude 72° 42′ W., the observed meridian altitud the sun's L.L. (lower limb) was 59° 42′ 10′′, bearing North; index error + 2′ 10, heigt eye 14 feet required the latitude. : The observation was made when the sun was on the meridian, that is, at apparent n the date therefore at the place of observation is January 15th, oh om os. But the meri of the place of observation is 72° 42′ W. of meridian of Greenwich, and therefore, the s 72° 42′ W. of meridian of Greenwich; or, in time 4h 50m 488, since 72° 42′ is equivale 4h 50m 48s (see below). It is, therefore, 4h 50m 48s past apparent noon at Greenwich, and the Greenwich date is found by adding 4h 50m 48 to the time of apparent noon at sh January 15th, thus : With this date the sun's declination must be taken out of Nautical Almanac, where it be found in page I for January. It may be reduced to Greenwich date by means of Tables, or by "hourly diff.," thus :— When true altitude exceeds yo', subtract 90° from it, |