154. To Reduce Equation of Time to Greenwich Date.The method of correcting the equation of time for the Greenwich date is similar to that for correcting the sun's declination, and the "Variation in 1 hour" may be used for the purpose (see Defs., pp. 168-169). RULE LXII. 1o. Get a Greenwich date, as before. NOTE. The time by chronometer when error and rate are applied to it, gives Mean Time at Greenwich. 2°. Take out of Nautical Almanac (page II of the month) the Equation of Time for the noon of Greenwich Date, and mark it additive or subtractive, according to the heading of Equation of Time at the top of the column in page I of the month, when it is required to turn apparent time into mean time; but according to the heading in page II if to convert mean time into apparent; also note whether it is increasing-when affix the sign +; or decreasing-affixing the sign ; at the same time take from the column in page I the "Var. in 1 hour."* NOTE.-Since the Equation of Time is used either for turning mean time into apparent time, or for turning apparent into mean time, it will be necessary to attend to the precept given at the head of the column of Equation of Time. When a line is placed at the heading of a column, a similar one comes between two days in the column itself; in which case it means that all the Equations of Time above the line are to be applied according to the directions above the line in the heading, and all the Equations of Time below the line must be applied as directed below the line in the heading. The line is placed between these two days in which Equation of Time changes from addition to subtraction, and vice versa, showing that at some particular instant in the interval the Equation of Time is om o3. Thus, in April, 1887, page I of the month, a black line is placed between the Eq. T. for the 15th and that for the 16th, indicating that a change of precept occurs between those days. The Equations above the line, page I, have to be added, those below have to be subtracted. 3°. Multiply the "Var. in 1 hour" by the hours of Greenwich time, and when great precision is necessary, by the fractional parts of an hour also. The result is the correction to be applied to the equation of time taken from the Nautical Almanac, and is to be added when equation of time is increasing, but subtracted when equation of time is decreasing; the result is the Equation of Time sought. As the equation of time is not a uniformly varying quantity, it is not quite accurate to compute its correction as above, by multiplying the given hourly difference by the number of hours in the Greenwich time; for that process assumes that this hourly difference is the same for each hour. The variations in the hourly difference are, however, so small that it is only when extreme precision is required that recourse must be had to the more exact method of interpolation for second differences. NOTE.-We may, as in reducing the declination (see preceding Rule LIX), take the Eq. T. and "Var. in 1h" from the Nautical Almanac for the nearest noon to the Greenwich time, and multiplying the "Var. in th" by the time that must elapse before noon; the correction thus obtained must be applied to the Eq. of T. taken out of Nautical Almanac in a contrary way to that directed above, that is to say, when correcting backwards the rule is Eq. T. increasing, subtract-Eq. T. decreasing, add. (See Exs. 3, 4, and 5). (a) When the correction being subtractive, exceeds the equation of time itself, subtract the equation of time from the correction; the remainder is the reduced equation of time sought-and it is to be subtracted from apparent (or mean) time, as the case may be, when equation of time at noon is directed to be added, but added to apparent (or mean) time when equation of time at noon is directed to be subtracted; i.e., the Equation has to be applied to A.T. according to the precept for the day following the given day. EXAMPLES. Ex. I. 1887, January 29th, 6h 53m 49° mean time at Greenwich: find Equation of time to be applied to apparent time in working the chronometer. Explanation.-In working this example, the Greenwich date being given in mean time, take the Eq. of time from page II of the month in the Nautical Almanac, and mark it additive to apparent time, as directed at the top of the column in page I (the Eq. T. being required to convert apparent into mean 'ime), also note that the Eq. T. is increasing. Next, the "Var. in 1h" is taken from the column in page I of the month. The Greenwich time being 6h 54 or 6h 9; hourly difference is multiplied by 6.9 giving the product 30015, and since there are three decimal figures in H.D. (435) and one in Greenwich time ('9) in all four, four decimal places are marked off from the right hand of the product, the result 30015 or 30 is the correction to be applied to the Eq. of time at noon, and is to be added to it because it is that due to time elapsed since noon while the Eq. T. is increasing. Ex. 2. 1887, September 29th, 13h 45m mean time at Greenwich: find the Equation of time to be applied to mean time to get apparent time in working the Time Azimuth or Reduction to Meridian. Or, proceeding according to note to 3o in Rule, we may take out the Eq. T. from the Nautical Almanac for the nearest noon to Greenwich time, viz., noon, Sept. 30th, and multiply the corresponding "Var. in 1b" by the time that must èlapse before noon, viz., (24h — 13h 45m =) 10h 15m; the result is the correction to be applied to the Eq. T. taken out of Nautical Almanac in a contrary way to that above. The work will stand thus: The Eq. T. would, in this case, be less 101h before noon than what it is at noon; the correction is therefore subtracted from the Eq. T. at noon. Ex. 3. 1887, December 24th, 12h 54m mean time at Greenwich: find the Equation of time to be applied to apparent time in working the chronometer. 16°0734 or, 168.1 In this case the correction is subtractive, and exceeds in amount the Eq. T. at noon, therefore the Eq. T. is taken from the correction, and the remainder is the reduced Eq. T. to be added to A.T., according to the precept for the day following the given day-a change of precept occurring between Dec. 24 h and Dec. 25th -which change is shown by means of a black line between the equations for the two named days. Ex. 4. 1887, June 14th, 22h 25m 21o mean time at Greenwich: find Equation of time to be applied to mean time to deduce apparent time. Green. date, June 14d 22h 25m Var. in 1h, page I, N.A. June 14th, noon 08-524 Time past noon 22'4 2096 1048 1048 In this case the correction is subtractive and exceeds the equation itself, therefore the equation is subtracted from the correction, and the difference is the reduced Eq. T., which is to be applied to mean time according to the precept on page II for the day following the given day. By using the Eq. T. corresponding to the nearest Greenwich noon, viz., that for June 15th, the work will stand thus: Ex. 5. 1887, August 31st, 19h 14m 24", mean time at Greenwich: find Equation of time to be applied to apparent time. In each of the following examples it is required to find the equation of time corresponding to the given Greenwich date, and how it is to be applied in the first six examples to Apparent Time to deduce Mean Time, and in the remaining examples, how it is to be applied to Mean Time to turn it into Apparent Time. 155. 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 semidiameter. Defs., pp. 164-166). (See 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 "semidiameter,"—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 IV, 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. TO CORRECT THE SUN'S ALTITUDE. RULE LXIII. 1o. Correct the observed altitude of the sun for index error, if any. 2o. 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, and 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, but subtracting it when the sun's upper limb (U.L.) is observed; the result thus obtained is the true altitude of the sun's centre. Table IX, NORIE, and Table 38, RAPER, contain the gross correction of altitude, or the corrections for dip, refraction, sun's semidiameter, and parallax-exclusive of index errorwhich are sometimes used in solving questions in nautical astronomy when great precision is not necessary. EXAMPLES. Ex. 1. 1887, 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. 1887, June 18th, the observed altitude sun's L L. 71° 19′ 20′′, index correction +3'46", height of eye 18 feet: required the true altitude. Dip (Table 5) App. alt. sun's L.L. 4 II 39 4 52 I 3 True alt. sun's L.L. 39 + 16 18 49 True altitude 39 20 7 |