Ex. 3. 1887, August 8th, observed altitude sun's U.L. 12° 52′ 30′′, index correction + 3' 10", height of eye 17 feet. TO FIND THE LATITUDE BY A MERIDIAN ALTITUDE OF THE SUN. RULE LXIV. 1o. With the ship's date and longitude in time, find the Greenwich date in apparent time (Rule LVIII, 5°, page 179). 2°. Take the sun's declination from Nautical Almanac, (page I of the month), and correct it for the Greenwich date (Rule LIX, page 183). Instead of proceeding according to 1o and 2o the declination may be found thus:-1. Take 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 LX, page 186.) 3°. Correct the observed altitude for index error, dip, semidiameter, and refraction and parallax, and thus get the true altitude (Rule LXIII, page 192); 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 when it bears North. 5°. Add together the declination and zenith distance, when they have the same name (see Exs. 1, 3, 6, and 7); but take the difference if their names be unlike (see Exs. 2, 4, 8, 9, 10, and 11); the latitude is N. or S. as the greater is. 6°. When the declination is o°, the zenith distance is the latitude, and of the same name as the zenith distance (see Exs. 5 and 12); and when the zenith distance is 。°, the declination is the latitude, which is of the same name as the declination (see Ex. 13). • When true altitude exceeds 90°, subtract 90° from it. EXAMPLES. Ex. 1. 1887, January 15th, in longitude 72° 42′ W., the observed meridian altitude of the sun's L.L. (lower limb) was 59° 42′ 10′′, bearing North; index error + 2′ 10′′, height of eye 14 feet: required the latitude. The observation was made when the sun was on the meridian, that is, at apparent noon; the date, therefore, at the place of observation is January 15th, oh om oo. But the meridian of the place of observation is 72° 42′ W. of meridian of Greenwich, and therefore the sun is 72° 42′ W. of meridian of Greenwich; or, in time 4h 50m 48, since 72° 42′ is equivalent to 4h 50m 48 (see below). It is, therefore, 4h 50m 488 past apparent noon at Greenwich, and the Greenwich date is found by adding 4h 50m 48 to the time of apparent noon at ship, January 15th, thus: Ship date, January Greenwich date, Jan. + 15d ob om o 15 4 50 48 72° 42' 4h50m48 With this date the sun's declination must be taken out of Nautical Almanac, where it will be found in page I for January. It may be reduced to Greenwich date by means of the Tables, or by "hourly diff.," thus: In working this example the H. diff. for the noon of the day is taken. We divide the minutes of Greenwich time by 6; thus, 6 is contained in 51 eight times and three over, 6 is contained in 30 (the remainder 3 with a o added) five times; hence we have the decimal 85, to this we prefix the hours (4), and we then have 4h 85 to multiply by. As the Greenwich date wants iom of 5 hours, we might have multiplied the hourly diff. by 5, and deducted one-sixth of hourly diff. from the product. Raper. Obs. alt. sun's L.L. 27" 64 X 4.85 13820 22112 Index error Dip (Table 30) 59° 42' 10" N. 34 Corr. alt. (Table 18) Ex. 2. 1887, February 3rd, in longitude 139° 42′ E., the observed meridian altitude of the sun's L.L. 56° 56′ 56′′, bearing South; index correction - 3′4′′; height of eye 14 feet. The observation was made when the sun was on the meridian, that is, at apparent noon; the date, therefore, at the place of observation is Feb. 3d oh om o. But the meridian of the place of observation is 139° 42′ E. of meridian of Greenwich, and, therefore, the sun is 139° 42′ E. of meridian of Greenwich; or, in time, 9h 18m 48-since 139° 42′ is equivalent to 9h 18m 48′ (see below). It is, therefore, 9h 18m 48′ before apparent noon at Greenwich, and the Greenwich date is found by subtracting 9h 18m 48 from the time of apparent noon at ship, thus: Ship date, February 3d oh om os Green. date, February 9 18 48 2 14 41 12 139°42' E. 6,0)55,8 48 9h18m48 We take out of the Nautical Almanac, page I of the month, the decl. and "var. in rh" for the nearest noon to the given Greenwich date, viz., for noon, Feb. 3rd; and since the long. is 9h 18m 48′, the Greenwich date is that amount before the noon of Feb. 3rd, we, therefore, multiply the "var. in 1" 44'16 by 9h3; the resulting figures are 410·688, or 6′ 51". The decl. at noon, decreasing, will evidently be more at that instant than 9h 19m before noon; therefore, the correction is 6′ 51′′ to be added (see Rule, 2o, note). Ex. 3. 1887, March 20th, longitude 178° 35′ W., observed meridian altitude of the sun's L.L. 52° 52′ 50′′, bearing South; index correction + 1'5"; height of eye 12 feet. Ex. 4. 1887, July 13th, longitude 100° W., observed meridian altitude sun's L.L. 68° 2′0′′", bearing North, index correction 2' 16", height of eye 17 feet. When the zenith distance and declination are numerically equal, and of contrary names, the ship is on the equator. Ex. 5. 1887, September 23rd, long. 44° 24′ E., observed meridian altitude of sun's L.L. 40° 9', bearing North, index correction + 20", height of eye 18 feet. Green. date (A.T.) Sept. 22nd 21h 2m24 90 Zenith distance 21 48 47 S. 21 48 47 N. Latitude Corr. alt. (Table 18) Semidiameter, N.A. True altitude Zenith distance Latitude I I 40 4 15 + 15 59 40 20 14 90 O O 49 39 46 S. O O о 49 39 46 S. By Raper Index correction + 20'; dip - 4′ 10′′; refr. — 1'9"; par. +7′′; semid. +15' 59"; true alt. 40° 20' 7"; latitude 49° 39′ 53′′ S. The foregoing examples show the form and method of computing the Latitude from a Meridian Altitude of the Sun, and the following examples illustrate every possible variety of form under which the latter part of the problem can occur. EXAMPLES. Exs. 6 and 7. Zenith Distance and Declination of same name, N. or S. Exs. 8 and 9. Zen Dist. and Decl. of different names, and Zen. Dist. greater than Decl., the Lat. is of same name as Zen. Dist. Exs. 10 and 11. Zen. Dist. and Decl. of different names, and Decl. greater than Zen. Dist., the Lat. is of the same name as the Decl. Latitude 6 36 24 S. In each of the following examples the latitude is required: |