15 38 18 cos. 9-983629 The true being to the right of magnetic. 2) 19'289424 sine 9:644712 Ex. 3. 1872, July 5th, mcan time at ship 61 55m 519 P.m., latitude 50° 53' N., longitude 119° 8' E., sun's bearing by compass N. 65° 30' W., observed altitude sun's L.L. 9° 40', index correction + 3'50", height of eye 18 feet. By Raper: Index corr. + 3' 50°, dip – 4' 10", ref. -- 5'31", par. + 8”, semid. + 15' 46". Truo alt. 9° 50' 3". Polar dist. 67 14 35 63 58 55 o 22 W. 3 15 40 cos. 9.999294 The true and magnetic azimuths being reckoned from opposite points, the 2) 19.847861 true is taken from 180°, and the re mainder reckoned from the opposite point, Half azimuth 57° 4' sine 9.923930 whence true azimuth is N. 65° 52' w. The true being to the left of magnetic, the variation is West. True azimuth 114 8 2 Ex. 4. 1872, February 1oth, at 8h 2m A.M, mean time at ship, latitude 50° 48' N., longitude 77° 30' W., sun's bearing by compass E. by S. & S., observed altitude sun's L.L. 7° 10' 40" , index correction - 1' 6", height of eye 15 feet: required the true azimuth and variation. Ex. 5. 1872, January 21st, at 10h 14" A.M. app. time at ship, latitude 39° 3' S., longitude 96° 28' E., sun's bearing by compass E. 2° 30' S., observed altitude sun's U.L. 46° 15', index correction 2'43", height of eye 19 feet: required the true azimuth and variation. Ex. 6. 1872, June ist, at 9h 40m A.m. mean time at ship, latitude 60° N., longitude 40° 20' W., observed altitude sun's L.L. 44° 48' 50", index correction + 3' 17", height of eye 18 feet, sun's bearing by compass S. i W.: required the true azimuth and variation. The Greenwich date is June id oh 21m 20%. True altitude (Norie) 45° 3' oʻ, hourly diff. of decl. 19":87 X th=7', which, added to decl. June 1st at noon, viz., 22° 8' 25"N, gives the red. decl. 22° 8' 32" N., polar distance 67° 51' 28", sum of logs. 19*220454 true azimuth S. 48° 6' E. True azimuth S. 48° 6' E. s. 1 point W. = Mag. azimuth S. 5 371 W. Sun's 4 22 N. 53 7E. 6 20 OP.M. 6 10 O P.M. 43 45 N. EXAMPLES FOR PRAOTICE. In each of the following examples it is required to find the true azimuth and variation: Obs. Ht. No. Civil date. M.T. ship. Latitude. Longitude. bearing by alt. sun's of 1872. compass. L.L. eye. 1. Jan. 24th, 8622m35%A.M. 26° 5'S. 50°53'W. E. 38°23'10" 16 2. Feb. 28th, 3 14 OP.M. 38 46 N. 97 16 W. S. 42' 36' W. 26 57 14 17 3. Mar. 27th, 4 6 W. N. 29 30 50 20 4. April 3rd, 49 59 N. 169 58 E. W. 14 10 S. II 43 0 17 5. May 27th, 9 3 20 A.M. 55 oN. I 33 W. S. 36 o E. 43 851 18 6. June zoth, 11 26 W. N. 50 20 W. 16 40 20 18 7. July 31st 8 46 30 A.M. 38 18 N. 65 4 W. S. 69 20 E. 43 24 58 18 8. Aug. 23rd, 5 54 58 A.M. 135 40 W. N. 56 20 E. 7 38 0 15 9. Sept. ist, 3 47 50 P.M. 10 40 S. 138 42 E. W. by N. & N. 30 4 10 15 10. Nov. 25th, 4 7 O P.M. 50 52 W. W. 9 10 S. 33 51 O 11. Dec. 17th, 9 10 30 A.M. 26 53 W. S. 79 20 E. 51 113 16 12. July 3rd, 8 26 50 A.M. 62 o E. N. 62 o E. 14 II 37 19 13. Jan. 6th, 5 2 14 P.M, 47 46 S. 33 11 E. N. 64 40 W. 26 37 27 28 14. April 25th, 756 41 A.M. 86 43 W. E. 12 10 N. 18 44 55 30 15. Jan, 29th, 3 36 35 P.M. 49 18 W. W. 17 13 38 46 16 16. Feb. ist, 3 44 51 P.M. 20 37 E. N. 70 50 W. 39 56 10 18 17. March 26th, 95 50 A.M. 43 6 N. 51 2 W. S. 34 30 E. 32 40 0 18 18. Feb. 26th, 2 48 OP.M. 5 o E. N. 128 15 W. 60 37 O 19 19. June 21st, 66 40 N. 55 20 W. S. 500 W. 15 38 0 18 20. Sept. uth, 37 19 o W. N. 44 50 E. 42 28 o 21. 1873, Jan. ist, 9 27 10 A.M. S.E. by S. 45 10 50 17 51 10 N. 14 39 58 8. 29 108. 32 ios. 27 20 S. 42 26 N. 33 51 S. os. ON. 167 O P.M. 322 7 0 O A.M. ON FINDING THE LATITUDE BY REDUCTION TO THE MERIDIAN. The latitude of a place is most simply determined by observation of the meridian altitude of a known heavenly body. When such an observation cannot be obtained by reason of the state of the weather, the altitude of the body may often be obtained a little before or a little after a its meridian passage. And if at the timo of observing such an altitude near the meridian, the hour-angle of the body is known, we may find by computation very nearly the difference of altitude by which to reduce the observed to the meridian altitude. The correction is called the “Reduction to the Meridian.” This method, in point of simplicity, is little inferior to the meridian altitude, to which it is next in importance. The latitude may also be determined by a direct process, deduced from spherical trigonometry. The former is the method used in the following pages. The term “near the meridian” implies a meridian distance limited according to the latitude and declination, and also the degree of precision with which the time is known (see Raper, Table 47). 23 37 16 22 RULE LXXIII.-METHOD I. 1°. To the time shown by the watch, expressed astronomically, apply the error of the watch for apparent time,* adding when the watch is slow (rejecting 24" when the sum exceeds 24" and putting the day one forward), subtracting when the watch is fast (increasing the time shown by watch by 24", if necessary, and putting the day one back.) 2°. Next turn into time the difference of longitude made since the error of the watch was determined ; adding when the difference of longitude is East, subtracting when difference of longitude is West; the result is apparent time at ship when the observation was made.f 3°. If apparent time at ship is P.M., it is the time from noon; when it is A.M., subtract it from 24", the remainder is the time from noon. Ex. 1. Suppose it is p.m, at ship, and Ex. 2. Again, suppose it is A.M. at the watch when corrected shows January ship, and the watch when corrected indi2d oh 16m 565 (see example i following); cates February 5d 23h 37m 165 (see exthen the time from noon is 16m 56s past ample 2 following), then we have noon of the 2nd. 24h Om os In this instance it is 22m 44* before noon of the 6th, 44 4°. With apparent time at ship and longitude, find Greenwich date in apparent time (Rule LV, pages 144 and 145). 5o. Take out of Nautical Almanac, page 1, the declination, and reduce it to the Greenwich date (Rule LVI, page 147). 6o. Correct the observed altitude oj' sun's upper or lower limb, and so get the true altitude of sun's centre (Rule LX, page 159). 7o. Take out log. rising of time from noon (Table 29, Norie), log. cos. declination (Table 25, Norie), and log. co8. of latitude (Table 25, Norie). 8o. Take the sum of these and find the natural number corresponding thereto. (Table 24, Norie). 9o. To the natural number just found add the natural sine of the true altitude, taken out to five figures (Table 26, Norie); the sum is natural cosine of meridian zenith distance, which take out of the Table, and name it North or South, according as the observer is North or South of the sun. 10°. Apply the reduced declination to the zenith distance, taking their sum if they are of the same name, but their difference if of contrary names; the result, in either case, is the latitude of the same name as the greater. The error of chronometer for apparent time at place, should be noted when the morning sights are taken for determining the longitude. This with the diff. long. made in the interval between this last time and the time of observing the ex-meridian altitude, will give the apparent time at shiy). + The reason for this rule will appear in considering that if a watch is set to the time at any given meridian, it will be slow for any meridian to the eastward, but fast for any meridian to the westward, at the rate of im for 15' diff. long., since the sun comes to the easterly meridian earlier, and to the westerly meridian later. |