THE VERIFICATION OF THE LATITUDE BY DOUBLE ALTITUDES OF THE SUN. SUMNER'S METHOD. 1. From the observed find the true altitudes as in the usual method of double altitudes. 2. Get the Greenwich date of each observation. 3. From the Nautical Almanac find the Sun's Declination for each date. 4. Select two latitudes, one of which is the degree (without odd minutes) less, and the other the next degree greater than the latitude by dead reckoning. Or, assume two latitudes from 15' to 45' on each side of the approximate latitude, such that there may be a difference of 1° between the two latitudes thus chosen. 5. Find the apparent time from noon in each of the following cases : (a). With the first altitude, the corresponding declination, and less latitude. (6). With the second altitude, the corresponding declination, and less latitude. (c). With the first altitude, the corresponding declination, and greater latitude. (d). With the second altitude, the corresponding declination and greater latitude. 6. Obtain the elapsed time corresponding to each assumed latitude thus:-If one observation be A.M. and the other P.M. take the sum of the apparent times found by (a) and (b); if both be A.M. or both P.M take the difference of the results of (a) and (b); call this sum or difference the elapsed time (e) for the less latitude. Proceed in the same manner, using the results of (c) and (d), to find the elapsed time, (f) for the greater latitude. 7 Take the difference of the elapsed time (e) for the less latitude and the true apparent elapsed time, calling the remainder too little if the former is less than the latter, but too much if the reverse is the case. Find also the difference of the elapsed time () for the greater latitude and the true apparent time, naming the re mainder on the same principle as before. 8. When one elapsed time is too much and the other too little take their sum, but if both are too much or both too little, take their difference for the error of elapsed time caused by an error of 1° of latitude. Lastly, make this proportion which can be computed by proportional logarithms : It will be at once seen that when the elapsed time of one assumed latitude is too little and that of the other too much, the true latitude is between the two assumed ones, consequently the correction must be added to the less or substracted from the greater assumed latitude, according to which is used for the determining of the correction. But both the elapsed times of the two assumed latitudes may be too much or both too little,—(each case is possible); then the correction must be applied to satisfy the following conditions ; if the elapsed time of the less assumed latitude differs from the true elapsed time by a given quantity, and that of the greater assumed latitude by a less quantity, then the true latitude must be greater than the greater assumed one ; also if the elapsed time of the greater assumed latitude differs from the true elapsed time by a given quantity, and that of the less assumed latitude by a less quantity, then the true latitude must be less than the less assumed one. N. B. This method of finding a ship's position admits of the figure being projected, but hitherto it has not been required by the Board of Examination. Much more might be said on the subject, did space admit; it is however hoped the rule will be found satisfactory, so far as the method by computation is concerned. Miscellaneous Examples for Practice. : 1. June 7th, 1854 : approximate latitude 42° : long. 142°E. : observed meridian altitude 7 39° 14' 40": observer N. of ( : index error +2' 15" : eye 24 feet : required the true latitude. 2. Dec. 29th, 1854: approximate latitude 47° : long. 152° W. the observed meridian altitude ( 60° 40' 15":( S. of observer : index error — 1' 23" : eye 19 feet : required the true latitude. 3. Sept. 9th, 1854 : A.M. at ship : approximate latitude 31° : long. 160°E. : observed meridian altitude ( 58° 11' 30" ; observer S. of ( : index error –1' 40" : eye 18 feet : required the true latitude. 4. Jan. 18th, 1854, at 7b 15 35P.M. mean time at ship long. 168° 40'E. : the observed altitude of Polaris off the meridian being 45° 10' 40" : eye 21 feet : required the latitude. 5. July 10th, 1854 : at 11h 54" 40 P.M. mean time at ship: long. 171° 50 E. : the observed altitude of Polaris off the meridian being 61° 0' 30" : index error, -1' 39" : eye 27 feet : required the latitude. 6. Sept. 10th, 1854 : at 2h 30 158 A.M. mean time at ship : long. 30° 17'W.: the observed altitude of Polaris off the meridian being 54° 0' 30" : eye 18 feet : required the latitude. 7. August 5th, 1854 : lat. 37° 3°N. : long. 15° 16 E. : equal altitudes of O being observed, when the corresponding times by chronometer were 4d 19h 40m 20% and 5d 1h 30" 405 : determine the error of the chronometer for apparent and mean time at the place of observation, and also on mean time at Greenwich. 8. March 2, 1854: lat. 16° 54'N.: long. 25° 22 W.: equal altitudes of were taken, when the corresponding times by chronometer were 10h 10m 48A.M. and 3h 56m 148P.M. determine the error of the chronometer for apparent and mean time at the place of observation, and also on mean time at Greenwich. 9. April 23, 1854 : at 8h 32m 40$ A.M. apparent time at ship: lat. 40° 10'N.: long. 34° 18'W.: determine the true and apparent altitudes of the sun and moon. 10. May 5, 1854 : at 5h 30m 32 P.m. mean time at ship lat. 48° 55'S.: long. 162° 8'E.: required the true and apparent altitudes of Spica (aVirginis), and of the moon. 11. May 9, 1854, the following double altitude of the sun was taken :app. time at ship, obs. alt. O, gd 206 13"40% 35° 11'21" bearing S.41°E. 9 0 23 40 59 49 8 the course and distance made in the interval S.70°W.6 miles per hour : eye, 22 feet: required the true latitude when the second altitude was taken: the ship's position at the time being by account lat. 46° 59'N.: long. 46° 35'W. 12. Feb. 19th 1854: the following double altitude of the sun was observed, app. time at ship, obs. alt. O 8h 45" 50% a.m. 41° 30' 45' bearing S.76°E. 0 58 74 20 27 eye 24 feet: the course and distance in the interval being N.24°E. 316 miles : required the true latitude when the second ki 50 p.m. |