.... 58 T. Alt. 43° 1'49" CORRECTIONS. Cosecant of Pol. Dist. or P. Dist. 105 22 32 Cosecant 10.015810+ 19 Secant of Decln. -827 Diff. 2)177 4 21 + 62 No. of Secs. 32 mult. H. Sum 88 32 10 Cosine .. 8.408161–827 116 174 Cor. .... 18,56 Cut off the two right- hand figures. I 7 31 being A.M. 19 gives Is cosine of H. Sum. 24 subt. from 24h Diff. ...... 8271 No. of Secs. IO ATS. 5–22 52 29 Eq.T. + 14 21 Cor. 827,10 2. EXAMPLES FOR PRACTICE. 1. 1885.—Nov. 1oth, P.M., at Ship; in Latitude 49° 13' S. The observed altitude of the sun's lower limb was 22° 28' 30". Height of eye 19 feet. Time by a chronometer iod 7h 31m 458 which was 12m 168 slow for mean noon at Greenwich June 30th ; and on September 5th was 16m 248 slow. Required the Longitude by chronometer, 1885.—October 17th, A.M., at Ship; in Latitude 42° 10'N. The observed altitude of the sun's lower limb was 23° 39' 40". Height of eye Time by a chronometer 17d 4h om 68 which was 178 fast for mean noon at Greenwich September 30th; and losing is daily Required the Longitude by chronometer. 3. 1885.—September 22nd P.M., at Ship; in Latitude oo. The observed altitude of the sun's lower limb was 34° 49' 18". Height of eye 18 feet. Time by a chronometer 22d 9h 16m os which was correct Greenwich mean time at time of observation. Required the Longitude by chro. nometer. 17 feet. 4. 1885.—July 4th, P.M., at Ship; in Latitude 39° 47' S. The observed altitude of the sun's lower limb was 13° 2' 30". Height of eye 20 feet. Time by a chronometer 3d 23h 7m 25$ which was correct for mean noon at Greenwich February 18th; and on May 19th was 7m 218 fast. Required the Longitude by chronometer. 5. 1885.—July 20th, A.M., at Ship; in Latitude 40° 11' N. The observed altitude of the sun's lower limb was 33° 23' 10". Height of eye 16 feet. Time by a chronometer 190 23h 1m 50s which was 7m 1oš slow for mean noon at Greenwich April 15th; and losing 3.58 daily. Required the Longitude by chronometer. 6. 1885.- June 9th, P.M., at Ship; in Latitude 50° 40' N. The observed altitude of the sun's lower limb was 29° 17' 20". Height of eye 21 feet. Time by a chronometer 9d 16h 5m 408 which was vir 538 fast for mean noon at Greenwich on February 6th ; and on May 15th was 5m 50s fast. Required the Longitude by chronometer. 7. 1885.—May 2nd, P.M., at Ship ; in Latitude 40° 35' S. The observed altitude of the sun's lower limb was 19° 44' 0". Height of eye 18 feet. Time by a chronometer jd 16h 44m 408 which was 2m 108 slow for mean noon at Greenwich on January ist; and on March 15th was 3m 55s fast. Required the Longitude by chronometer. 8. 1885.-April 15th, P.M., at Ship; in Latitude 39° 40' N. The observed altitude of the sun's lower limb was 27° 11' 0". Height of eye 23 feet. Time by a chronometer 15d 5h 6m os which was 3m 159 slow for mean noon at Greenwich February 28th ; and gaining 6s daily. Required the Longitude by chronometer. 9. 1885.—May 2nd, A.M., at Ship; in Latitude 30° 15' S. The observed altitude of the sun's lower limb was 11° 17' 10". Height of eye 22 feet. Time by a chronometer id 13h 23m jos which was 3m 258 slow for mean noon at Greenwich February Ist; and on March 29th was 4m 21$ slow. Required the Longitude by chronometer. 10. 1885.—April 8th, A.M., at Ship; in Latitude 48° 43' N. The observed altitude of the sun's lower limb was 9° 11' 40%. Height of eye 20 feet. Time by a chronometer 7d 9h 7m 555 which was 4m 37s fast for mean noon at Greenwich January ist, and gaining 1.88 daily. Required the Longitude by chronometer. 1885:- January ist, P.M., at Ship ; in Latitude 40° 27' N. The observed altitude of the sun's lower limb was 13° 38' 10''. Height of eye 19 feet. Time by a chronometer 1d 6h 30m 408 which was 19m 208 slow for mean noon at Greenwich on June roth, 1884; and on October 15th was com os slow. Required the Longitude by chronometer. 1885.-March 20th, P.M., at Ship; in Latitude 43° 15' N. The observed altitude of the sun's lower limb was 35° 6' 10". Height of eye 12 feet. Time by a chronometer 190 23h 33m 128 which was correct for mean noon at Greenwich January ist, and losing 6.48 daily. Required the Longitude by chronometer. E 11. 12. AZIMUTH. 2. 1.-If the Ship's time is If the mean time at given. Greenwich is given. Find the Declination and TO FIND THE GREENWICH the Polar Distance, also the Equation of time exactly as MEAN TIME. in “Longitude by ChronoWrite down the year, meter." Then to the mean time at Greenwich apply the month, the day, hours, minutes, and seconds, and the Eq. Time as directed on if it is A.M. at Ship, add 12 page II. of the month. The hours and take off one day. result is the Apparent Time Then turn the Longitude at Greenwich, to which into time and place it below apply the Longitude in Time. the ship's time. If Long. is W., add. If W. Long., subtract. If E. Long., add. If Long. is E., subtract. This will give the AppaThe result is the Green rent Time at Ship. If more wich mean time. than 12 hours, subtract 12 Find the Declination and hours from it. The result Polar Distance as in “ Lon- is the Apparent Time for gitude by Chronometer." entering Burdwood's Tables. TO FIND THE TRUE ALTITUDE.-Proceed as in “ Longitude by Chronometer." TO FIND THE TRUE AZIMUTH.-Write down the true altitute, and below it place the latitude and the polar distance; add these quantities together; divide the sum by 2, and subtract the polar distance from the half sum, or the half sum from the polar distance. The result is the remainder. Then take out from Table XXV. the following logs. to the nearest mile : Secant of altitude. Cosine of remainder. Add these four logs, together, throw off 20 from the index, then divide by two. This gives the log. sine of half the true azimuth, which take out to the nearest minute, and multiply by 2. The result is the true azimuth. TO NAME THE TRUE AZIMUTH.-On the left-hand side put N. if the Lat. is S., and S. if the Lat. is N. On the right-hand side put E. if A.M. at ship, and W. if P.M. at ship. Note.-If the true azimuth is N., and the observed is S., or if the true azimuth is S., and the observed N., the true azimuth must be subtracted from 180°, and only then. TO FIND THE ERROR OF THE COMPASS.—Below the true azimuth place the observed, which must always be reckoned from N. or from S. If the two azimuths are both E. or both W., subtract, but if one is E. and the other W., add. The sum or remainder is the error of the compass. This error is E. when the true azimuth is on the right of the observed, and W. when on the left, reckoning both from N. or from S. TO FIND THE DEVIATION.-Place the variation below the error of the compass, and proceed as in the amplitude, page 41 to which you are referred. Note. In this problem if the Lat. is o you should assume it to be S., if the observed bearing is Northerly, assume it to be N. if the observed bearing is Southerly; this will avoid having to subtract the true azimuth from 180°. TO FIND THE TRUE AZIMUTH FROM BURDWOOD's TABLES.-Enter the tables with latitude on the top of the page, taking care to note if the latitude and declination are of the same or of contrary names. Then with the apparent time at ship at the side, and declination on the top take out the true azimuth. TO NAME THE TRUE AZIMUTH.-To be named the same name as the latitude; towards the E. if A.M. towards the W. if P.m. Then proceed as before to find the error of the compass and the deviation. EXAMPLE I.-(WITH THE MEAN TIME AT SHIP GIVEN.) 1885.-August 15th, at 8h 30m A.M., mean time at ship in Latitude 35° S. Longitude 50° E. The observed altitude of the Sun's lower limb 20° 1' 50". Height of eye 17 feet. Bearing by compass N.E. & E. Variation 150 E. Required the Error of the Compass, also the Deviation. I 2 13 20 1885. h. m. s. Long. Aug. 15th 8 30 o A.M. 50° o' E. Dec. Aug. 14th 14° 14' 51"N. H. diff. 465.53 4 G.M.T. 17.2 14 20 30 0 6,0)20,0 O 14 I 31 9306 90 32571 3 20 0 3 20 0 4653 Pol. Dist. .. 104 I 31 G.M.T. 14 17 10 O 6,0)80,0.316 Obsd. Alt. 20° 1'50" Eq. T. 8.42 G.M.T. 17.2 980 M.T.S... 8h 30m Of 3430 Eq. T. .. 4-5 13 20 4.68 490 Semidr. + 15 50 A.T.S... 8 25 55 Par. + 8 8.4280 19 55 18 T. Alt. 20 II 16 |