Example 2. January 10th, 1836, in latitude 36:15 south, and longitude by account 47:30 east, at 13:40:0: correct mean time, the mean of several observed distances between the moon's remote limb and the nearest limb of Jupiter was 91:14'46"; at the same time the mean of an equal number of altitudes of the moon's lower limb was 24:57:38; but, for want of the necessary assistants, the altitude of the planet could not be taken :-the index error of the sextant used in measuring the distance was 1'10" additive; and the height of the eye above the level of the sea 18 feet; required the true longitude of the place of observation? Jupiter's mer.zen.dis.=59:26:14" Nat. ver. sine 491518 126193Log. 5. 101036 Jupiter's true altitude=22:28:32" Nat. co-v.si. 617711 + 2.15 The observed altitude of the 's lower limb reduced to the apparent 25:59.26" Correction of ditto = + 50, 4 Jupiter's appar. alt. = 22:30:47% altitude is,. = Apparent cent. dist. 91 0:28%; half=45:30:14: SeeM. IX., p.492. Half difference of the apparent altitudes 1. 44. 191⁄2. -L. diff. 19. 996979 Sum of ditto and half apparent distance=47:14:334"L. sine 9.865835 Difference = 43.45. 54 L. sine 9.839920 Sum, the index of the log. difference increased by 10 = 39.702734 True central distance = 90:39:50" Nearest preced.dis. at 9*—89. 48. 52 P, L. 2471.—Diff. 12 decreasing ; Long. of ditto, in time = 3 955-47:28:45" East. Note.-If Jupiter's semidiameter were not applied to the observed distance, it would produce an error of about 11 miles in the resulting longitude. Example 3. September 25th, 1836, in latitude 39:13 north, and longitude by account 42:56. west, at 16:42 20 correct mean time, the mean of, several observed distances between the moon's nearest limb and the centre of Mars was 93:31:34"; the index error of the sextant was 1'10" subtractive; required the true longitude of the place of observation? Mean time of observ. 16:42 20: || Mn. sun's red. R.A.=12:20:33: Moon's appar. alt. = 28:24:45" || Logarithmic difference=9.996727 To find the true Central Distance, and the Longitude. Appar. central dist. 93:50:11"; half=46:55′ 51′′ -L.diff. Sum of ditto,and half the apparent dist.=87:32:24L.co-si.8. 632658 Difference = 6. 17.46 L.co-si.9.997372 Sum, the index of the log. difference being increased by 10=38. 626757 Half sum = Half sum of the true alts.=41: 1:344"Log. co-sine= +19.313378 9.877607 =True central distance = = 93: 5: 0% Nearest prec. dist. at 18=93. 54. 25 Prop. log. 2767.-Diff.15 increas. Long. of ditto, in time = 2:51 3:=42:45:45′′ West. Note.-The two last Examples and that given in page 516 comprehend the principal varieties to be found in a lunar observation when a planet is in question :-but, as hinted at in the last paragraph of page 519, the angular distance between the moon and a fixed star should be always taken in preference to the moon's distance from a planet :for, whilst the planets are moving with unequal velocities, the fixed stars are as motionless points in the heavens, from which the moon's distance can be correctly, and easily determined; and to which distance we can always refer with an unbounded degree of confidence. - PROBLEM XI. Given the observed Altitudes and Distance of the Moon and Sun, the Time, per Watch, NOT REGULATED, and the Longitude by Account; to find the Latitude, the correct Mean Time, and the Longitude of the Place of Observation, viz., to determine both Latitude and Longitude from the same set of Observations. RULE. Reduce the mean time of observation, per watch, to the meridian of Greenwich, by Problem III., page 342; to which let the moon's semidiameter and horizontal parallax be reduced by Problem XV., page 361, and let the reduced semidiameter be increased by the augmenta tion in Table IV. Find the apparent and the true altitude of each object's centre by the respective Problems for that purpose, contained between pages 374 and 378. Correct the observed distance for index error, if any; to which let the respective semidiameters of the objects be added, and the result will be the apparent central distance. Then, with the apparent altitudes, the apparent central distance, and the true altitudes, compute the true central distance by any of the Methods given in Problem VII., between pages 481 and 495; and find the correct mean time at Greenwich corresponding thereto, by Problem XXX., page 383. To the correct mean time at Greenwich, thus found, reduce the true sun's right ascension and declination, and also the equation of time, by Problem XIV., page 357; and the moon's right ascension and declination, by Problem XVI., page 364; and find the difference of the right ascensions.-Then, With the true central distance between the two objects, their true altitudes, reduced declinations, and difference of right ascension, let the latitude be determined by the General Rule in page 409, belonging to Problem VIII.-Now, with the latitude, the altitude, and the declination of the sun, compute the mean time of observation, by Problem II., page 435; the difference between which and the correct mean time at Greenwich will be the longitude of the place of observa tion in time. East, if the time at ship be the greatest; otherwise, west. Note. Should the sun be too near the meridian, let the mean time be deduced from the moon's true altitude, by Problem III., page Example 437. At sea, in south latitude, January 22nd, 1836, at 3:40:0: mean time per watch not regulated, the mean of several observed distances between the moon and sun was 56:56:17; at the same time, the mean of an equal number of altitudes of the sun's lower limb was 40:37:22%, and that of the moon's lower limb 50:11:54"; the height of the eye above the level of the sea was 16 feet; the instruments were free from errors, and the longitude by account 35:6 west: required the latitude, the correct mean time, and the true longitude of the place of observation? |