Remark.-Instead of finding the interval between the time of observing the lunar distance and that of taking the sun's altitude, as above; this part of the operation may be performed as follows; which, perhaps, may be more intelligible to those who are not very conversant with this subject. Mean time deduced from the sun's altitude Error of the watch, which is slow for mean time Correct mean time of observing ditto Correct mean time at Greenwich, per lunar distance Longitude, in time, the same as above = 20:20 5! 20.20. 0 +05: 10.28. 0 10:28 5: 7.30.13 2:57:52: Note. The young navigator must bear in mind that the longitude determined in this manner will not be for the place where the lunar distance was observed; but for that in which the sun's altitude was taken for the purpose of finding the correct mean time at ship, or the error of the watch. Remark.-In taking a lunar observation, it is customary to have three assistants, two of whom are to observe the altitudes of the objects at the moment that the principal observer measures the distance; the third is to be provided with a watch, showing seconds, and to note down carefully the respective times of observation, with the corresponding distances and altitudes, as expressly pointed out in Article 79, page 335. But, since it sometimes happens, particularly in small ships, that the necessary assistant observers cannot be in readiness, or at liberty to attend, the following instance is given, by which it will be seen how one person may take the whole of the observations himself, without any other assistant than merely a person to note down the times of observation, per watch, with their respective distances and altitudes. Example 7. August 24th, 1836, in latitude 43:23 south, and longitude by account 46:20 west, the following observations were made for the purpose of determining the true longitude: the index error of the sextant used in measuring the distance was 1'40" subtractive; and the height of the eye above the level of the sea 17 feet. To find the Star's Altitude at the Time of taking the mean Distance. 1sttime72040: 1stalt.27:51 0 1sttime7 20 40: 1stalt.27:51 07 2d time7.27. 0 2d alt.28.58.30 Time of mean dist. } 7.23.50 As 0 620 are to 1: 7:30% so are 0 310: to + 33.45 Star's observed alt. at time of taking the mean distance = 28:24:45′′ To find the Moon's Altitude at the Time of taking the mean Distance. 1st time722 0: 1stalt.43:45:20 1st time722 0: 1stalt.43:45:20? 2d time7.25. 40 2d alt.44. 16. 0 Time of mean dist. } 7.23.50 As 0 340: are to 0:30:40% so are 0 150: to. + 15.20 Moon's altitude at time of taking the mean distance = 44: 0:40. L L Star's true altitude = 28:19: 3 Moon's true altitude= 44:55:26" Logarithmic difference 9. 994877. = Alt. of p's lower limb Appar. cent. dist. = 26:32:25" Half=13:16:12" Difference of ditto = 0:43:19 Prop. log. 6186 Long. of ditto in time 3 5 30: 46:22:30 West. Note. In this Example we see the necessity of attending to the correction contained in Table A: the neglecting of that would, in the present instance, produce an error of 12 miles in the longitude. Remarks.-1. Proportional logarithms will be found very convenient in the reduction of the altitudes of the objects to the time of taking the mean lunar distance: thus, to the arithmetical complement of the proportional logarithm of the first term, add the proportional logarithms of the second and third terms; and the sum, abating 10 in the index, will be the proportional logarithm of the reduction of altitude.—See Example, page 75 or 76. 2. In taking the means of the several observations, those which are evidently doubtful or erroneous ought to be rejected. A doubtful altitude or distance may be readily discovered, by observing if the successive differences of altitude or distance be proportional to those of the times of observation. If, however, the time (which is supposed to be accurately noted) and two of the observations be correct, the erroneous observation may be easily rectified by the rule of proportion. In order to attain the greatest accuracy in deducing the mean from a series of observations, these ought to be taken at equal intervals of time, as nearly as possible; such as, one minute, one minute and a half, or two minutes. Example 8. January 21st, 1835, in latitude 14:10: north, and longitude by account 94:30: cast; at 18:517, correct mean time, the mean of several observed distances between the moon's bright limb and that of Venus was 51:03"; at the same time the mean of an equal number of altitudes of the moon's upper limb was 85:12:29", and that of the 516 lower limb of Venus 54:31:32 the height of the eye above the level of the sea was 20 feet, and no error in the sextant; required the true longitude of the place of observation? Mean time of observ. 18 517: D's aug. semidiameter = 16:23: in time = -6.18. 0 Greenwich time= . 11:47 17: Auxiliary angle = 30:24: 2 Observed alt. Venus's lower limb= . . Semidiam. of Venus= Dip of hor. for 20 feet= 22: 54:31:32: Observed distance = limb = 51: 0: 3: +16.23 Venus's do., rem. limb= 0.22 App. central distance=51:16: 4: True central dist. = 51: 2:20 Natural versed sine Long. of do., in time 6:1751: 94:27:45" East. x This alt. is assumed 14° 18'57" more than the trieth for the purpose of showing the advantages which the modes of computation referred to in the 2 paragraph. p. 517 possesses oper the generality of mithids for clearing He distance. ว |