Method II. RULE. I. Find the difference of the apparent altitudes of the objects, and the corrections of their altitudes. II. To the correction of the apparent altitude of the Sun, Planet, or Star, add the correction of the Moon's apparent altitude, the sum being added to the difference of the apparent altitudes when the Moon has the higher altitude, or subtracted from the difference of the apparent altitudes when the Sun, Planet, or Star has the higher altitude, will give the difference of the true altitudes. III. Find the difference between the apparent distance and the difference of the apparent altitudes, and also the sum of the apparent distance and the difference of the apparent altitudes; omitting the seconds in the apparent distance. IV. To the logarithm of the Moon's apparent altitude add the logarithms of the difference and sum, the sum of these three logarithms will be the log. of a natural number, to this number add the N.V.S of the difference of the true altitudes; this will give the N.V.S. of an arc, to which add the seconds omitted in the apparent distance, the sum will be the true distance. EXAMPLES. I. Let the apparent distance between the Moon and a Star be 60° 0' 0", the Star's apparent altitude 24° 0′, and that of the Moon 16° 0' when the Moon's hor. par. is 58′ 0′′. Required the true distance. II. Suppose the apparent distance between the Sun and Moon is 70° 5′ 52", the apparent altitude of the Sun 58° 2′, the Moon's apparent altitude 36° 40′ and hor. par. 54′ 50′′. Required the true If the Moon have the higher altitude, the corrections of the apparent altitudes may be added to the differences of the apparent altitudes for the purpose of finding the difference of the true altitudes, without first adding the corrections together, as is mentioned in Precept I. of the Rule. Thus, in the next Example. III. Let the apparent distance between the Sun and Moon be 81° 23′ 38′′, the Sun's apparent altitude 27° 43′, and that of the Moon 48° 22′ when the Moon's hor. par. is 58′ 45". Required the true distance. To find the Mean Time at Greenwich, answering to a Given True Distance between the Moon and Sun, or one of the Planets or Stars used in the Nautical Almanac. RULE. 1. In one of the pages XIII. &c. to XVIII., of the month in the Nautical Almanac, opposite to the given day, or to that which immediately precedes or follows it, find two distances of the Moon from 2. Take out the first+ of these in order of time, the pro. log. between them (which is the pro. log. of their difference), and the three hourly interval at the head of the column in which the first distance is found. 3. From the pro. log. (Table XIX.) of the difference, between the first true distance and the given true distance subtract the pro. log. taken out of the Nautical Almanac. The remainder will be the pro. log. of a portion of time, which, added to the three hourly interval taken out, will be the Greenwich mean time required (nearly). 4. The Greenwich mean time thus found, is subject to a correction on account of the inequality of the Moon's motion, called the correction of second differences, the Table containing this correction, and the directions for applying it, are found on page 550, Nautical Almanac, examples and instructions on pages 572-3-4, Nautical Almanac. EXAMPLE. 1844. August 10th. True distance of the Moon from Jupiter, required the corresponding Greenwich M. T. N.A. p. XV., S. d. h. m. 94° 6' 10" x of pro. logs. in N. A. 10 decreasing. As the description of the Sextant, &c. with instructions for taking the observations necessary in finding the longitude by the lunar method, may be found in all the modern works on Navigation, it has been judged unnecessary to enter fully into that subject here. The Sextant case should be a fixture for the voyage, in a position out of the way of carelessness, and where it can be opened easily. It should be of that shape, size, and internal arrangement, to admit of the Sextant lying in it, with the Telescope screwed in ready for use, and the index at any part of the arc. All the tubes should be adjusted to the eye of the observer, and marked with a pencil or ink. The constant sliding in and out of a tube will slacken it so much, as scarcely to admit of its being touched without losing the focus. A Navigator should never allow another person to touch his + When the distance between the Moon and the object observed is increasing, the first distance in the Nautical Almanac will be less than the given true distance. When the distance is decreasing between the Moon and the object observed, the Sextant, otherwise its adjustment, or error, cannot be depended on, and that perhaps at a moment when most required. When running for land in unsettled weather, and in want of sights, those persons who have no cabin on deck, will find it convenient to have a common deal box, secured upon a skylight, or elsewhere, out of harm's way, to hold the Sextant all ready for use, and set to an expected altitude. A few seconds become of importance near the land in an uncertain climate. The Navigator, who is methodical in his arrangements, will obtain a set of sights for time or latitude, before the man without method gets his Sextant in hand. The index error of the Sextant should be ascertained by the Sun's diameter, after observing distances, because a glare of light unfits the eye for the correct observation of a fainter object like the Moon. When reading off the Sextant, it should be so held that the light may always fall upon the vernier in the same direction, both when ascertaining the index error and observing distances, particularly at night. A large error may arise by not attending to this point, as the position of the vernier alone furnishes the liability to a parallax. A person can become an expert and correct observer by practice only; therefore those who have not been accustomed to observe lunar distances, should not be discouraged, although their first attempts may not answer their expectations. By a steady perseverance, with a due attention to the directions in the Epitomes of Navigation, it will be found that the lunar distances may, in ordinary cases, be as easily observed as common altitudes, and so correctly that the longitude deduced from a set will seldom differ 10 miles from the truth. Perhaps some of the following hints may be of service to those who are desirous of acquiring expertness in the practice of observing the lunar distances. 1. When the Ship is pitching hard, the observer should place himself as near the midships as possible, provided the objects can be seen in that situation, the motion there being much less violent than it is near the head or stern; if the vessel be sailing nearly before the wind, and rolling very much, it will be useful to brace forward the yards and alter the course a little, during the time of taking the observations. The Sextant should be held as slack in the hand as is consistent with its safety; most observers at first grasp it too hard, which renders the hand very unsteady. 2. When observing with the Direct Telescope, great care must be taken that the line of sight be parallel with the plane of the instrument, otherwise the observed distance will be too great; the middle of the telescope should be set opposite to the middle of the transparent part of the horizon glass, and the observation made when the objects appear in this situation; for if the objects be observed too near either the inner, or outer side of the transparent part of the horizon glass, the observed distance will exceed the truth, therefore the least distance 3. When the Inverting Telescope is used, the observation is to be made when the objects appear in contact in the middle of the space between the wires, these being placed parallel to the plane of the Sextant. This Telescope is in general to be preferred to the direct one, on account of its greater magnifying power: but an observer should accustom himself to the use of both, because, when the motion of a ship is very great, the distance may be more easily observed with the direct Telescope than with the inverting one. It appears rather difficult to most people at first to observe with the Inverting Telescope, but practice soon renders its use, in ordinary cases, as easy as the other. When observing with this telescope, should the objects get out of the field of view, the Telescope must not be moved in the direction in which the objects appear to move but in the contrary one: for instance, suppose the Sextant is held in a vertical position, when the objects appear to go out of the field of view at the upper part of the Telescope, they actually go out at the lower part, therefore the object-end of the Telescope must be moved downwards to bring the objects again into the field of view. 4. The best way to acquire confidence in the longitude, deduced from the lunar distances, is to make a practice of finding the longitude by the lunar method, when near any place, the longitude of which is well ascertained: then if the observation give the longitude east of the true longitude, the observed distance has been too great, or too small, according as the distance between the Moon and the other object is decreasing or increasing: but if the observation give the longitude west of the truth, the contrary is the case, that is, the observed distance must have been too great or too small, according as the Moon's distance from the other object is increasing or decreasing; and the error in the observed distance, in any case, will be about two seconds, for every minute of error in the longitude. 5. The following is the usual method of writing down a set of lunar distances, with the altitudes of the objects observed at the same time, and of finding the mean observed distance and altitudes. Dist. and D Alts. O's 1.limb. Alts. D's up. limb. 91° 19′ 10 Times per watch. 37° 58' 49° 58' If one of the objects be at a sufficient distance from the meridian, for the purpose of finding the time with correctness, when the distance is observed, it is not absolutely necessary to take the time of each observation by a watch, because the mean time of observation may be d 2 0 37 38 50 17 |