When the star is to the left hand of the moon, the sextant must be held with its face upwards; but if the star be to the right hand of the moon, with its face downwards. Set the index to the distance roughly computed, and placing the face of the octant by the foregoing rules, direct the telescope to the star. Then place the sextant so that, if seen edge-ways, it may seem to form a line passing through the moon and star, and give it a sweep round a line parallel to the axis of the telescope, and the reflected image of the moon will pass so near by the star, that you will see it in the field of the telescope; a proof that the sight is directed to the right star. The enlightened edge of the moon, whether east or west, must then be brought into contact with the star, by moving the index. To know whether the contact is perfect, let the quadrant gently vibrate in a line parallel to the axis of vision, for the star should just graze the edge, without entering at all within the body of the moon; when this is the case, the index will shew the apparent distance of the moon from the star, which, when corrected, gives the true one, Correction 1. For the semi-diameter of the moon. This may be found in the Nautical Almanack for every noon and midnight, at Greenwich; and from thence computed, by the rules there given, for the time of observation. If the observed or enlightened limb be nearest the star, the semi-diameter thus found is to be added; if the enlightened edge be the furthest from the star, then the semi-diameter is to be subtracted. Correction 2. Is for refraction and parallax, to be found from the table as directed before for the sun and moon. These corrections being properly made, you have the true distance of the moon's centre from the star, as seen from the centre of the earth. From this dis tance, and the time of observation, the longitude may be found.* The star to be observed is always one of the brightest, and lies in a line nearly perpendicular to the horns of the moon, or her longer axis; but if you have any doubt whether the sight be directed to the proper star, set the index to the supposed distance as before, hold the sextant as near as you can judge, so The longitude of a place can be very exactly obtained by taking observations, with the sextant, of the moon's apparent distance from the sun, and at the same time both their apparent altitudes. The following are the most perspicuous rule and familiar example for the working of a lunar observation, in order to obtain the true distance, and thereby, with the distances given in the Nautical Almanack for every three hours, ascertain the true longitude of the place of observation. Rule. To the log. sine of the moon's horizontal parallax, add the log. sine of her apparent zenith distance, reject 10 in the index of their sum, which gives the log. sine of her parallax in altitude; from this subtract her refraction which will give a correction to be subtracted from her apparent zenith distance, to give her true zenith distance. From the sun's refraction, subtract his parallax adding the remainder to his apparent zenith distance, which will give his true zenith distance. Add the apparent lunar distance to the apparent zenith distances; and subtract each of the two latter from the half sum, noting the remainders. Add the log. sines of these two remainders, to the ar-co-arcs of the log. sines of the apparent zenith distances and the log. sines of the true zenith distances. From half the sum of these six logarithms subtract the log. sine of half the difference of the true zenith distances, and the remainder is the tangent of an arc. Subtract the log. sine of this arc from the above half sum, and the remainder gives the log. sine of half the true distance. In the Nautical Almanack, as the lunar distances are only given for every three hours, the corresponding time, for any distance between these, must be found by proportional parts. The observer is supposed to know, by his watch or chronometer, the apparent time, exactly, at the place, or, for example, having previously adjusted the chronometer to apparent time, by double altitudes of the sun, and by a mean of three several observations of the distance and altitudes of the sun and moon, having the following results, the true longitude of the place of observation is required from Greenwich. that its plane, seen edge-ways, may coincide with the line of the moon's shorter axis, and moving it in On June 1, 1815, in latitude 20° north, at 20h 5′ 20′′ per chronometer apparent time, suppose observed as follows: Moon's apparent altitude, lower limb 70° 5' 0") 70°20′ 21′′ True distance as found 64°34' 11" A. Distance Naut. Ephe. June 2, noon 64 45 37 B. Ditto. Time at Greenw. 24h 23′ 45′′ B-A1 diff. 0° 11' 26" Prop. log. 1.1971 Ditto at place.. 20 5 20 B-C 2 diff. 1 26 40 Prop. log. 3174 Ob 23' 45" Longitude 4 18 25 West. noon or 24 1 = 0.8797 24 23 45 app. t. at Greenw. Edit. 408 DISTANCE BETWEEN THE MOON AND STARS, that plane, seek the reflected image of the moon through the telescope. Having found the reflected image of the moon, turn the sextant round the incident ray, that is, a line passing from the moon to the instrument, and you will perceive through the telescope all those stars which have the distance shewn by the index; but the star to be observed lies in a line nearly perpendicular to the horns of the moon, there will, therefore, be no fear of mistaking it.* For the requisite promptitude in taking lunar distances, a correct observer for the distance, and two assistants for the altitudes, are necessary, but a single observer may perform it with a considerable degree of accuracy in the following manner, as given by Mr. Vince in his Practical Astronomy, 1790, note page 56. "Let him first take the altitude of the moon and then of the sun or star, his assistant noting the times; then let him take several distances of the moon from the sun or star at 1 or 2 minutes distance of time from each other, and note the times; and lastly let him again take the altitude of the moon, and then of the sun or star, noting the times. Then take the mean of all the distances, and the mean of the times when they were taken, and you have the moon's distance from the sun or star at that mean time. Take the difference of the moon's altitudes at the two observations and the difference of their times, and then say, as that difference of times, is to the difference between the time of the first observation of her altitude, and the mean of the times at which the distances were taken, so is the variation of the moon's altitude between the 1st and 2d observations, to the variation of her altitude from the time of the first observation to the above mean time, which added to, or subtracted from, her first observed altitude, according as she ascends or descends, gives her altitude at that mean time. In the same manner you may get the sun's or star's altitude at the same time. Thus you may get the two altitudes and corresponding distance." *The sextant being principally used in observations of bodies not on the meridian, and more particularly for measuring the distances of comets, planets, &c. from two fixed stars, from which data their accurate positions are afterwards computed; but refraction opperating in a vertical direction, the distances measured by the sextant can never be the true ones, because the two bodies being elevated by refraction, will appear nearer to one another than they really are, and this not being exemplified by any astronomical writers, I shall here give the following rule for correcting the observed distances of two bodies, neither of them being affected by parallax, as given by Dr. Maskelyne. Add together the tangents of half the sum and half the difference of the zenith distances, their sum, abating 10 from the index, is the tangent of arc the first, TO OBSERVE CORRESPONDING ALTITUDES OF THE SUN. The basis of all astronomical observation is the To the tangent of arc the first add the co-tangent of half the distance of the observed bodies, the sum, abating 10 from the index, is the tangent of arc the second. Then add together the tangent of double the first arc, the cosecant of double the second arc, and the constant log. 2.05690. The sum of these three, abating 20 from the index, is the log. of the number of seconds required by which the observed distance of the two bodies is contracted by the effect of refraction, which therefore added to the observed distance, gives the true distance cleared from refraction. Example. Nov. 3, 1812, the apparent distance of Lyra and Aquila as measured by the sextant. 34°13' 30" 34 14 0 Apparent distance 54 10 58 per sextant. At same time took the altitudes of the two stars, which, after applying the proper corrections, gave zen. dis. Lyra zen. dist. Aquilla 49° 2 30) 11° 0 30 Required correction= 1.62977 = 42′′ 63, N. B. By computation from the tabulated situations of these two stars, the real distance comes out 34° 11′ 42′′, being an error of only 1".37. EDIT, |