To find the constant Error. EXAMPLE. Whampoa, March 20th, 1820, I took an altitude of the sun with the artificial horizon, which was the last day of trial, which made the apparent time, afternoon, 4h 20' 10" Equation from Nautical Almanac, 20th March, add Mean time at Whampoa, 7 41 4 27 51 add 12 Longitude of Whampoa 113.25 E. in time, Mean time at Greenwich, by civil account, (and which is 20h 44' 11" on the 19th, by astronomical account) is on the 20th Time shown by chronometer, 16 27 51 7 33 40 A. M. 8 54 11 8 36 39 Slow of Greenwich time, and constant error, 17 32 N. B. In this case I add twelve hours instead of twenty-four, as hereafter directed. The Grand Ladrone, on the 8th of April, 1820, bearing due north, I observed the sun's altitude, which gave 3h 19' 2" P. M. apparent time, the equation reduced to Greenwich time being 1' 54" additive. Apparent time, add 3h 19' 2" 1 54 Rate of losing, 19 days, at 2" per day, Longitude in time, Which gives the longitude by chronometer, east, 113° 44' 00" And the grand Ladrone being in 113.44, shows the constant. rror and rate to be correct. To Rate a Chronometer by an Artificial Horizon. THE artificial horizon is a vessel filled with quicksilver, tar, molasses, or water, by which an observation may be obtained on shore with a sextant, when the altitude is not more than sixty degrees; and with a quadrant, when the altitude is not more than forty-five degrees. Remark. The quadrant, in such case, must have screens fixed to let down before the horizon glass, to screen the eye from the sun's glare. Find the sun's image in the artificial horizon, and bring the sun's image found by the instrument in contact with the image formed by the fluid, and you will obtain a double altitude. An artificial horizon has a floating glass, and a roof made of glass, to prevent the wind from disturbing the fluid. If tar, molasses, or water be used, without a screen, it must be put where the wind will not disturb it; and the molasses or tar must be first strained, to clear it of lumps. You must use half this angle shown on the arch of the instrument, and it must be corrected for semi-diameter, parallax, and refraction; but no dip must be allowed. If the nearest limbs are brought in contact, the semidiameter must be added; but if the farthest limbs be brought in contact, the semi-diameter must be subtracted. Half the index error must be used, when observing by the artificial horizon. Care should be taken that the glass covering the quicksilver does not adhere to the side of the vessel containing the quicksilver, which would throw it out of its horizontal position. The method I have adopted has been to level the dish, with a small quantity of quicksilver, by placing small pieces of paper under the lowest side. If this be first done, the floating glass will not adhere to the side, which will prevent error in the observation. I have used the roof formed of two plates of glass, the two sides of each being ground perfectly plain, and parallel to each other; but to prevent any bad effects, care must be taken to put the roof on the same way; that is, the same side towards the observer, every time he makes use of it, so that the observation be uniform. To know if the glasses are ground parallel to each other, look obliquely at some image reflected in the glass, as the roof of á house, &c. and if the object be in one, that is, if it look of its natural shape, without any double, or other imperfect appearance, the glasses are parallel and good. In a very still time, the roof may be made use of, without the floating glass, which will prevent error from the above cause. On Rating a Chronometer by the Artificial Horizon. 29 In rating a chronometer from the altitude of the sun, it ought to be done on the same side of the meridian; because the atmosphere in the morning is more dense than in the afternoon, the sun not having time to rarefy it; and of course the refraction in the morning will be greater than in the afternoon; so that if the altitude be sometimes observed in the forenoon, and at other times in the afternoon, they cannot be uniform. I have been at anchor at different places, when I found that my morning and afternoon observations made a difference of three, and sometimes four miles, in finding the longitude by the chronometer. Now, if the sun should rise or fall at the rate of twelve miles in a minute, then, if there should be a difference of four miles in the altitude between the morning and afternoon, it will occasion a difference of one-third of a minute in time, and one-third of a minute will occasion an error of five miles in longitude, and more or less in proportion to the difference in the altitude. If possible, the altitude ought to be taken as near the same time each day, or when the altitudes are about the same, which will make the index fall on the same part of the arch nearly. This will obviate any imperfections in the graduation of the arch of the instrument. If possible the same screens or glasses ought to be used; as they may sometimes make a difference of one mile in the altitude; and if the sun alter in altitude at the rate of twelve miles in a minute, the error will be onetwelfth of a minute in time, which is five seconds in time. This is trifling in finding the longitude, but in rating chronometers, it is of consequence, and I have found the least haze to make a difference of several seconds in time, from a comparison with altitudes taken but a few minutes before or after, when the atmosphere was perfectly clear. As the tangent screw of the sextant has a spring or elasticity, it is best to tighten it before the objects are quite in contact. This may prevent an error of a few seconds, either in the altitude taken by the artificial horizon, or when taking the distance. This is applicable when the distance and altitudes are decreasing: but if they be increasing, then the objects ought to be lapped a little; and the screw tightened. In both these cases wait till the objects come exactly in contact, and the observation will be made. Suppose the instrument showed forty degrees, forty minutes, and twenty seconds altitude of the sun, at four hours fifty minutes P. M. on the 20th of April, 1817, in longitude seventyfive west of Greenwich, latitude forty degrees forty minutes *This is when the altitude is not more than eight or ten degrees high. north, the index error thirty seconds additive, the half of which, fifteen seconds, is to be added to the altitude. " Double alt. 40 40 20 Sun's dec. April 20, 1817,11 29 30 Correction for 4h 50' from Half sum sine equal 36° 23' 28" H. angle, 9.77327 2 Hour angle, 72 46 56, which being reduced to time, at the rate of fifteen degrees to an hour; or, more briefly, by Table XIII, gives four hours, fifty-one minutes eight seconds, P.M. Apparent time, Longitude 75 west in time, Time at Greenwich, 4h 51' 08" 500 9 51 8 Equation April 20th, 1817 for noon at Greenwich, Equation for longitude, 75 west, 1' 6".9 5.2 1 12.1 Apparent time, 4h 51' 8" Equation, 1 12 On Rating a Chronometer by the Artificial Horizon. 31 Time by chronometer when the observation was taken, Mean time deduced from observation, Difference, 4h 49' 59" 4 49 56' 3 When the sun's altitude is observed in the forenoon the cosines of the four logarithms must be used in place of the sine as above. The observation must be repeated every day, when the sun is clear. See examples for rating the chronometer in Liverpool and Whampoa in the preceding pages. The most proper time for making these observations is when the sun is nearly due east or west. The rate of the chronometer is obtained this way; but the absolute time is not given by it, nor how much the chronometer is too slow or too fast for mean time at the meridian of Greenwich. This must be found by observing the altitude of the sun immediately before the ship sails, by the horizon of the sea, or double altitudes with the artificial horizon, if the former be open towards the east or west at the place of observation. Suppose off Cape Henlopen, seventy-five degrees west longitude, the mean time is found to be Longitude seventy-five west in time, Mean time at Greenwich, Time shown by Chronometer, Chronometer slow of Greenwich time, 4h 20' 10" 5 Which one hour ten minutes must be applied to the time by Suppose in seventy-five degrees of east longitude, Longitude seventy-five east in time, Mean time at Greenwich, Time by Chronometer, Chronometer too fast for Greenwich time, 6h afternoon. 1 subtract. 4 3 const, err. Suppose on the 20th May at 2 P. M. both by civil and astro omical time, longitude ninety degrees east. |