To save the trouble of referring to the Nautical Almanac for setting the index on the distance, it will be more convenient to bring the objects to lap a little; then screw in the telescope, and they will be found with ease in the field of the telescope. Explanation of the Principles by which Lunar Distances are cleared from the Effects of Parallax and Refraction. WITH a little reflection it will be conceived that neither parallax nor refraction can alter the angle ZD, fig. 15: for the sun, whether seen at or at D, and the moon, whether seen ator T, in the heavens, will be in the same point of the compass, and affected only by their altitudes, which affects the distance. The apparent distance, the sun and moon's apparent zenith distance, together with the horizontal parallax, are given to find the true distance. The triangle (ZO corresponds to the apparent distance of the sun and moon, and their apparent zenith distances. The apparent zenith distances, DZ and OZ, must now be corrected for parallax and refraction, to find their true zenith distance. It has been already observed, that to a spectator on the surface, the moon's altitude appears more depressed, and the sun's altitude more elevated, than they really are. The correction of the moon's altitude, therefore, is always additive to her apparent altitude, and the sun's correction is always subtractive, as he is more elevated by refraction than depressed by parallax. Here two cases of oblique spherical triangles must be computed, before the distance can be corrected, and the true distance found. To work by this method would be only perplexing; it is merely inserted to explain the principle on which the apparent distance of the sun and moon, or moon and star, is cleared of the effects of parallax and refraction. It will be seen, by fig. 15, that the line D is the apparent distance, and TD the true distance. On Rating a Chronometer. IN rating a chronometer it is absolutely necessary to know whether or not it has altered its rate of going whilst under trial. If it should, all the observations must be rejected which were made before the alteration took place, retaining only those made afterwards. Should there be no material alteration in its rate, during the time of trial, take the difference between the time it was too fast or too slow, on the first day of observation, and what it was too fast or too slow on the last day, if they be the same: that is, both fast, or both slow. But add them together, if two fast in one instance, and too slow in the other. This sum or difference being divided by the number of days elapsed between the first and last observation, the quotient will be the numher of seconds and parts of seconds that it gains or loses per day. If the chronometer be faster at the end of the trial than at the beginning, of course its rate is gaining; but losing if it be slower. Those who choose chronometers should be careful to observe that the minutes on the dial-plate be equally divided, otherwise it will be difficult to rate them. The second hand will vary when the minute hand comes to each minute; and it is most likely that such chronometers as are not equally divided on the dial-plate are good for nothing. It matters not whether the second hand be on the 60 at each minute, or not, provided it always be on the same second. I had a chronometer to rate by one of which the dial-plate was equally divided; and the method I pursued was to compare them each day, at the same hour and minute; but this could not be done when rating it by the sun's altitude. The Uncertainty of finding a new Rate of a Chronometer on making Land by its known Longitude. SOME have asserted that whenever a ship touches at a port, or arrives off any headland or island, of which the longitude is known, a new rate of the time-keeper may be obtained. In or der to warn persons against being misled by this mistaken idea, I invite attention to the following remarks. Suppose a ship to sail from a port in the United States, bound to Canton. If she makes the island of St. Paul's in the Indian Ocean, in sixty days, when it is discovered that the longitude shown by time-keeper is thirty miles wrong, or that it has erred 24 On Rating a Chronometer. two minutes in time, it is plain to every one, that if the timekeeper altered its rate immediately on leaving port, and continued to go uniformly afterwards, it must have altered its rate exactly two seconds a day. If it did not alter its rate till onethird of the time had elapsed, and went uniformly afterwards, it must have altered its rate three seconds a day. If it did not alter its rate till half the time was expired, it must have altered its rate four seconds a day. If not till two-thirds of the time were elapsed, it must have altered its rate six seconds a day; and if not till the day before the ship arrived off the island of St. Paul's, it must have altered its rate two minutes a day. Now, if we conceive the time-keeper to have altered its rate gradually (which would be most probable) or admit the probability that it might have gone first faster, and afterwards slower, or first slower, and afterwards faster, than it was going at the commencement of the voyage, the quantity of a rate obtained as above could not be computed, as a due allowance could not be made for the variations of the time-keeper. I have proved the variations of several time keepers, which I have had under trial to rate. Some of them I have found to go uniformly for a time, and afterwards to change their rate suddenly. After their changes I commenced new trials. See example of rating a chronometer at Whampoa, on board the ship William Savary, of Philadelphia, in the following pages. It has already been mentioned, that observations for rating a chronometer ought to be taken either uniformly in the forenoon or uniformly in the afternoon, because the refraction of the forenoon differs from that of the afternoon. The best time for taking these observations is when the sun bears as nearly as possible either due east or west; but not when it is less than eight or ten degrees high. But if observations should be made both morning and afternoon on each day, too much confidence must not be placed in them, made at those altitudes, if there should be any material difference between the heights of the thermometer, at the times of the morning's and afternoon's ubservations; and, indeed, observations taken at those altitudes, even if taken only in the morning, or in the afternoon of each day uniformly, if there should be any material difference in the heights of the thermometer at each time of observation, too much confidence cannot be placed in them so taken, as the dif. ference of temperature of the atmosphere varies the refraction with low altitudes. These remarks apply only to the rating of chronometers, as in that particular great precision is required. The following will show the mode I took to rate a chronometer in 1819. Rate of Baraud's Chronometer, No. 748. Liverpool, 1819. Gaining a little more than two seconds per day from 24th July 1819. In the foregoing example all the gainings, and all the losings, during the forty-eight days, the chronometer was under trial, were added up separately, and the difference of the sums taken, which made its rate more than half a second gain per day. EXAMPLE. I took an altitude of the sun with the artificial horizon on the 24th July 1819, which was the last day of trial, by which I made the apparent time, Equation from Nautical Almanac, 24th July 1819, Mean time at Liverpool, 24th July 1819, Mean time at Greenwich, 4h 2' 22' 6 7 The constant error is to be applied to the time by chronometer each time of observation, for finding the longitude by it, and in this case it is subtractive from the time shown by chro nometer. The following will show an example different from the former, being the mode I pursued to rate the same chronometer on board the ship William Savary, then lying at anchor at Whampoa. Finding from the foregoing that an alteration took place on the 27th of February, I commenced a new trial, from the 28th of that month until the 20th of March; which being twenty days, and the difference being nearly regular during that time, I subtracted what the chronometer was too slow on the 28th of February, from what it was too slow on the 20th of March, and divided the difference by twenty, the number of days elapsed. On the 28th February it was slow of Whampoa mean time, On the 20th March it was slow of ditto 7h 50' 30" 7 51 13 43 The difference of forty-three seconds gives two seconds and one-tenth the chronometer loses. |