tend no further than 30 miles adjoining to the coast, the proposer should have no more than half the rewards. The act also appoints the first Lord of the Admiralty, the Speaker of the House of Commons, the first Commissioner of Trade, the Admirals of the Red, White and Blue Squadrons, the Master of Trinity House, the President of the Royal Society, the Royal Astronomer at Greenwich, the two Savilian Professors at Oxford, and the Lucasian and Plumian Professors at Cambridge, with several other persons, as Commissioners for the Longitude at Sea. The Lowndian Professor at Cambridge was afterwards added. After this act of parliament, several other acts passed in the reigns of GEORGE II and III, for the encouragement of finding the longitude. At last, in 1774, an act passed, repealing all other acts, and offering separate rewards to any person who should discover the longitude, either by the watch keeping true time within certain limits, or by the lunar method, or by any other means. The act pro poses as a reward for a time-keeper, for finding the longitude at sea, though not within the above limits. Provided however, that if such person or persons shall afterwards make any further discovery as to come within the abovementioned limits, such sum or sums as they may have received, shall be consi dered as part of such greater re ward, and deducted therefrom ac cordingly. 189. After the decease of Mr. FLAMSTEAD, Dr. HALLEY, who was appointed to succeed him, made a series of observations on the moon's transit over the meridian, for a complete revolution of the moon's apogee, which observations being compared with the computations from the tables then extant, he was enabled to correct the tables of the moon's motions. And as Mr. HADLEY had then invented an instrument by which the altitudes and distances of the heavenly bodies could be taken at sea, Dr. HALLEY strongly recommend ed the lunar method of finding the longitude. TIME-KEEPER. the sum of 5000/. if it determine the TO FIND THE LONGITUDE BY A longitude to 1° or 60 geographical miles; the sum of 7,5001. if it determine it to 40 miles; and the sum of 10,000/. if it determine it to 30 miles, after proper trials specified in the act. If the method be by improved solar and lunar tables, constructed upon Sir I. NEWTON's Theory of Gravitation, the author shall be entitled to 5000/. if such tables shall show the distance of the moon from the sun and stars, within fifteen seconds of a degree, answering to about seven minutes of longitude, after allowing half a degree for the errors of observation. And for any other method, the same rewards are offered as those for timekeepers, provided it gives the longitude true within same limits, and be practicable at sea. The commissioners have also a power of giving smaller rewards, as they shall judge proper, to any ene who shall make any discovery 190. The sun appears to move round the earth from east to west, or to describe 360°, in 24 hours, and therefore he appears to move 15° in an hour. If therefore the meridians of two places, make an angle of 15° with each other, or if the two places differ 15° in longitude, the sun will come to the eastern meridian 1 hour before it comes to the western meridian, and therefore when it is 12 o'clock at the former place, it is only 11 at the latter; and in general, the difference between the times by the clock at any two places, will be the difference of their longitudes, converted into time at the rate of 15° for an hour, the time at the eastern place being the forwardest. If therefore we can tell what o'clock it is at any two places, at the same instant of time, we can find the difference of their longitudes, by allowing 15° for every hour that the clocks differ. 191. Let therefore the timekeeper be well regulated and set to the time at Greenwich, that being the place from which we reckon our longitude; then if the watch neither gains nor loses, it will always show the time at Greenwich, wherever you may be. Now to find the time by the clock at any other place, take the sun's altitude, and thence find the time by article 61; now the time thus found is apparent time, or that found by the sun, which differs from the time shown by the clock by the equation of time, as we have shown in article 79; we must therefore apply the equation of time to the time found by the sun, and we shall get the time by the clock; and the difference between the time by the clock so found, and the time by the time-keeper, or the time at Greenwich, converted into degrees at the rate of 15° for an hour, gives the longitude of the place from Greenwich. For example, let the time by the time-keeper, when the sun's altitude was taken, be 6h. 19', and let the time deduced from the sun's altitude be 9h. 27', and suppose at that time the equation of time to be 7', showing how much the sun is that day behind the clock, then the time by the clock is, 9h. 34', the difference between which and 6h. 1 is 3h. 15'; and this converted into degrees, at the rate of 15° for 1 hour, gives 48°. 45′. the longitude of the place from Greenwich; and as the time is forwarder than that at Greenwich, the place lies to the east of Greenwich. Thus the longitude could be very easily determined, if you could depend upon the time-keeper. But as a watch will always gain or lose, before the timekeeper is sent out, its gaining or losing every day for some time, a month for instance, is observed; this is called the rate of going of the watch, and from thence the mean rate of going is thus found. 192. Suppose I examine the rate of a watch for 30 days; on some of those days I find it has gained, and on some it has lost; add together all the quantities it has gained, and suppose they amount to 17"; add together all the quantities it has lost, and suppose they amount to 13", then, upon the whole, it has gained 4" in 30 days, and this is called the mean rate for that time, and this divided by 30, gives 133 for the mean daily rate of gaining; so that if the watch had gained regularly ',133 every day, at the end of the 30 days it would have gained just as much as it really did gain, by sometimes gaining and sometimes losing. Or you may get the mean daily rate thus. Take the difference between what the clock was too fast, or too slow, on the first and last days of observation, if it be too fast, or too slow, on each day; but take the sum, if it be too fast on one day and too slow on the other, and divide by the number of days between the observations, and you get the mean daily rate. Thus, if the watch was too fast on the first day 18", and too fast on the last day 32′′, the difference 14′′ divided by 30 gives 0,466 the mean daily rate of gaining. But if the watch was too fast on the first day 7", and too slow on the last day 10", the sum 17" divided by 30 gives 0",566 the mean daily rate of losing. After having thus got the mean daily rate of gaining or losing, and knowing how much the watch was too fast or too slow at first, you can tell, according to that rate of going, how much it is too fast or too slow, at any other time. In the first case, for instance, let the watch have been 1'. 17" too fast at first, and I want to know how much it is too fast 50 days after that time; now it gains 0,133 every day, if this be multiplied by 50 it gives 6" ,65 for the whole gain in 50 days; therefore at the end of that time the watch would be 1'. 23′′,65 too fast. This would be the error, if the watch continued to gain at the which is deduced from a lunar ob servation, till you can get another. Thus the watch may be rendered of great service in navigation. above rate; and although, from the 193. As the rate of going of a FIND THE LONGITUDE BY AN ECLIPSE OF THE MOON, AND OF JUPITER'S SATEL LITES. 195. By an eclipse of the moon. This eclipse begins when the umbra of the earth first touches the moon, and ends when it leaves the moon. Having the times calculated when the eclipse begins and ends at Greenwich, observe the times when it begins and ends at the place where you are; and the difference of these times, converted into degrees, gives the difference of the longitudes. For as the phases of the moon in an eclipse, happen at the same instant at all places, the difference of the times at different places when the same phase is observed, arises from the difference of the clocks at those places, and that difference (as before observed) converted into degrees, gives the difference of longitudes. If the beginning of an eclipse happen at 6 o'clock at one place, and at 8 o'clock at another, these places differ 2 hours, or 30°, in longitude. This would be a very ready and accurate method, if the times of the first and last contact of the earth's umbra and the moon could be accurately observed; but the darkness of the penumbra continues to increase till it comes to the umbra, so that until the umbra actually gets upon the moon, it is not discovered. The umbra itself is also badly defined. The beginning and end of a lunar eclipse, cannot, in general, be determined nearer than 1' of time, and often not nearer than 2′ or 3′. Upon these accounts, the longitude, thus deduced, is subject to a considerable degree of uncertainty. Astronomers therefore determine the difference of longitudes of two places, by corresponding observa tions of other phases, that is, when the umbra bisects any spots upon the surface. And this can be determined to a greater degree of accuracy, than the beginning and end; for when the umbra is got upon the moon's surface, the observer has leisure to consider and fix upon the proper line of termination, in which he will be assisted by running his eye along the circumference of the umbra. Thus the coincidence of the umbra with the spots, may be observed to a considerable degree of accuracy. The observer therefore should have a good map of the moon at hand, that he may not mistake. The telescope to observe a lunar eclipse, should have but a small magnifying power with a great quantity of light. The shadow comes upon the moon on the east side, and goes off on the west; but if the telescope invert, the appearance will be the con trary. 196. Thee clipses of jupiter's sa tellites afford the readiest method of determining the longitude of places upon land. It was also hoped, that some method might be invented to observe them at sea, and Mr. InWIN made a chair to swing for that purpose, for the observer to sit in; but Dr. MASKELYNE, in a voyage to Barbadoes, under the direction of the commissioners of longitude, found it totally impracticable to derive any benefit from it; and he observes, that "considering the great power requisite in a telescope for making these observations well, and the violence as well as the irregularities of the motion of the ship, I am afraid the complete management of a telescope on ship board, will always remain among the desiderata. However, I would not be understood to mean to discourage any attempt, founded on good principles, to get over the dificulty." The telescopes proper for making these observations, are common refracting ones from 15 to 20 feet; reflecting ones of 18 inches or 2 feet; or the 46 inches achromatic. On account of the uncertainty of the theory of the satellites, Dr. MasKELYNE advises the observer to be settled at his telescope, 3 minutes before the expected time of immersion of the first satellite; 6′ or s before that of the second or third; and a quarter of an hour before that of the fourth. And if the longitude of the place be also uncertain, he must look out proportionably sooner. Thus, if the longitude be uncertain to 2°, answering to 8 minutes of time, he must begin to look out 3 minutes sooner than is mentioned above. However, when he has observed one eclipse and found the error of the tables, he may allow the same correction to the calculations of the Ephemeris for several months, which will advertise him very nearly of the time of expecting the eclipses of the same satellite, and dispense with his attending so long. Before the opposition of jupiter to the sun, the immersions and emersions happen on the west side of jupiter; and after opposition, on the east side; but if the telescope invert, the appearance will be the contrary. Before opposition, the immersions only of the first satellite are visible; and after opposition, the emersions only. The same is generally the case in respect to the second, satellite; but both immersion and emersion are frequently observed in the third and fourth. 197. When the observer is waiting for an emersion, as soon as he suspects that he sees it, he should look at his watch and note the second; or begin to count the beats of the clock, till he is sure it is the satellite, and then look at the clock and subtract the number of seconds which he has counted, and he will have the time of emersion. If jupiter be & above the horizon, and the sun as much below, an eclipse will be visible; this may be deter mined near enough by a common `giole. 193. The emersion or immersion being observed according to apparent time, the longitude of the place from Greenwich is found, by taking the difference between that time and the time set down in the Nautical Almanac, which is calculated for apparent time. Ex. Suppose the emersion of a satellite to have been observed at the Cape of Good Hope, May 9, 1767, at 10h. 46'. 45" apparent time; now the time in the Nautical Almanac is 9h. 33. 12"; the difference of which time is 1h. 13'. 33" the longitude of the Cape east of Greenwich in time, or 18°. 23'. 15". 199. But to find the longitude of a place from an observation of an eclipse of a satellite, it is better to compare it with an observation made under some well-known meridian, than with the calculations in the Ephemeris, because of the imperfection of the theory; but where a corresponding observation cannot be obtained, find what correction the calculations in the Ephemeris require, by the nearest observations to the given time that can be obtained; and this correction applied to the calculation of the eclipse in the Ephemeris, renders it almost equivalent to an actual observation. The observer must be careful to regulate his clock or watch to apparent time, or at least to know the difference. 200. In order the better to know the difference of longitudes of two places, from corresponding observations, the observer should be furnished with the same kind of telescopes. For at an immersion, as the satellite enters the shadow, it grows fainter and fainter, till at last the quantity of light is so small that it becomes invisible, even before it is wholly immersed in the shadow; the instant therefore that it becomes invisible will depend upon the quantity of light which the telescope receives, and its magnifying power. The instant therefore of its appearance will be later, the better the telescope is; and the sooner it will appear at its emersion. Now the immersion is the instant the satel lite is got into the shadow, and the emersion is the instant before it begins to emerge from the shadow; if therefore two telescopes show the disappearance or appearance of the satellite at the same distance of time from the immer sion or emersion, the difference of the times will be the same as the difference of the true times of immersion or emersion, and therefore will show the difference of longitudes accurately. But if the observ. ed time at one place and the computed time at another be compared, we must allow for the difference of the apparent and true times of immersion and emersion, in order to get the true time where the obser vation was made, to compare with the true time from computation at the other place. This difference may be found, by observing an eclipse at any place whose longitude is known, and comparing it with the time by computation. Observers, therefore, should settle the difference by the mean of a great number of observations thus compared with the computations, by which means the longitude will be more accurately ascertained. After all, however, the different states of the air, and of the eye, will cause some uncertainty; but the latter may in a great measure be obviated, if the observer remove himself from all warmth and light, for a little time before he observes. ΤΟ FIND THE 201. The steps by which we find the longitude by this method, are these: 1. From the observed altitudes of the moon and the sun, or a star, and their observed distance, find their true distance. 2. From the Nautical Almanac find the apparent time at Greenwich when the moon was at that distance. |