Letters on Astronomy / in which the Elements of the Science are Familiarly Explained in Connection with Biographical Sketches of the Most Eminent Astronomers

by Denison Olmsted

The situation of any place is known by its latitude and longitude. As charts of every ocean and sea are furnished to the sailor, in which are laid down the latitudes and longitudes of every point of land, whether on the shores of islands or the main, he has, therefore, only to ascertain his latitude and longitude at any particular place on the ocean, in order to find where he is, with respect to the nearest point of land, although this may be, and may always have been, entirely out of sight to him.

To determine the latitude of a place is comparatively an easy matter, whenever we can see either the sun or the stars. The distance of the sun from the zenith, when on the meridian, on a given day of the year, (which distance we may easily take with the sextant,) enables us, with the aid of the tables, to find the latitude of the place; or, by taking the altitude of the north star, we at once obtain the latitude.

The longitude of a place may be found by any method, by which we may ascertain how much its time of day differs from that of Greenwich at the same moment. A place that lies eastward of another comes to the meridian an hour earlier for every fifteen degrees of longitude, and of course has the hour of the day so much in advance of the other, so that it counts one o'clock when the other place counts twelve. On the other hand, a place lying westward of another comes to the meridian later by one hour for every fifteen degrees, so that it counts only eleven o'clock when the other place counts twelve. Keeping these principles in view, it is easy to see that a comparison of the difference of time between two places at the same moment, allowing fifteen degrees for an hour, sixty minutes for every four minutes of time, and sixty seconds for every four seconds of time, affords us an accurate mode of finding the difference of longitude between the two places. This comparison may be made by means of a chronometer, or from solar or lunar eclipses, or by what is called the lunar method of finding the longitude.

Chronometers are distinguished from clocks, by being regulated by means of a balance-wheel instead of a pendulum. A watch, therefore, comes under the general definition of a chronometer; but the name is more commonly applied to larger timepieces, too large to be carried about the person, and constructed with the greatest possible accuracy, with special reference to finding the longitude. Suppose, then, we are furnished with a chronometer set to Greenwich time. We arrive at New York, for example, and compare it with the time there. We find it is five hours in advance of the New-York time, indicating five o'clock, P.M., when it is noon at New York. Hence we find that the longitude of New York is 5×15=75 degrees.[11] The time at New York, or any individual place, can be known by observations with the transit-instrument, which gives us the precise moment when the sun is on the meridian.

It would not be necessary to resort to Greenwich, for the purpose of setting our chronometer to Greenwich time, as it might be set at any place whose longitude is known, having been previously determined. Thus, if we know that the longitude of a certain place is exactly sixty degrees east of Greenwich, we have only to set our chronometer four hours behind the time at that place, and it will be regulated to Greenwich time. Hence it is a matter of the greatest importance to navigation, that the longitude of numerous ports, in different parts of the earth, should be accurately determined, so that when a ship arrives at any such port, it may have the means of setting or verifying its chronometer.

This method of taking the longitude seems so easy, that you will perhaps ask, why it is not sufficient for all purposes, and accordingly, why it does not supersede the move complicated and laborious methods? why every sailor does not provide himself with a chronometer, instead of finding his longitude at sea by tedious and oft-repeated calculations, as he is in the habit of doing? I answer, it is only in a few extraordinary cases that chronometers have been constructed of such accuracy as to afford results as exact as those obtained by the other methods, to be described shortly; and instruments of such perfection are too expensive for general use among sailors. Indeed, the more common chronometers cost too much to come within the means of a great majority of sea-faring men. Moreover, by being transported from place to place, chronometers are liable to change their rate. By the rate of any timepiece is meant its deviation from perfect accuracy. Thus, if a clock should gain one second per day, one day with another, and we should find it impossible to bring it nearer to the truth, we may reckon this as its rate, and allow for it in our estimate of the time of any particular observation. If the error was not uniform, but sometimes greater and sometimes less than one second per day, then the amount of such deviation is called its "variation from its mean rate." I introduce these minute statements, (which are more precise than I usually deem necessary,) to show you to what an astonishing degree of accuracy chronometers have in some instances been brought. They have been carried from London to Baffin's Bay, and brought back, after a three years' voyage, and found to have varied from their mean rate, during the whole time, only a second or two, while the extreme variation of several chronometers, tried at the Royal Observatory at Greenwich, never exceeded a second and a half. Could chronometers always be depended on to such a degree of accuracy as this, we should hardly desire any thing better for determining the longitude of different places on the earth. A recent determination of the longitude of the City Hall in New York, by means of three chronometers, sent out from London expressly for that purpose, did not differ from the longitude as found by a solar eclipse (which is one of the best methods) but a second and a quarter.

Eclipses of the sun and moon furnish the means of ascertaining the longitude of a place, because the entrance of the moon into the earth's shadow in a lunar eclipse, and the entrance of the moon upon the disk of the sun in a solar eclipse, are severally examples of one of those instantaneous occurrences in the heavens, which afford the means of comparing the times of different places, and of thus determining their differences of longitude. Thus, if the commencement of a lunar eclipse was seen at one place an hour sooner than at another, the two places would be fifteen degrees apart, in longitude; and if the longitude of one of the places was known, that of the other would become known also. The exact instant of the moon's entering into the shadow of the earth, however, cannot be determined with very great precision, since the moon, in passing through the earth's penumbra, loses its light gradually, so that the moment when it leaves the penumbra and enters into the shadow cannot be very accurately defined. The first contact of the moon with the sun's disk, in a solar eclipse, or the moment of leaving it,—that is, the beginning and end of the eclipse,—are instants that can be determined with much precision, and accordingly they are much relied on for an accurate determination of the longitude. But, on account of the complicated and laborious nature of the calculation of the longitude from an eclipse of the sun, (since the beginning and end are not seen at different places, at the same moment,) this method of finding the longitude is not adapted to common use, nor available at sea. It is useful, however, for determining the longitude of fixed observatories. The lunar method of finding the longitude is the most refined and accurate of all the modes practised at sea. The motion of the moon through the heavens is so rapid, that she perceptibly alters her distance from any star every minute; consequently, the moment when that distance is a certain number of degrees and minutes is one of those instantaneous events, which may be taken advantage of for comparing the times of different places, and thus determining their difference of longitude. Now, in a work called the 'Nautical Almanac,' printed in London, annually, for the use of navigators, the distance of the moon from the sun by day, or from known fixed stars by night, for every day and night in the year, is calculated beforehand. If, therefore, a sailor wishes to ascertain his longitude, he may take with his sextant the distance of the moon from one of these stars at any time,—suppose nine o'clock, at night,—and then turn to the 'Nautical Almanac,' and see what time it was at Greenwich when the distance between the moon and that star was the same. Let it be twelve o'clock, or three hours in advance of his time: his longitude, of course, is forty-five degrees west.

This method requires more skill and accuracy than are possessed by the majority of seafaring men; but, when practised with the requisite degree of skill, its results are very satisfactory. Captain Basil Hall, one of the most scientific commanders in the British navy, relates the following incident, to show the excellence of this method. He sailed from San Blas, on the west coast of Mexico, and, after a voyage of eight thousand miles, occupying eighty-nine days, arrived off Rio de Janeiro, having, in this interval, passed through the Pacific Ocean, rounded Cape Horn, and crossed the South Atlantic, without making any land, or even seeing a single sail, with the exception of an American whaler off Cape Horn. When within a week's sail of Rio, he set seriously about determining, by lunar observations, the precise line of the ship's course, and its situation at a determinate moment; and having ascertained this within from five to ten miles, ran the rest of the way by those more ready and compendious methods, known to navigators, which can be safely employed for short trips between one known point and another, but which cannot be trusted in long voyages, where the moon is the only sure guide. They steered towards Rio Janeiro for some days after taking the lunars, and, having arrived within fifteen or twenty miles of the coast, they hove to, at four in the morning, till the day should break, and then bore up, proceeding cautiously, on account of a thick fog which enveloped them. As this cleared away, they had the satisfaction of seeing the great Sugar-Loaf Rock, which stands on one side of the harbor's mouth, so nearly right ahead, that they had not to alter their course above a point, in order to hit the entrance of the harbor. This was the first land they had seen for three months, after crossing so many seas, and being set backwards and forwards by innumerable currents and foul winds. The effect on all on board was electric; and the admiration of the sailors was unbounded. Indeed, what could be more admirable than that a man on the deck of a vessel, by measuring the distance between the moon and a star, with a little instrument which he held in his hand, could determine his exact place on the earth's surface in the midst of a vast ocean, after having traversed it in all directions, for three months, crossing his track many times, and all the while out of sight of land?

The lunar method of finding the longitude could never have been susceptible of sufficient accuracy, had not the motions of the moon, with all their irregularities, been studied and investigated by the most laborious and profound researches. Hence Newton, while wrapt in those meditations which, to superficial minds, would perhaps have appeared rather curious than useful, inasmuch as they respected distant bodies of the universe which seemed to have little connexion with the affairs of this world, was laboring night and day for the benefit of the sailor and the merchant. He was guiding the vessel of the one, and securing the merchandise of the other; and thus he contributed a large share to promote the happiness of his fellow-men, not only in exalting the powers of the human intellect, but also in preserving the lives and fortunes of those engaged in navigation and commerce. Principles in science are rules in art; and the philosopher who is engaged in the investigation of these principles, although his pursuits may be thought less practically useful than those of the artisan who carries out those principles into real life, yet, without the knowledge of the principles, the rules would have never been known. Studies, therefore, the most abstruse, are, when viewed as furnishing rules to act, often productive of the highest practical utility.

Since the tides are occasioned by the influence of the sun and moon, I will conclude this Letter with a few remarks on this curious phenomenon. By the tides are meant the alternate rising and falling of the waters of the ocean. Its greatest and least elevations are called high and low water; its rising and falling are called flood and ebb; and the extraordinary high and low tides that occur twice every month are called spring and neap tides. It is high or low tide on opposite sides of the globe at the same time. If, for example, we have high water at noon, it is also high water to those who live on the meridian below us, where it is midnight. In like manner, low water occurs simultaneously on opposite sides of the meridian. The average amount of the tides for the whole globe is about two and a half feet; but their actual height at different places is very various, sometimes being scarcely perceptible, and sometimes rising to sixty or seventy feet. At the same place, also, the phenomena of the tides are very different at different times. In the Bay of Fundy, where the tide rises seventy feet, it comes in a mighty wave, seen thirty miles off, and roaring with a loud noise. At the mouth of the Severn, in England, the flood comes up in one head about ten feet high, bringing certain destruction to any small craft that has been unfortunately left by the ebbing waters on the flats and as it passes the mouth of the Avon, it sends up that small river a vast body of water, rising, at Bristol, forty or fifty feet.