Letters on Astronomy Part 11

The Athenians adopted the metonic cycle four hundred and thirty-three years before the Christian era, for the regulation of their calendars, and had it inscribed in letters of gold on the walls of the temple of Minerva. Hence the term _golden number_, still found in our almanacs, which denotes the year of the lunar cycle. Thus, fourteen was the golden number for 1837, being the fourteenth year of the lunar cycle.

The inequalities of the moon's motions are divided into periodical and secular. _Periodical_ inequalities are those which are completed in comparatively short periods. _Secular_ inequalities are those which are completed only in very long periods, such as centuries or ages. Hence the corresponding terms _periodical equations_ and _secular equations_.

As an example of a secular inequality, we may mention the acceleration of the _moon's mean motion_. It is discovered that the moon actually revolves around the earth in a less period now than she did in ancient times. The difference, however, is exceedingly small, being only about ten seconds in a century. In a lunar eclipse, the moon's longitude differs from that of the sun, at the middle of the eclipse, by exactly one hundred and eighty degrees; and since the sun's longitude at any given time of the year is known, if we can learn the day and hour when an eclipse occurred at any period of the world, we of course know the longitude of the sun and moon at that period. Now, in the year 721, before the Christian era, Ptolemy records a lunar eclipse to have happened, and to have been observed by the Chaldeans. The moon's longitude, therefore, for that time, is known; and as we know the mean motions of the moon, at present, starting from that epoch, and computing, as may easily be done, the place which the moon ought to occupy at present, at any given time, she is found to be actually nearly a degree and a half in advance of that place. Moreover, the same conclusion is derived from a comparison of the Chaldean observations with those made by an Arabian astronomer of the tenth century.

This phenomenon at first led astronomers to apprehend that the moon encountered a resisting medium, which, by destroying at every revolution a small portion of her projectile force, would have the effect to bring her nearer and nearer to the earth, and thus to augment her velocity.

But, in 1786, La Place demonstrated that this acceleration is one of the legitimate effects of the sun's disturbing force, and is so connected with changes in the eccentricity of the earth's...o...b..t, that the moon will continue to be accelerated while that eccentricity diminishes; but when the eccentricity has reached its minimum, or lowest point, (as it will do, after many ages,) and begins to increase, then the moon's motions will begin to be r.e.t.a.r.ded, and thus her mean motions will oscillate for ever about a mean value.

LETTER XVIII.

ECLIPSES.

----"As when the sun, new risen, Looks through the horizontal misty air, Shorn of his beams, or from behind the moon, In dim eclipse, disastrous twilight sheds On half the nations, and with fear of change Perplexes monarchs: darkened so, yet shone, Above them all, the Archangel."--_Milton._

HAVING now learned various particulars respecting the earth, the sun, and the moon, you are prepared to understand the explanation of solar and lunar eclipses, which have in all ages excited a high degree of interest. Indeed, what is more admirable, than that astronomers should be able to tell us, years beforehand, the exact instant of the commencement and termination of an eclipse, and describe all the attendant circ.u.mstances with the greatest fidelity. You have doubtless, my dear friend, partic.i.p.ated in this admiration, and felt a strong desire to learn how it is that astronomers are able to look so far into futurity. I will endeavor, in this Letter, to explain to you the leading principles of the calculation of eclipses, with as much plainness as possible.

An _eclipse of the moon_ happens when the moon, in its revolution around the earth, falls into the earth's shadow. An _eclipse of the sun_ happens when the moon, coming between the earth and the sun, covers either a part or the whole of the solar disk.

The earth and the moon being both opaque, globular bodies, exposed to the sun's light, they cast shadows opposite to the sun, like any other bodies on which the sun s.h.i.+nes. Were the sun of the same size with the earth and the moon, then the lines drawn touching the surface of the sun and the surface of the earth or moon (which lines form the boundaries of the shadow) would be parallel to each other, and the shadow would be a cylinder infinite in length; and were the sun less than the earth or the moon, the shadow would be an increasing cone, its narrower end resting on the earth; but as the sun is vastly greater than either of these bodies, the shadow of each is a cone whose base rests on the body itself, and which comes to a point, or vertex, at a certain distance behind the body. These several cases are represented in the following diagrams, Figs. 39, 40, 41.

[Ill.u.s.tration Figs. 39, 40, 41.]

It is found, by calculation, that the length of the moon's shadow, on an average, is just about sufficient to reach to the earth; but the moon is sometimes further from the earth than at others, and when she is nearer than usual, the shadow reaches considerably beyond the surface of the earth. Also, the moon, as well as the earth, is at different distances from the sun at different times, and its shadow is longest when it is furthest from the sun. Now, when both these circ.u.mstances conspire, that is, when the moon is in her perigee and along with the earth in her aphelion, her shadow extends nearly fifteen thousand miles beyond the centre of the earth, and covers a s.p.a.ce on the surface one hundred and seventy miles broad. The earth's shadow is nearly a million of miles in length, and consequently more than three and a half times as long as the distance of the earth from the moon; and it is also, at the distance of the moon, three times as broad as the moon itself.

An eclipse of the sun can take place only at new moon, when the sun and moon meet in the same part of the heavens, for then only can the moon come between us and the sun; and an eclipse of the moon can occur only when the sun and moon are in opposite parts of the heavens, or at full moon; for then only can the moon fall into the shadow of the earth.

[Ill.u.s.tration Fig. 42.]

The nature of eclipses will be clearly understood from the following representation. The diagram, Fig. 42, exhibits the relative position of the sun, the earth, and the moon, both in a solar and in a lunar eclipse. Here, the moon is first represented, while revolving round the earth, as pa.s.sing between the earth and the sun, and casting its shadow on the earth. As the moon is here supposed to be at her average distance from the earth, the shadow but just reaches the earth's surface. Were the moon (as is sometimes the case) nearer the earth her shadow would not terminate in a point, as is represented in the figure, but at a greater or less distance nearer the base of the cone, so as to cover a considerable s.p.a.ce, which, as I have already mentioned, sometimes extends to one hundred and seventy miles in breadth, but is commonly much less than this. On the other side of the earth, the moon is represented as traversing the earth's shadow, as is the case in a lunar eclipse. As the moon is sometimes nearer the earth and sometimes further off, it is evident that it will traverse the shadow at a broader or a narrower part, accordingly. The figure, however, represents the moon as pa.s.sing the shadow further from the earth than is ever actually the case, since the distance from the earth is never so much as one third of the whole length of the shadow.

It is evident from the figure, that if a spectator were situated where the moon's shadow strikes the earth, the moon would cut off from him the view of the sun, or the sun would be totally eclipsed. Or, if he were within a certain distance of the shadow on either side, the moon would be partly between him and the sun, and would intercept from him more or less of the sun's light, according as he was nearer to the shadow or further from it. If he were at _c_ or _d_, he would just see the moon entering upon the sun's disk; if he were nearer the shadow than either of these points, he would have a portion of this light cut off from his view, and more, in proportion as he drew nearer the shadow; and the moment he entered the shadow, he would lose sight of the sun. To all places between _a_ or _b_ and the shadow, the sun would cast a partial shadow of the moon, growing deeper and deeper, as it approached the true shadow. This partial shadow is called the moon's _penumbra_. In like manner, as the moon approaches the earth's shadow, in a lunar eclipse, as soon as she arrives at _a_, the earth begins to intercept from her a portion of the sun's light, or she falls in the earth's penumbra. She continues to lose more and more of the sun's light, as she draws near to the shadow, and hence her disk becomes gradually obscured, until it enters the shadow, when the sun's light is entirely lost.

As the sun and earth are both situated in the plane of the ecliptic, if the moon also revolved around the earth in this plane, we should have a solar eclipse at every new moon, and a lunar eclipse at every full moon; for, in the former case, the moon would come directly between us and the sun, and in the latter case, the earth would come directly between the sun and the moon. But the moon is inclined to the ecliptic about five degrees, and the centre of the moon may be all this distance from the centre of the sun at new moon, and the same distance from the centre of the earth's shadow at full moon. It is true, the moon extends across her path, one half her breadth lying on each side of it, and the sun likewise reaches from the ecliptic a distance equal to half his breadth.

But these luminaries together make but little more than a degree, and consequently, their two semidiameters would occupy only about half a degree of the five degrees from one orbit to the other where they are furthest apart. Also, the earth's shadow, where the moon crosses it, extends from the ecliptic less than three fourths of a degree, so that the semidiameter of the moon and of the earth's shadow would together reach but little way across the s.p.a.ce that may, in certain cases, separate the two luminaries from each other when they are in opposition.

Thus, suppose we could take hold of the circle in the figure that represents the moon's...o...b..t, (Fig. 42, page 197,) and lift the moon up five degrees above the plane of the paper, it is evident that the moon, as seen from the earth, would appear in the heavens five degrees above the sun, and of course would cut off none of his light; and it is also plain that the moon, at the full, would pa.s.s the shadow of the earth five degrees below it, and would suffer no eclipse. But in the course of the sun's apparent revolution round the earth once a year he is successively in every part of the ecliptic; consequently, the conjunctions and oppositions of the sun and moon may occur at any part of the ecliptic, and of course at the two points where the moon's...o...b..t crosses the ecliptic,--that is, at the nodes; for the sun must necessarily come to each of these nodes once a year. If, then, the moon overtakes the sun just as she is crossing his path, she will hide more or less of his disk from us. Since, also, the earth's shadow is always directly opposite to the sun, if the sun is at one of the nodes, the shadow must extend in the direction of the other node, so as to lie directly across the moon's path; and if the moon overtakes it there, she will pa.s.s through it, and be eclipsed. Thus, in Fig. 43, let BN represent the sun's path, and AN, the moon's,--N being the place of the node; then it is evident, that if the two luminaries at new moon be so far from the node, that the distances between their centres is greater than their semidiameters, no eclipse can happen; but if that distance is less than this sum, as at E, F, then an eclipse will take place; but if the position be as at C, D, the two bodies will just touch one another.

If A denotes the earth's shadow, instead of the sun, the same ill.u.s.tration will apply to an eclipse of the moon.

[Ill.u.s.tration Fig. 43.]

Since bodies are defined to be in conjunction when they are in the _same_ part of the heavens, and to be in opposition when they are in _opposite_ parts of the heavens, it may not appear how the sun and moon can be in conjunction, as at A and B, when they are still at some distance from each other. But it must be recollected that bodies are in conjunction when they have the same longitude, in which case they are situated in the same great circle perpendicular to the ecliptic,--that is, in the same secondary to the ecliptic. One of these bodies may be much further from the ecliptic than the other; still, if the same secondary to the ecliptic pa.s.ses through them both, they will be in conjunction or opposition.

In a total eclipse of the moon, its disk is still visible, s.h.i.+ning with a dull, red light. This light cannot be derived directly from the sun, since the view of the sun is completely hidden from the moon; nor by reflection from the earth, since the illuminated side of the earth is wholly turned from the moon; but it is owing to refraction from the earth's atmosphere, by which a few scattered rays of the sun are bent round into the earth's shadow and conveyed to the moon, sufficient in number to afford the feeble light in question.

It is impossible fully to understand the _method of calculating eclipses_, without a knowledge of trigonometry; still it is not difficult to form some general notion of the process. It may be readily conceived that, by long-continued observations on the sun and moon, the laws of their revolution may be so well understood, that the exact places which they will occupy in the heavens at any future times may be foreseen and laid down in tables of the sun and moon's motions; that we may thus ascertain, by inspecting the tables, the instant when these two bodies will be together in the heavens, or be in conjunction, and when they will be one hundred and eighty degrees apart, or in opposition.

Moreover, since the exact place of the moon's node among the stars at any particular time is known to astronomers, it cannot be difficult to determine when the new or full moon occurs in the same part of the heavens as that where the node is projected, as seen from the earth. In short, as astronomers can easily determine what will be the relative position of the sun, the moon, and the moon's nodes, for any given time, they can tell when these luminaries will meet so near the node as to produce an eclipse of the sun, or when they will be in opposition so near the node as to produce an eclipse of the moon.

A little reflection will enable you to form a clear idea of the situation of the sun, the moon, and the earth, at the time of a solar eclipse. First, suppose the conjunction to take place at the node; that is, imagine the moon to come _directly_ between the earth and the sun, as she will of course do, if she comes between the earth and the sun the moment she is crossing the ecliptic; for then the three bodies will all lie in one and the same straight line. But when the moon is in the ecliptic, her shadow, or at least the axis, or central line, of the shadow, must coincide with the line that joins the centres of the sun and earth, and reach along the plane of the ecliptic towards the earth.

The moon's shadow, at her average distance from the earth, is just about long enough to reach the surface of the earth; but when the moon, at the new, is in her apogee, or at her greatest distance from the earth, the shadow is not long enough to reach the earth. On the contrary, when the moon is nearer to us than her average distance, her shadow is long enough to reach beyond the earth, extending, when the moon is in her perigee, more than fourteen thousand miles beyond the centre of the earth. Now, as during the eclipse the moon moves nearly in the plane of the ecliptic, her shadow which accompanies her must also move nearly in the same plane, and must therefore traverse the earth across its central regions, along the terrestrial ecliptic, since this is nothing more than the intersection of the plane of the celestial ecliptic with the earth's surface. The motion of the earth, too, on its axis, in the same direction, will carry a place along with the shadow, though with a less velocity by more than one half; so that the actual velocity of the shadow, in respect to places over which it pa.s.ses on the earth, will only equal the difference between its own rate and that of the places, as they are carried forward in the diurnal revolution.

We have thus far supposed that the moon comes to her conjunction precisely at the node, or at the moment when she is crossing the ecliptic. But, secondly, suppose she is on the north side of the ecliptic at the time of conjunction, and moving towards her descending node, and that the conjunction takes place as far from the node as an eclipse can happen. The shadow will not fall in the plane of the ecliptic, but a little northward of it, so as just to graze the earth near the pole of the ecliptic. The nearer the conjunction comes to the node, the further the shadow will fall from the polar towards the equatorial regions.

In a solar eclipse, the shadow of the moon travels over a portion of the earth, as the shadow of a small cloud, seen from an eminence in a clear day, rides along over hills and plains. Let us imagine ourselves standing on the moon; then we shall see the earth partially eclipsed by the moon's shadow, in the same manner as we now see the moon eclipsed by the shadow of the earth; and we might calculate the various circ.u.mstances of the eclipse,--its commencement, duration, and quant.i.ty,--in the same manner as we calculate these elements in an eclipse of the moon, as seen from the earth. But although the general characters of a solar eclipse might be investigated on these principles, so far as respects the earth at large, yet, as the appearances of the same eclipse of the sun are very different at different places on the earth's surface, it is necessary to calculate its peculiar aspects for each place separately, a circ.u.mstance which makes the calculation of a solar eclipse much more complicated and tedious than that of an eclipse of the moon. The moon, when she enters the shadow of the earth, is deprived of the light of the part immersed, and the effect upon its appearance is the same as though that part were painted black, in which case it would be black alike to all places where the moon was above the horizon. But it not so with a solar eclipse. We do not see this by the shadow cast on the earth, as we should do, if we stood on the moon, but by the interposition of the moon between us and the sun; and the sun may be hidden from one observer, while he is in full view of another only a few miles distant. Thus, a small insulated cloud sailing in a clear sky will, for a few moments, hide the sun from us, and from a certain s.p.a.ce near us, while all the region around is illuminated. But although the a.n.a.logy between the motions of the shadow of a small cloud and of the moon in a solar eclipse holds good in many particulars, yet the velocity of the lunar shadow is far greater than that of the cloud, being no less than two thousand two hundred and eighty miles per hour.

The moon's shadow can never cover a s.p.a.ce on the earth more than one hundred and seventy miles broad, and the s.p.a.ce actually covered commonly falls much short of that. The portion of the earth's surface ever covered by the moon's penumbra is about four thousand three hundred and ninety-three miles.

The apparent diameter of the moon varies materially at different times, being greatest when the moon is nearest to us, and least when she is furthest off; while the sun's apparent dimensions remain nearly the same. When the moon is at her average distance from the earth, she is just about large enough to cover the sun's disk; consequently, if, in a central eclipse of the sun, the moon is at her mean distance, she covers the sun but for an instant, producing only a momentary eclipse. If she is nearer than her average distance, then the eclipse may continue total some time, though never more than eight minutes, and seldom so long as that; but if she is further off than usual, or towards her apogee, then she is not large enough to cover the whole solar disk, but we see a ring of the sun encircling the moon, const.i.tuting an _annular eclipse_, as seen in Fig. 44. Even the elevation of the moon above the horizon will sometimes sensibly affect the dimensions of the eclipse. You will recollect that the moon is nearer to us when on the meridian than when in the horizon by nearly four thousand miles, or by nearly the radius of the earth; and consequently, her apparent diameter is largest when on the meridian. The difference is so considerable, that the same eclipse will appear total to a spectator who views it near his meridian, while, at the same moment, it appears annular to one who has the moon near his horizon. An annular eclipse may last, at most, twelve minutes and twenty-four seconds.

[Ill.u.s.tration Fig. 44.]

Eclipses of the sun are more frequent than those of the moon. Yet lunar eclipses being visible to every part of the terrestrial hemisphere opposite to the sun, while those of the sun are visible only to a small portion of the hemisphere on which the moon's shadow falls, it happens that, for any particular place on the earth, lunar eclipses are more frequently visible than solar. In any year, the number of eclipses of both luminaries cannot be less than two nor more than seven: the most usual number is four, and it is very rare to have more than six. A total eclipse of the moon frequently happens at the next full moon after an eclipse of the sun. For since, in a solar eclipse, the sun is at or near one of the moon's nodes,--that is, is projected to the place in the sky where the moon crosses the ecliptic,--the earth's shadow, which is of course directly opposite to the sun, must be at or near the other node, and may not have pa.s.sed too far from the node before the moon comes round to the opposition and overtakes it. In total eclipses of the sun, there has sometimes been observed a remarkable radiation of light from the margin of the sun, which is thought to be owing to the zodiacal light, which is of such dimensions as to extend far beyond the solar orb. A striking appearance of this kind was exhibited in the total eclipse of the sun which occurred in June, 1806.

A total eclipse of the sun is one of the most sublime and impressive phenomena of Nature. Among barbarous tribes it is ever contemplated with fear and astonishment, and as strongly indicative of the displeasure of the G.o.ds. Two ancient nations, the Lydians and Medes, alluded to before, who were engaged in a b.l.o.o.d.y war, about six hundred years before Christ, were smitten with such awe, on the appearance of a total eclipse of the sun, just on the eve of a battle, that they threw down their arms, and made peace. When Columbus first discovered America, and was in danger of hostility from the Natives, he awed them into submission by telling them that the sun would be darkened on a certain day, in token of the anger of the G.o.ds at them, for their treatment of him.

Among cultivated nations, a total eclipse of the sun is recognised, from the exactness with which the time of occurrence and the various appearances answer to the prediction, as affording one of the proudest triumphs of astronomy. By astronomers themselves, it is of course viewed with the highest interest, not only as verifying their calculations, but as contributing to establish, beyond all doubt, the certainty of those grand laws, the truth of which is involved in the result. I had the good fortune to witness the total eclipse of the sun of June, 1806, which was one of the most remarkable on record. To the wondering gaze of childhood it presented a spectacle that can never be forgotten. A bright and beautiful morning inspired universal joy, for the sky was entirely cloudless. Every one was busily occupied in preparing smoked gla.s.s, in readiness for the great sight, which was to be first seen about ten o'clock. A thrill of mingled wonder and delight struck every mind when, at the appointed moment, a little black indentation appeared on the limb of the sun. This gradually expanded, covering more and more of the solar disk, until an increasing gloom was spread over the face of Nature; and when the sun was wholly lost, near mid-day, a feeling of horror pervaded almost every beholder. The darkness was wholly unlike that of twilight or night. A thick curtain, very different from clouds, hung upon the face of the sky, producing a strange and indescribably gloomy appearance, which was reflected from all things on the earth, in hues equally strange and unnatural. Some of the planets, and the largest of the fixed stars, shone out through the gloom, yet with their usual brightness. The temperature of the air rapidly declined, and so sudden a chill came over the earth, that many persons caught severe colds from their exposure. Even the animal tribes exhibited tokens of fear and agitation. Birds, especially, fluttered and flew swiftly about, and domestic fowls went to rest.

Indeed, the word _eclipse_ is derived from a Greek word, (= ekleipsis=, _ekleipsis_,) which signifies to fail, to faint or swoon away; since the moon, at the period of her greatest brightness, falling into the shadow of the earth, was imagined by the ancients to sicken and swoon, as if she were going to die. By some very ancient nations she was supposed, at such times, to be in pain; and, in order to relieve her fancied distress, they lifted torches high in the atmosphere, blew horns and trumpets, beat upon brazen vessels, and even, after the eclipse was over, they offered sacrifices to the moon. The opinion also extensively prevailed, that it was in the power of witches, by their spells and charms, not only to darken the moon, but to bring her down from her orbit, and to compel her to shed her baleful influences upon the earth.

In solar eclipses, also, especially when total, the sun was supposed to turn away his face in abhorrence of some atrocious crime, that either had been perpetrated or was about to be perpetrated, and to threaten mankind with everlasting night, and the destruction of the world. To such superst.i.tions Milton alludes, in the pa.s.sage which I have taken for the motto of this Letter.

The Chinese, who, from a very high period of antiquity, have been great observers of eclipses, although they did not take much notice of those of the moon, regarded eclipses of the sun in general as unfortunate, but especially such as occurred on the first day of the year. These were thought to forebode the greatest calamities to the emperor, who on such occasions did not receive the usual compliments of the season. When, from the predictions of their astronomers, an eclipse of the sun was expected, they made great preparation at court for observing it; and as soon as it commenced, a blind man beat a drum, a great concourse a.s.sembled, and the mandarins, or n.o.bility, appeared in state.

LETTER XIX.

LONGITUDE.--TIDES.

"First in his east, the glorious lamp was seen, Regent of day, and all the horizon round Invested with bright rays, jocund to run His _longitude_ through heaven's high road; the gray Dawn and the Pleiades before him danced, Shedding sweet influence."--_Milton._

THE ancients studied astronomy chiefly as subsidiary to astrology, with the vain hope of thus penetrating the veil of futurity, and reading their destinies among the stars. The moderns, on the other hand, have in view, as the great practical object of this study, the perfecting of the art of navigation. When we reflect on the vast interests embarked on the ocean, both of property and life, and upon the immense benefits that accrue to society from a safe and speedy intercourse between the different nations of the earth, we cannot but see that whatever tends to enable the mariner to find his way on the pathless ocean, and to secure him against its multiplied dangers, must confer a signal benefit on society.

In ancient times, to venture out of sight of land was deemed an act of extreme audacity; and Horace, the Roman poet, p.r.o.nounces him who first ventured to trust his frail bark to the stormy ocean, endued with a heart of oak, and girt with triple folds of bra.s.s. But now, the navigator who fully avails himself of all the resources of science, and especially of astronomy, may launch fearlessly on the deep, and almost bid defiance to rocks and tempests. By enabling the navigator to find his place on the ocean with almost absolute precision, however he may have been driven about by the winds, and however long he may have been out of sight of land, astronomers must be held as great benefactors to all who commit either their lives or their fortunes to the sea. Nor have they secured to the art of navigation such benefits without incredible study and toil, in watching the motions of the heavenly bodies, in investigating the laws by which their movements are governed, and in reducing all their discoveries to a form easily available to the navigator, so that, by some simple observation on one or two of the heavenly bodies, with instruments which the astronomer has invented, and prepared for his use, and by looking out a few numbers in tables which have been compiled for him, with immense labor, he may ascertain the exact place he occupies on the surface of the globe, thousands of miles from land.

The situation of any place is known by its lat.i.tude and longitude. As charts of every ocean and sea are furnished to the sailor, in which are laid down the lat.i.tudes and longitudes of every point of land, whether on the sh.o.r.es of islands or the main, he has, therefore, only to ascertain his lat.i.tude 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 _lat.i.tude_ 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 s.e.xtant,) enables us, with the aid of the tables, to find the lat.i.tude of the place; or, by taking the alt.i.tude of the north star, we at once obtain the lat.i.tude.

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 515=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 s.h.i.+p 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 astonis.h.i.+ng 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.