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 pa.s.sing 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 s.e.xtant 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, pa.s.sed 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 pa.s.ses the mouth of the Avon, it sends up that small river a vast body of water, rising, at Bristol, forty or fifty feet.
Tides are caused by the unequal attractions of the sun and moon upon different parts of the earth. Suppose the projectile force by which the earth is carried forward in her orbit to be suspended, and the earth to fall towards one of these bodies,--the moon, for example,--in consequence of their mutual attraction. Then, if all parts of the earth fell equally towards the moon, no derangement of its different parts would result, any more than of the particles of a drop of water, in its descent to the ground. But if one part fell faster than another, the different portions would evidently be separated from each other. Now, this is precisely what takes place with respect to the earth, in its fall towards the moon. The portions of the earth in the hemisphere next to the moon, on account of being nearer to the centre of attraction, fall faster than those in the opposite hemisphere, and consequently leave them behind. The solid earth, on account of its cohesion, cannot obey this impulse, since all its different portions const.i.tute one ma.s.s, which is acted on in the same manner as though it were all collected in the centre; but the waters on the surface, moving freely under this impulse, endeavor to desert the solid ma.s.s and fall towards the moon.
For a similar reason, the waters in the opposite hemisphere, falling less towards the moon than the solid earth does, are left behind, or appear to rise.
[Ill.u.s.tration Fig. 46.]
But if the moon draws the waters of the earth into an oval form towards herself, raising them simultaneously on the opposite sides of the earth, they must obviously be drawn away from the intermediate parts of the earth, where it must at the same time be low water. Thus, in Fig. 46, the moon, M, raises the waters beneath itself at Z and N, at which places it is high water, but at the same time depresses the waters at H and R, at which places it is low water. Hence, the interval between the high and low tide, on successive days, is about fifty minutes, corresponding to the progress of the moon in her orbit from west to east, which causes her to come to the meridian about fifty minutes later every day. There occurs, however, an intermediate tide, when the moon is on the lower meridian, so that the interval between two high tides is about twelve hours, and twenty-five minutes.
Were it not for the impediments which prevent the force from producing its full effects, we might expect to see the great tide-wave, as the elevated crest is called, always directly beneath the moon, attending it regularly around the globe. But the inertia of the waters prevents their instantly obeying the moon"s attraction, and the friction of the waters on the bottom of the ocean still further r.e.t.a.r.ds its progress. It is not, therefore, until several hours (differing at different places) after the moon has pa.s.sed the meridian of a place, that it is high tide at that place.
The _sun_ has an action similar to that of the moon, but only _one third_ as great. On account of the great ma.s.s of the sun, compared with that of the moon, we might suppose that his action in raising the tides would be greater than the moon"s; but the nearness of the moon to the earth more than compensates for the sun"s greater quant.i.ty of matter.
As, however, wrong views are frequently entertained on this subject, let us endeavor to form a correct idea of the advantage which the moon derives from her proximity. It is not that her actual amount of attraction is thus rendered greater than that of the sun; but it is that her attraction for the _different parts_ of the earth is very unequal, while that of the sun is nearly uniform. It is the _inequality_ of this action, and not the absolute force, that produces the tides. The sun being ninety-five millions of miles from the earth, while the diameter of the earth is only one twelve thousandth part of this distance, the effects of the sun"s attraction will be nearly the same on all parts of the earth, and therefore will not, as was explained of the moon, tend to separate the waters from the earth on the nearest side, or the earth from the waters on the remotest side, but in a degree proportionally smaller. But the diameter of the earth is one thirtieth the distance of the moon, and therefore the moon acts with considerably greater power on one part of the earth than on another.
As the sun and moon both contribute to produce the tides, and as they sometimes act together and sometimes in opposition to each other, so corresponding variations occur in the height of the tide. The _spring tides_, or those which rise to an unusual height twice a month, are produced by the sun and moon"s acting together; and the _neap tides_, or those which are unusually low twice a month, are produced by the sun and moon"s acting in opposition to each other. The spring tides occur at the syzygies: the neap tides at the quadratures. At the time of new moon, the sun and moon both being on the same side of the earth, and acting upon it in the same line, their actions conspire, and the sun may be considered as adding so much to the force of the moon. We have already seen how the moon contributes to raise a tide on the opposite side of the earth. But the sun, as well as the moon, raises its own tide-wave, which at new moon coincides with the lunar tide-wave. This will be plain on inspecting the diagram, Fig. 47, on page 220, where S represents the sun, C, the moon in conjunction, O, the moon in opposition, and Z, N, the tide-wave. Since the sun and moon severally raise a tide-wave, and the two here coincide, it is evident that a peculiarly high tide must occur when the two bodies are in conjunction, or at new moon. At full moon, also, the two luminaries conspire in the same way to raise the tide; for we must recollect that each body contributes to raise a tide on the opposite side. Thus, when the sun is at S and the moon at O, the sun draws the waters on the side next to it away from the earth, and the moon draws the earth away from the waters on that side; their united actions, therefore, conspire, and an unusually high tide is the result.
On the side next to O, the two forces likewise conspire: for while the moon draws the waters away from the earth, the sun draws the earth away from the waters. In both cases an unusually low tide is produced; for the more the water is elevated at Z and N, the more it will be depressed at H and R, the places of low tide.
[Ill.u.s.tration Fig. 47.]
Twice a month, also, namely, at the quadratures of the moon, the tides neither rise so high nor fall so low as at other times, because then the sun and moon act against each other. Thus, in Fig. 48, while F tends to raise the water at Z, S tends to depress it, and consequently the high tide is less than usual. Again, while F tends to depress the water at R, S tends to elevate it, and therefore the low tide is less than usual.
Hence the difference between high and low water is only half as great at neap as at spring tide. In the diagrams, the elevation and depression of the waters is represented, for the sake of ill.u.s.tration, as far greater than it really is; for you must recollect that the average height of the tides for the whole globe is only about two and a half feet, a quant.i.ty so small, in comparison with the diameter of the earth, that were the due proportions preserved in the figures, the effect would be wholly insensible.
[Ill.u.s.tration Fig. 48.]
The variations of distance in the sun are not great enough to influence the tides very materially, but the variations in the moon"s distances have a striking effect. The tides which happen, when the moon is in perigee, are considerably greater than when she is in apogee; and if she happens to be in perigee at the time of the syzygies, the spring tides are unusually high.
The motion of the tide-wave is not a _progressive_ motion, but a mere undulation, and is to be carefully distinguished from the currents to which it gives rise. If the ocean completely covered the earth, the sun and moon being in the equator, the tide-wave would travel at the same rate as the earth revolves on its axis. Indeed, the correct way of conceiving of the tide-wave, is to consider the moon at rest, and the earth, in its rotation from west to east, as bringing successive portions of water under the moon, which portions being elevated successively, at the same rate as the earth revolves on its axis, have a relative motion westward, at the same rate.
The tides of rivers, narrow bays, and sh.o.r.es far from the main body of the ocean, are not produced in those places by the direct action of the sun and moon, but are subordinate waves propagated from the great tide-wave, and are called _derivative_ tides, while those raised directly by the sun and moon are called _primitive_ tides.
[Ill.u.s.tration Fig. 49.]
The velocity with which the tide moves will depend on various circ.u.mstances, but princ.i.p.ally on the depth, and probably on the regularity, of the channel. If the depth is nearly uniform the tides will be regular; but if some parts of the channel are deep while others are shallow, the waters will be detained by the greater friction of the shallow places, and the tides will be irregular. The direction, also, of the derivative tide may be totally different from that of the primitive.
Thus, in Fig. 49, if the great tide-wave, moving from east to west, is represented by the lines 1, 2, 3, 4, the derivative tide, which is propagated up a river or bay, will be represented by the lines 3, 4, 5, 6, 7. Advancing faster in the channel than next the bank, the tides will lag behind towards the sh.o.r.es, and the tide-wave will take the form of curves, as represented in the diagram.
On account of the r.e.t.a.r.ding influence of shoals, and an uneven, indented coast, the tide-wave travels more slowly along the sh.o.r.es of an island than in the neighboring sea, a.s.suming convex figures at a little distance from the island, and on opposite sides of it. These convex lines sometimes meet, and become blended in such a way, as to create singular anomalies in a sea much broken by islands, as well as on coasts indented with numerous bays and rivers. Peculiar phenomena are also produced, when the tide flows in at opposite extremities of a reef or island, as into the two opposite ends of Long-Island Sound. In certain cases, a tide-wave is forced into a narrow arm of the sea, and produces very remarkable tides. The tides of the Bay of Fundy (the highest in the world) are ascribed to this cause. The tides on the coast of North America are derived from the great tide-wave of the South Atlantic, which runs steadily northward along the coast to the mouth of the Bay of Fundy, where it meets the northern tide-wave flowing in the opposite direction. This acc.u.mulated wave being forced into the narrow s.p.a.ce occupied by the Bay, produces the remarkable tide of that place.
The largest lakes and inland seas have no perceptible tides. This is a.s.serted by all writers respecting the Caspian and Euxine; and the same is found to be true of the largest of the North-American lakes, Lake Superior. Although these several tracts of water appear large, when taken by themselves, yet they occupy but small portions of the surface of the globe, as will appear evident from the delineation of them on the artificial globe. Now, we must recollect that the primitive tides are produced by the _unequal_ action of the sun and moon upon the different parts of the earth; and that it is only at points whose distance from each other bears a considerable ratio to the whole distance of the sun or moon, that the inequality of action becomes manifest. The s.p.a.ce required to make the effect sensible is larger than either of these tracts of water. It is obvious, also, that they have no opportunity to be subject to a derivative tide.
Although all must admit that the tides have _some connexion_ with the sun and the moon, yet there are so many seeming anomalies, which at first appear irreconcilable with the theory of gravitation, that some are unwilling to admit the explanation given by this theory. Thus, the height of the tide is so various, that at some places on the earth there is scarcely any tide at all, while at other places it rises to seventy feet. The time of occurrence is also at many places wholly unconformable to the motions of the moon, as is required by the theory, being low water where it should be high water; or, instead of appearing just beneath the moon, as the theory would lead us to expect, following it at the distance of six, ten, or even fifteen, hours; and finally, the moon sometimes appears to have no part at all in producing the tide, but it happens uniformly at noon and midnight, (as is said to be the case at the Society Islands,) and therefore seems wholly dependent on the sun.
Notwithstanding these seeming inconsistencies with the law of universal gravitation, to which the explanation of the tides is referred, the correspondence of the tides to the motions of the sun and moon, in obedience to the law of attraction, is in general such as to warrant the application of that law to them, while in a great majority of the cases which appear to be exceptions to the operation of that law, local causes and impediments have been discovered, which modified or overruled the uniform operation of the law of gravitation. Thus it does not disprove the reality of the existence of a force which carries bodies near the surface of the earth towards its centre, that we see them sometimes compelled, by the operation of local causes, to move in the opposite direction. A ball shot from a cannon is still subject to the law of gravitation, although, for a certain time, in obedience to the impulse given it, it may proceed in a line contrary to that in which gravity alone would carry it. The fact that water may be made to run up hill does not disprove the fact that it usually runs down hill by the force of gravity, or that it is still subject to this force, although, from the action of modifying or superior forces, it may be proceeding in a direction contrary to that given by gravity. Indeed, those who have studied the doctrine of the tides most profoundly consider them as affording a striking and palpable exhibition of the truth of the doctrine of universal gravitation.
FOOTNOTE:
[11] The exact longitude of the City Hall, in the city of New York, is 4h. 56m. 33.5s.
LETTER XX.
PLANETS.--MERCURY AND VENUS.
"First, Mercury, amidst full tides of light, Rolls next the sun, through his small circle bright; Our earth would blaze beneath so fierce a ray, And all its marble mountains melt away.
Fair Venus next fulfils her larger round, With softer beams, and milder glory crowned; Friend to mankind, she glitters from afar, Now the bright evening, now the morning, star."--_Baker._
THERE is no study in which more is to be hoped for from a lucid arrangement, than in the study of astronomy. Some subjects involved in this study appear very difficult and perplexing to the learner, before he has fully learned the doctrine of the sphere, and gained a certain familiarity with astronomical doctrines, which would seem very easy to him after he had made such attainments. Such an order ought to be observed, as shall bring out the facts and doctrines of the science just in the place where the mind of the learner is prepared to receive them.
Some writers on astronomy introduce their readers at once to the most perplexing part of the whole subject,--the planetary motions. I have thought a different course advisable, and have therefore commenced these Letters with an account of those bodies which are most familiarly known to us, the earth, the sun, and the moon. In connexion with the earth, we are able to acquire a good knowledge of the artificial divisions and points of reference that are established on the earth and in the heavens, const.i.tuting the doctrine of the sphere. You thus became familiar with many terms and definitions which are used in astronomy.
These ought to be always very clearly borne in mind; and if you now meet with any term, the definition of which you have either partially or wholly forgotten, let me strongly recommend to you, to turn back and review it, until it becomes as familiar to you as household words.
Indeed, you will find it much to your advantage to go back frequently, and reiterate the earlier parts of the subject, before you advance to subjects of a more intricate nature. If this process should appear to you a little tedious, still you will find yourself fully compensated by the clear light in which all the succeeding subjects will appear. This clear and distinct perception of the ground we have been over shows us just where we are on our journey, and helps us to find the remainder of the way with far greater ease than we could otherwise do. I do not, however, propose by any devices to relieve you from the trouble of thinking. Those who are not willing to incur this trouble can never learn much of astronomy.
In introducing you to the planets, (which next claim our attention,) I will, in the first place, endeavor to convey to you some clear views of these bodies individually, and afterwards help you to form as correct a notion as possible of their motions and mutual relations.
The name _planet_ is derived from a Greek word, (= planetes=, _planetes_,) which signifies a _wanderer_, and is applied to this cla.s.s of bodies, because they shift their positions in the heavens, whereas the fixed stars constantly maintain the same places with respect to each other. The planets known from a high antiquity are, Mercury, Venus, Earth, Mars, Jupiter, and Saturn. To these, in 1781, was added Ura.n.u.s, (or _Herschel_, as it is sometimes called, from the name of its discoverer;) and, as late as the commencement of the present century, four more were added, namely, Ceres, Pallas, Juno, and Vesta. These bodies are designated by the following characters:
1. Mercury, [Planet: Mercury]
2. Venus, [Planet: Venus]
3. Earth, [Planet: Earth]
4. Mars, [Planet: Mars]
5. Vesta, [Planet: Vesta]
6. Juno, [Planet: Juno]
7. Ceres, [Planet: Ceres]
8. Pallas, [Planet: Pallas]
9. Jupiter, [Planet: Jupiter]
10. Saturn, [Planet: Saturn]
11. Ura.n.u.s, [Planet: Ura.n.u.s]
The foregoing are called the _primary_ planets. Several of these have one or more attendants, or satellites, which revolve around them as they revolve around the sun. The Earth has one satellite, namely, the Moon; Jupiter has four; Saturn, seven; and Ura.n.u.s, six. These bodies are also planets, but, in distinction from the others, they are called _secondary_ planets. Hence, the whole number of planets are twenty-nine, namely, eleven primary, and eighteen secondary, planets.
You need never look for a planet either very far in the north or very far in the south, since they are always near the ecliptic. Mercury, which deviates furthest from that great circle, never is seen more than seven degrees from it; and you will hardly ever see one of the planets so far from it as this, but they all pursue nearly the same great route through the skies, in their revolutions around the sun. The new planets, however, make wider excursions from the plane of the ecliptic, amounting, in the case of Pallas, to thirty-four and a half degrees.
Mercury and Venus are called _inferior_ planets, because they have their orbits nearer to the sun than that of the earth; while all the others, being more distant from the sun than the earth, are called _superior_ planets. The planets present great diversities among themselves, in respect to distance from the sun, magnitude, time of revolution, and density. They differ, also, in regard to satellites, of which, as we have seen, three have respectively four, six, and seven, while more than half have none at all. It will aid the memory, and render our view of the planetary system more clear and comprehensive, if we cla.s.sify, as far as possible, the various particulars comprehended under the foregoing heads. As you have had an opportunity, in preceding Letters, of learning something respecting the means which astronomers have of ascertaining the distances and magnitudes of these bodies, you will not doubt that they are really as great as they are represented; but when you attempt to conceive of s.p.a.ces so vast, you will find the mind wholly inadequate to the task. It is indeed but a comparatively small s.p.a.ce that we can fully comprehend at one grasp. Still, by continual and repeated efforts, we may, from time to time, somewhat enlarge the boundaries of our mental vision. Let us begin with some known and familiar s.p.a.ce, as the distance between two places we are accustomed to traverse. Suppose this to be one hundred miles. Taking this as our measure, let us apply it to some greater distance, as that across the Atlantic Ocean,--say three thousand miles. From this step we may advance to some faint conception of the diameter of the earth; and taking that as a new measure, we may apply it to such greater s.p.a.ces as the distance of the planets from the sun. I hope you will make trial of this method on the following comparative statements respecting the planets.
_Distances from the Sun, in miles._
1. Mercury, 37,000,000 2. Venus, 68,000,000 3. Earth, 95,000,000 4. Mars, 142,000,000 5. Vesta, 225,000,000 6. Juno, } 7. Ceres, } 261,000,000 8. Pallas, } 9. Jupiter, 485,000,000 10. Saturn, 890,000,000 11. Ura.n.u.s, or Herschel, 1800,000,000