The Story of Eclipses(txt+pdf+epub+mobi电子书下载)

作者：Chambers, George F. (George Frederick)

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The Story of Eclipses试读：

It may, I fear, be taken as a truism that “the man in the street” (collectively, the “general public”) knows little and cares less for what is called physical science. Now and again when something remarkable happens, such as a great thunderstorm, or an earthquake, or a volcanic eruption, or a brilliant comet, or a total eclipse, something in fact which has become the talk of the town, our friend will condescend to give the matter the barest amount of attention, whilst he is filling his pipe or mixing a whisky and soda; but there is not in England that general attention given to the displays of nature and the philosophy of those displays, which certainly is a characteristic of the phlegmatic German. However, things are better than they used to be, and the forthcoming total eclipse of the Sun of May 28, 1900 (visible as it will be as a partial eclipse all over Great Britain and Ireland, and as a total eclipse in countries so near to Great Britain as Spain and Portugal, to say nothing of the United States), will probably not only attract a good deal of attention on the part of many millions of English-speaking people, but may also be expected to induce a numerically respectable remnant to give their minds and thoughts, with a certain amount of patient attention, to the Science and Philosophy of Eclipses.

There are other causes likely to co-operate in bringing this about. It is true that men’s minds are more enlightened at the end of the 19th century than they were at the end of the 16th century, and that a trip to Spain will awaken vastly different thoughts in the year 1900 to those which would have been awakened, say in the year 1587; but for all that, a certain amount of superstition still lingers in the world, and total eclipses as well as comets still give rise to feelings of anxiety and alarm amongst ill-educated villagers even in so-called civilized countries. Some amusing illustrations of this will be presented in due course. For the moment let me content myself by stating the immediate aim of this little book, and the circumstances which have led to its being written. What those circumstances are will be understood generally from what has been said already. Its aim is the unambitious one of presenting in readable yet sound scientific language a popular account of eclipses of the Sun and Moon, and (very briefly) of certain kindred astronomical phenomena which depend upon causes in some degree similar to those which operate in connection with eclipses. These kindred phenomena are technically known as “Transits” and “Occultations.” Putting these two matters entirely aside for the present, we will confine our attention in the first instance to eclipses; and as eclipses of the Sun do not stand quite on the same footing as eclipses of the Moon, we will, after stating the general circumstances of the case, put the eclipses of the Moon aside for a while.CHAPTER II.GENERAL IDEAS.

The primary meaning of the word “Eclipse” (ἔϰλειψις) is a forsaking, quitting, or disappearance. Hence the covering over of something by something else, or the immersion of something in something; and these apparently crude definitions will be found on investigation to represent precisely the facts of the case.

Inasmuch as the Earth and the Moon are for our present purpose practically “solid bodies,” each must cast a shadow into space as the result of being illuminated by the Sun, regarded as a source of light. What we shall eventually have to consider is: What results arise from the existence of these shadows according to the circumstances under which they are viewed? But before reaching this point, some other preliminary considerations must be dealt with.

The various bodies which together make up the Solar system, that is to say, in particular, those bodies called the “planets”—some of them “primary,” others “secondary” (alias “Satellites” or “Moons”)—are constantly in motion. Consequently, if we imagine a line to be drawn between any two at any given time, such a line will point in a different direction at another time, and so it may occasionally happen that three of these ever-moving bodies will come into one and the same straight line. Now the consequences of this state of things were admirably well pointed out nearly half a century ago by a popular writer, who in his day greatly aided the development of science amongst the masses. “When one of the extremes of the series of three bodies which thus assume a common direction is the Sun, the intermediate body deprives the other extreme body, either wholly or partially, of the illumination which it habitually receives. When one of the extremes is the Earth, the intermediate body intercepts, wholly or partially, the other extreme body from the view of the observers situate at places on the Earth which are in the common line of direction, and the intermediate body is seen to pass over the other extreme body as it enters upon or leaves the common line of direction. The phenomena resulting from such contingencies of position and direction are variously denominated Eclipses, Transits, and Occultations, according to the relative apparent magnitudes of the interposing and obscured bodies, and according to the circumstances which attend them.”[1]

The Earth moves round the Sun once in every year; the Moon moves round the Earth once in every lunar month (27 days). I hope everybody understands those essential facts. Then we must note that the Earth moves round the Sun in a certain plane (it is nothing for our present purpose what that plane is). If the Moon as the Earth’s companion moved round the Earth in the same plane, an eclipse of the Sun would happen regularly every month when the Moon was in “Conjunction” (“New Moon”), and also every month at the intermediate period there would be a total eclipse of the Moon on the occasion of every “Opposition” (or “Full Moon”). But inasmuch as the Moon’s orbit does not lie in quite the same plane as the Earth’s, but is inclined thereto at an angle which may be taken to average about 5⅛°, the actual facts are different; that is to say, instead of there being in every year about 25 eclipses (solar and lunar in nearly equal numbers), which there would be if the orbits had identical planes, there are only a very few eclipses in the year, never, under the most favourable circumstances, more than 7, and sometimes as few as 2. Nor are the numbers equally apportioned. In years where there are 7 eclipses, 5 of them may be of the Sun and 2 of the Moon; where there are only 2 eclipses, both must be of the Sun. Under no circumstances can there be in any one year more than 3 eclipses of the Moon, and in some years there will be none. The reasons for these diversities are of a technical character, and a full elucidation of them would not be of interest to the general reader. It may here be added, parenthetically, that the occasions will be very rare of there being 5 solar eclipses in one year. This last happened in 1823,[2] and will only happen once again in the next two centuries, namely in 1935. If a total eclipse of the Sun happens early in January there may be another in December of the same year, as in 1889 (Jan. 1 and Dec. 22). This will not happen again till 2057, when there will be total eclipses on Jan. 5 and Dec. 26. There is one very curious fact which may be here conveniently stated as a bare fact, reserving the explanation of it for a future page, namely, that eclipses of the Sun and Moon are linked together in a certain chain or sequence which takes rather more than 18 years to run out when the sequence recurs and recurs ad infinitum. In this 18-year period, which bears the name of the “Saros,” there usually happen 70 eclipses, of which 41 are of the Sun and 29 of the Moon. Accordingly, eclipses of the Sun are more numerous than those of the Moon in the proportion of about 3 to 2, yet at any given place on the Earth more lunar eclipses are visible than solar eclipses, because the former when they occur are visible over the whole hemisphere of the Earth which is turned towards the Moon whilst the area over which a total eclipse of the Sun is visible is but a belt of the Earth no more than about 150 to 170 miles wide. Partial eclipses of the Sun, however, are visible over a very much wider area on either side of the path traversed by the Moon’s shadow. Fig. 2.—THEORY OF A TOTAL ECLIPSE OF THE SUN.

Confining our attention in the first instance to eclipses of the Sun, the diagrams fig. 2 and fig. 3 will make clear, with very little verbal description, the essential features of the two principal kinds of eclipses of the Sun. In these figures S represents the Sun, M the Moon and E the Earth. They are not, of course, even approximately drawn to scale either as to the size of the bodies or their relative distances, but this is a matter of no moment as regards the principles involved. M being in sunshine receives light on, as it were, the left hand side, which faces S the Sun. The shadow of the Moon cast into space is, in the particular case, thrown as regards its tip on to the Earth and is intercepted by the Earth. Persons at the moment situated on the Earth within the limits of this shadow will not see any part of the Sun at all; they will see, in fact, nothing but the Moon as a black disc with only such light behind and around it as may be reflected back on to the sky by the illuminated (but to the Earth invisible) hemisphere of the Moon, or as may proceed from the Sun’s Corona (to be described presently). The condition of things therefore is that known as a “total” eclipse of the Sun so far as regards the inhabitants of the narrow strip of Earth primarily affected. Fig. 3.—THEORY OF AN ANNULAR ECLIPSE OF THE SUN.

Fig. 3 represents nearly but not quite the same condition of things. Here the Earth and the Moon are in those parts of their respective orbits which put the two bodies at or near the maximum distance possible from the Sun and from one another. The Moon casts its usual shadow, but the tip does not actually reach any part of the Earth’s surface. Or, in other words, to an observer on the Earth the Moon is not big enough to conceal the whole body of the Sun. The result is this; at the instant of central coincidence the Moon covers up only the centre of the Sun, leaving the outer edge all round uncovered. This outer edge shows as a bright ring of light, and the eclipse is of the sort known as an “annular” eclipse of the Sun.[3] As the greatest breadth of the annulus can never exceed 1½ minutes of arc, an annular eclipse may sometimes, in some part of its track, become almost or quite total, and vice versâ.ANNULAR ECLIPSE Fig. 4.—OF THE SUN.

The idea will naturally suggest itself, what exactly does happen to the inhabitants living outside (on the one side or the other) of the strip of the Earth where the central line of shadow falls? This depends in every case on circumstances, but it may be stated generally that the inhabitants outside the central line but within 1000 to 2000 miles on either side, will see a larger or smaller part of the Sun concealed by the Moon’s solid body, simultaneously with the total concealment of the Sun to the favoured individuals who live, or who for the moment are located, within the limits of the central zone.PARTIAL ECLIPSE Fig. 5.—OF THE SUN.

Now we must advance one stage in our conceptions of the movements of the Earth and the Moon, so far as regards the bearing of those movements on the question of eclipses. The Earth moves in a plane which is called the “Plane of the Ecliptic,” and correspondingly, the Sun has an apparent annual motion in the same plane. The Moon moving in a different plane, inclined to the first mentioned one to the extent of rather more than 5°, the Moon’s orbit will evidently intersect the ecliptic in two places. These places of intersection are called “Nodes,” and the line which may be imagined to join these Nodes is called the “Line of Nodes.” When the Moon is crossing the ecliptic from the S. to the N. side thereof, the Moon is said to be passing through its “Ascending Node” (☊); the converse of this will be the Moon passing back again from the N. side of the ecliptic to the S. side, which is the “Descending Node” (☋). Such changes of position, with the terms designating them, apply not only to the Moon in its movement round the Earth, but to all the planets and comets circulating round the Sun; and also to satellites circulating round certain of the planets, but with these matters we have no concern now.Footnotes:

[1] D. Lardner, Handbook of Astronomy, 3rd ed., p. 288.

[2] But not one of them was visible at Greenwich.

[3] Latin Annulus, a ring.CHAPTER III.THE “SAROS” AND THE PERIODICITY OF ECLIPSES.

To bring about an eclipse of the Sun, two things must combine: (1) the Moon must be at or near one of its Nodes; and (2), this must be at a time when the Moon is also in “Conjunction” with the Sun. Now the Moon is in Conjunction with the Sun (= “New Moon”) 12 or 13 times in a year, but the Sun only passes through the Nodes of the Moon’s orbit twice a year. Hence an eclipse of the Sun does not and cannot occur at every New Moon, but only occasionally. An exact coincidence of Earth, Moon, and Sun, in a straight line at a Node is not necessary to ensure an eclipse of the Sun. So long as the Moon is within about 18½° of its Node, with a latitude of not more than 1° 34′, an eclipse may take place. If, however, the distance is less than 15¼° and the latitude less than 1° 23′ an eclipse must take place, though between these limits[4] the occurrence of an eclipse is uncertain and depends on what are called the “horizontal parallaxes” and the “apparent semi-diameters” of the two bodies at the moment of conjunction, in other words, on the nearness or “far-offness” of the bodies in question. Another complication is introduced into these matters by reason of the fact that the Nodes of the Moon’s orbit do not occupy a fixed position, but have an annual retrograde motion of about 19¼°, in virtue of which a complete revolution of the Nodes round the ecliptic is accomplished in 18 years 218⅞ days (= 18.5997 years).

The backward movement of the Moon’s Nodes combined with the apparent motion of the Sun in the ecliptic causes the Moon in its monthly course round the Earth to complete a revolution with respect to its Nodes in a less time (27.2 days) than it takes to get back to Conjunction with the Sun (29.5 days); and a curious consequence, as we shall see directly, flows from these facts and from one other fact. The other fact is to the Sun starting coincident with one of the Moon’s Nodes, returns on the Ecliptic to the same Node in 346.6 days. The first named period of 27.2 days is called the “Nodical Revolution of the Moon” or “Draconic Month,” the other period of 29.5 days is called the “Synodical Revolution of the Moon.” Now the curious consequence of these figures being what they are is that 242 Draconic Months, 223 Lunations, and 19 Returns of the Sun to one and the same Node of the Moon’s orbit, are all accomplished in the same time within 11 hours. Thus (ignoring refinements of decimals):—DaysDays.Years.Days.Hours.242 times27.2=6585.36=18108½==223 times29.56585.3218107¾19 times346.6=6585.78=181018¾

The interpretation to be put upon these coincidences is this: that supposing Sun and Moon to start together from a Node they would, after the lapse of 6585 days and a fraction, be found again together very near the same Node. During the interval there would have been 223 New and Full Moons. The exact time required for 223 Lunations is such that in the case supposed the 223rd conjunction of the two bodies would happen a little before they reached the Node; their distance therefrom would be 28′ of arc. And the final fact is that eclipses recur in almost, though not quite, the same regular order every 6585⅓ days, or more exactly, 18 years, 10 days, 7 hours, 42 minutes.[5] This is the celebrated Chaldean “Saros,” and was used by the ancients (and can still be used by the moderns in the way of a pastime) for the prediction of eclipses alike of the Sun and of the Moon.

At the end of a Saros period, starting from any date that may have been chosen, the Moon will be in the same position with respect to the Sun, nearly in the same part of the heavens, nearly in the same part of its orbit, and very nearly indeed at the same distance from its Node as at the date chosen for the terminus a quo of the Saros. But there are trifling discrepancies in the case (the difference of about 11 hours between 223 lunations and 19 returns of the Sun to the Moon’s Node is one) and these have an appreciable effect in disturbing not so much the sequence of the eclipses in the next following Saros as their magnitude and visibility at given places on the Earth’s surface. Hence, a more accurate succession will be obtained by combining 3 Saros periods, making 54 years, 31 days; while, best of all, to secure an almost perfect repetition of a series of eclipses will be a combination of 48 Saroses, making 865 years for the Moon; and of about 70 Saroses, or more than 1200 years for the Sun.

These considerations are leading us rather too far afield. Let us return to a more simple condition of things. The practical use of the Saros in its most elementary conception is somewhat on this wise. Given 18 or 19 old Almanacs ranging, say, from 1880 to 1898, how can we turn to account the information they afford us in order to obtain from them information respecting the eclipses which will happen ydhmbetween 1899 and 1917? Nothing easier. Add 18 10 7 42 to the middle time of every eclipse which took place between 1880 and 1898 beginning, say, with the last of 1879 or the first of 1880, and we shall find what eclipses will happen in 1898 and 17 following years, as witness by way of example the following table:—Error of Saros bym.d.h.Exact Calculation.26 p.m.Moon.1879Dec.284(Mag. 0.17)1810742(Mag. 0.16)(civil time) +3 m.1898Jan.8128 a.m. m.d.h.48 p.m.Sun.1880Jan.1110(Total)1810742(Total)(civil time) -1 h. 7 m.1898Jan.22630 a.m. m.d.h.50 p.m.Moon.1880June221(Mag. Total)1811742(Mag. 0.93)July32 p.m.189839+35 m. m.d.h.July35 p.m.Sun.188071(Mag. 1811742Annular)(Mag. July17 p.m.1898189+1 h. 10 m.Annular) m.d.h.(civil time).Sun.1880Dec.2311 a.m.(Mag. 0.04)1811742(Mag. 0.02)1898Dec.131053 a.m.-1 h. 5 m. m.d.h.39 p.m.Moon.1880Dec.163(Mag. Total)1811742(Mag. Total)21 p.m.1898Dec.2711-13 m. m.d.h.45 p.m.Sun.1880Dec.311(Mag. 0.71)1811742(Mag. 0.72)27 p.m.1899Jan.119-1 h. 11 m.

There having been 5 recurrences of Feb. 29 between Dec. 1879 and Jan. 1899, 5 leap years having intervened, we have to add an extra day to the Saros period in the later part of the above Table.[6]

Let us make another start and see what we can learn from the eclipses, say, of 1883.Error of Saros bym.d.h.Exact Calculation.1882139 a.AprilMoon321m.1(Mag. 0.8)187421(Mag. 19021 p.May37+51 m.Penumbral)1m. m.d.h.18845 p.MayVisible, Philippines.Sun693m.1(Mag. Total)187421190127 a.(Mag. Total)May(civil time). -2 m.518m. m.d.h.188154 a.Visible, California.MoonOct.636m.1(Mag. 0.28)187421190236 p.(Mag. 0.23)Oct.2-39 m.17m. m.d.h.1883137 p.Visible, N. Japan.SunOct.301m.(Mag. 118742Annular)1(Mag. 190119 a.(civil time) +1 m.Nov.7Annular)11m.

The foregoing does not by any means exhaust all that can be said respecting the Saros even on the popular side.

If the Saros comprised an exact number of days, each eclipse of a second Saros series would be visible in the same regions of the Earth as the corresponding eclipse in the previous series. But since there is a surplus fraction of nearly one-third of a day, each subsequent eclipse will be visible in another region of the Earth, which will be roughly a third of the Earth’s circumference in longitude backwards (i.e. about 120° to the W.), because the Earth itself will be turned on its axis one-third forwards.

After what has been said as to the Saros and its use it might be supposed that a correct list of eclipses for 18.03 years would suffice for all ordinary purposes of eclipse prediction, and that the sequence of eclipses at any future time might be ascertained by adding to some one eclipse which had already happened so many Saros periods as might embrace the years future whose eclipses it was desired to study. This would be true in a sense, but would not be literally and effectively true, because corresponding eclipses do not recur exactly under the same conditions, for there are small residual discrepancies in the times and circumstances affecting the real movements of the Earth and Moon and the apparent movement of the Sun which, in the lapse of years and centuries, accumulate sufficiently to dislocate what otherwise would be exact coincidences. Thus an eclipse of the Moon A.D.which in 565 was of 6 digits[7] was in 583 of 7 digits, and in 601 nearly 8. In 908 the eclipse became total, and remained so for about twelve periods, or until 1088. This eclipse continued to diminish until the beginning of the 15th century, when it disappeared in 1413. Let us take now the life of an eclipse of the Sun. One appeared at the North

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