ECLIPSE

, a privation of the light of one of the luminaries, by the interposition of some opaque body, either between it and the eye, or between it and the sun.

The ancients had terrible ideas of eclipses; supposing them presages of some dreadful events. Plutarch assures | us, that at Rome it was not allowed to talk publicly of any natural causes of eclipses; the popular opinion running so strongly in favour of their supernatural production, at least those of the moon; for as to those of the sun, they had some idea that they were caused by the interposition of the moon between us and the sun; but were at a loss for a body to interpose between us and the moon, which they thought must be the way, if the eclipses of the moon were produced by natural causes. They therefore made a great noise with brazen instruments, and set up loud shouts, during eclipses of the moon; thinking by that means to ease her in labour: whence Juvenal, speaking of a talkative woman, says, Una laboranti poterit succurrere lunæ. Others attributed the eclipse of the moon to the arts of magicians, who, by their inchantments, plucked her out of heaven, and made her skim over the grass.

The natives of Mexico keep fast during eclipses; and particularly their women, who beat and abuse themselves, drawing blood from their arms, &c; imagining the moon has been wounded by the sun, in some quarrel between them.

The Chinese fancy that eclipses are occasioned by great dragons, who are ready to devour the sun and moon; and therefore when they perceive an eclipse, they rattle drums and brass kettles, till they think the monster, terrified by the noise, lets go his prey.

The superstitious notions entertained of eclipses, were once of considerable advantage to Christopher Columbus, the discoverer of America, who being driven on the island of Jamaica in the year 1493, and distressed for want of provisions, was refused relief by the natives; but having threatened them with a plague, and foretelling an eclipse as a token of it, which happened according to his prediction, the barbarians were so terrified, that they strove who should be the first in bringing him supplies, throwing them at his feet, and imploring forgiveness.

Duration of an Eclipse, is the time of its continuance, or between the immersion and emersion.

Immersion, or Incidence, of an Eclipse, is the moment when the eclipse begins, or when part of the sun, moon, or planet first begins to be obscured.

Emersion, or Expurgation, of an Eclipse, is the time when the eclipsed luminary begins to re-appear, or emerge out of the shadow.

Quantity of an Eclipse, is the part of the luminary eclipsed. To determine the quantity eclipsed, it is usual to divide the diameter of the luminary into 12 equal parts, called digits; whence the eclipse is said to be of so many digits according to the number of them contained in that part of the diameter which is eclipsed or obseured.

Eclispses are divided, with respect to the luminary eclipsed, into Eclipses of the sun, of the moon, and of the satellites; and with respect to the circumstances, into total, partial, annular, central, &c.

Annular Eclipse, is when the whole is eclipsed, except a ring, or annulus, which appears round the border or edge.

Central Eclipse, is one in which the centres of the two luminaries and the earth come into the same straight line.

Partial Eclipse, is when only a part of the luminary is eclipsed. And a

Total Eclipse, is that in which the whole luminary is darkened.

Eclipse of the Moon, is a privation of the light of the moon, occasioned by an interposition of the body of the earth directly between the sun and moon, and so intercepting the sun's rays that they cannot arrive at the moon, to illuminate her. Or, the obscuration of the moon may be considered as a section of the earth's conical shadow, by the moon passing through some part of it.

The manner of this eclipse is represented in this figure, where S is the sun, E the earth, and M or M the moon.

Lunar Eclipses only happen at the time of full moon; because it is only then the earth is between the sun and moon: nor do they happen every full moon, because of the obliquity of the moon's path with respect to the sun's; but only in such full moons as happen either at the intersection of those two paths, called the moon's nodes, or very near them; viz, when the moon's latitude, or distance between the centres of the earth and moon, is less than the sum of the apparent semidiameters of the moon and the earth's shadow.

The chief Circumstances in Lunar Eclipses, are the following:—1. All lunar Eclipses are universal, or visible in all parts of the earth which have the moon above their horizon; and are every where of the same magnitude, with the same beginning and end.—2. In all lunar eclipses, the eastern side is what first immerges and emerges again, i. e. the left-hand side of the moon as we look towards her, from the north; for the proper motion of the moon being swifter than that of the earth's shadow, the moon approaches it from the west, overtakes and passes through it with the moon's east side foremost, leaving the shadow behind, or to the westward.—3. Total eclipses, and those of the longest duration, happen in the very nodes of the ecliptic; because the section of the earth's shadow, then falling on the moon, is considerably larger than her disc. There may however be total eclipses within a small distance of the nodes; but their duration is the less as they are farther from it; till they become only partial ones, and at last, none at all.—4. The moon, even in the middle of an eclipse, has usually a faint appearance of light, resembling tarnished copper; which Gassendus, Ricciolus, Kepler, &c, attribute to the light of the sun, refracted by the earth's atmosphere, and so transmitted thither. —Lastly, she grows sensibly paler and dimmer, before entering into the real shadow; owing to a penumbra which surrounds that shadow to some distance.

Astronomy of Lunar Eclipses, or the method of calculating their times, places, magnitudes, and other phenomena. | The 1st preliminary is to find the length of the earth's conical shadow. This may be found either from the distance between the earth and sun, and the proportion of their diameters, or from the angle of the sun's apparent magnitude at the time. Thus, suppose the semiaxis of the earth's orbit 95,000000 miles, and the eccentricity of the orbit 1,377000 miles, making the greatest distance 96,377000 miles, or 24194 semidiameters of the earth; and the sun's semidiameter being to the earth's, as 112 to 1; then as AD : BE :: DB : EC, that is, 111 : 1 :: 24194 : 218 semidiameters of the earth = EC the length of the earth's shadow. Otherwise, suppose the angle AES, or the sun's apparent semidiameter be 15′ 56″, and the angle BAE, or the sun's parallax 8.6″, then is their difference, or the angle ACE = 15′ 47.4″; hence, as tang. 15′ 47.4″: radius :: BE or 1 : 218 nearly = CE, the same distance as before. Hence, as the moon's least distance from the earth is scarce 56 semidiameters, and the greatest not more than 64, the moon, when in opposition to the sun, in or near the nodes, will fall into the earth's shadow, and will be eclipsed, as the length of the shadow is almost 4 times the moon's distance.

2. To sind the apparent semidiameter of the earth's shadow, in the place where the moon passes through it, at any given time. Add together the sun and moon's parallaxes, and from the sum subtract the apparent semidiameter of the sun; so shall the remainder be the apparent semidiameter of the shadow at the place of the moon's passage. For ex. the 28th of April 1790, at midnight, the moon's parallax is 61′ 9″, to which add 8.6″, or 9″, for the sun's parallax, from the sum 61′ 18″ take 15′ 56″, the sun's apparent semidiameter, and the remainder 45′ 22″ is the semidiameter of the shadow at the place where the moon passes through at that time. N. B. Some omit the sun's parallax, as of no consequence; but increase the apparent semidiameter of the shadow by one whole minute, for the shadow of the atmosphere; which would give the semidiameter of the shadow, in the case above, 46′ 13″.

3. There must also be had, the true distance of the moon from the node, at the mean opposition; also the true time of the opposition, with the true place of the sun and moon, reduced to the ecliptic; likewise the moon's true latitude at the time of the true opposition; the angle of the moon's way with the ecliptic, and the true horary motions of the sun and moon: from which all the circumstances of her eclipse may be computed by common arithmetic and trigonometry.

Let EW be a part of the ecliptic, and C the centre of the earth's shadow, through which draw perpendicular to EW, the line CN towards the north, if the moon have north latitude at the time of the eclipse, or CS southward, if she have south latitude. Make the angle NCD equal to the angle of the moon's way with the ecliptic, which may be always taken at 5° 35′, on an average, without any sensible error; and bisect this angle by the right line CF; in which line it is that the true equal time of opposition of the sun and moon falls, as given by the tables.

From a convenient scale of equal parts, representing minutes of a degree, take the moon's latitude at the true time of full moon, and set it from C to G, on the line CF; and through the point G, at right-angles to CD, draw the right line HKGLI for the path of the moon's centre. Then is L the point in the earth's shadow, where the moon's centre is at the middle of the eclipse; G the point where her centre is at the tabular time of her being full; and K the point where her centre is at the instant of her ecliptic opposition: also I the moon's centre at the moment of immersion, and H her centre at the end of the eclipse.

With the moon's semidiameter as a radius, and the points I, L, H, as centres, describe circles for the moon at the beginning, middle, and end of the eclipse-

Finally, the length of the line of path IH, measured on the same scale, will serve to determine the duration of the eclipse, viz, by saying, As the moon's horary motion from the sun is to IH :: 1 hour or 60 min. to the whole duration of the eclipse.

To Compute a Lunar Eclipse. This will be very easy from the foregoing construction. For, 1st, in the triangle CGL, right-angled at L, there are given the hypothenuse CG=the moon's latitude at the time of full moon, and the angle GCL=the half of 5° 35′; to find the legs CL and LG.—2d, In the right-angled triangle CHL or CIL, are given the leg CL, and CH or CI, the sum of the semidiameters of the moon and the earth's shadow; to find LH or LI, half the difference of the sun's and moon's motions during the time of the eclipse.—3d, As the difference of the horary motions of the luminaries is to one hour, or 60 min. :: HL to the semiduration of the eclipse, and :: GL to the difference between the opposition and middle of the eclipse; this last therefore taken from the time of full moon, gives the time of the middle of the eclipse; from which subtracting the time in LI, or semiduration before found, gives the beginning of the eclipse; or add the same, and it gives the end of it.—Lastly, from CO the semidiameter of the shadow, take CL, leaves LO; to which add LP, the moon's semidiameter, when necessary, gives OP the quantity eclipsed.

Note, When the moon's distance from the node exceeds 12°, there can be no eclipse of the moon; or, more accurately, the limit is from 10 1/2 and 12 1/30 degrees, according to the distances of the sun, earth, and moon.

Eclipse of the Sun, is an occultation of the sun's | body, occasioned by an interposition of the moon between the earth and sun. On which account it is by some considered as an eclipse of the earth, since the light of the sun is hid from the earth by the moon, whose shadow involves a part of the earth.

The manner of a solar eclipse is represented in this figure; where S is the sun, m the moon, and CD the earth, rmso the moon's conical shadow, travelling over a part of the earth CoD, and making a complete eclipse to all the inhabitants residing in that track, but no where else; excepting that for a large space around it there is a fainter shade, included within all the space CDs, which is called the Penumbra.

Hence, Solar Eclipses happen when the moon is in conjunction with the sun, or at the new moon, and also in the nodes or near them, the limit being about 17 degrees on each side of it; and such eclipses only happen when the latitude of the moon, viewed from the earth, is less than the sum of the apparent semidiameters of the sun and moon; because the moon's way is oblique to the ecliptic, or sun's path, making an angle of nearly 5° 35′ with it.

In the nodes, when the moon has no visible latitude, the occultation is total; and with some continuance, when the disc of the moon in perigee appears greater than that of the sun in apogee, and its shadow is extended beyond the surface of the earth; and without continuance at moderate distances when the cusp, or point of the moon's shadow, barely touches the earth. Lastly, out of the nodes, but near them, the eclipses are partial.

The other circumstances of solar eclipses are, 1. That none of them are universal; that is, none of them are seen throughout the whole hemisphere which the sun is then above; the moon's disc being much too little, and much too near the earth, to hide the sun from the whole disc of the earth. Commonly the moon's dark shadow covers only a spot on the earth's surface, about 180 miles broad when the sun's distance is greatest, and the moon's least. But her partial shadow, or penumbra, may then cover a circular space of 4900 miles in diameter, within which the sun is more or less eclipsed, as the places are nearer to or farther from the centre of the penumbra. In this case the axis of the shade passes through the centre of the earth, or the new moon happens exactly in the node, and then it is evident that the section of the shadow is circular; but in every other case the conical shadow is cut obliquely by the surface of the earth, and the section will be an oval, and very nearly a true ellipsis.

2. Nor does the Eclipse appear the same in all parts of the earth, where it is seen; but when in one place it is total, in another it is only partial. Farther, when the moon appears much less than the sun, as is chiefly the case when she is in apogee and he in perigee, the vertex of the lunar shadow is then too short to reach the earth, and though she be in a central conjunction with the sun, is yet not large enough to cover his whole disc, but lets his limb appear like a lucid ring or bracelet, and so causes an Annular Eclipse.

3. A Solar Eclipse does not happen at the same time, in all places where it is seen; but appears more early to the western parts, and later to the eastern; as the motion of the moon, and consequently of her shadow, is from west to east.

4. In most Solar Eclipses the moon's disc is covered with a faint light; which is attributed to the reflexion of the light from the illuminated part of the earth.

Lastly, in total Eclipses of the sun, the moon's limb is seen surrounded by a pale circle of light; which some astronomers consider as an indication of a lunar atmosphere; but others as the atmosphere of the sun, because it has been observed to move equally with the sun, and not with the moon; and besides, it is generally believed that the moon is without any atmosphere, unless it be one that is very small, and very rare.

If the moon's parallax were insensible, the bounds of a solar eclipse would be determined after the same manner as those of a lunar; but because here is a sensible parallax, the method is a little altered, viz.

1. Add together the apparent semidiameters of the luminaries, both in apogee and perigee; which gives 33′ 6″ for the greatest sum of them, and 30′ 31″ for the least sum.

2. Since the parallax diminishes the northern latitude and augments the southern, therefore let the greatest parallax in latitude be added to the former sums, and also subtracted from them: Thus in each case there will be had the true latitude, beyond which there can be no eclipse. This latitude being given, the moon's distance from the nodes, beyond which eclipses cannot happen, is found as for a lunar eclipse. This limit is nearly between 16 1/2 and 18 1/3 degrees distance from the nodes.

To find the Digits eclipsed. Add the apparent semidiameters of the luminaries into one sum; from which subtract the moon's apparent latitude; the remainder is the scruples, or parts of the diameter eclipsed. Then say, As the semidiameter of the sun is to the scruples eclipsed; so are 6 digits reduced into scruples, viz 360 scruples or minutes, to the digits &c eclipsed.

To determine the Duration of a Solar Eclipse. Find the horary motion of the moon from the sun, for one hour before the conjunction, and another hour after; then say, As the former horary motion is to the seconds in an hour, so are the scruples of half duration (found as in a lunar eclipse) to the time of immersion; and as the latter horary motion is to the same seconds, so are the same scruples of half duration to the time of emersion. Lastly, adding the times of immersion and emersion together, the aggregate is the total duration.

The moon's apparent diameter when largest, ex- | ceeds the sun's when least, only 2′ of a degree; and at the greatest solar eclipse that can happen at any time and place, the total darkness cannot continue any longer than whilst the moon is moving through this 2′ from the sun in her orbit, which is about 4 minutes of time: for the motion of the shadow on the earth's disc is equal to the moon's motion from the sun, which on account of the earth's rotation on its axis towards the same way, or eastward, is about 30 1/2 minutes of a degree every hour, at a mean rate; but so much of the moon's orbit is equal to 30 1/2 degrees of a great circle on the earth, because the circumference of the moon's orbit is about 60 times that of the earth; and therefore the moon's shadow goes 30 1/2 degrees, or 1830 geographical miles in an hour, or 30 1/2 miles in a minute.

To determine the Beginning, Middle, and End, of a Solar Eclipse. From the moon's latitude, for the time of conjunction, find the arch GL (last fig. but one), or the distance of the greatest obscurity. Then say, as the horary motion of the moon from the sun, before the conjunction, is to 1 hour; so is the distance of the greatest darkness, to the interval of time between the greatest darkness and the conjunction. Subtract this interval, in the 1st and 3d quarter of the anomaly, from the time of the conjunction; and in the other quarters, add it to the same; the result is the time of the greatest darkness. Lastly, from the time of the greatest darkness subtract the time of incidence, and add it to the time of emersion; the difference in the first case will be the beginning; and the sum, in the latter case, the end of the eclipse.

To Calculate Eclipses of the Sun. First, find the mean new moon, and thence the true one; with the place of the luminaries for the apparent time of the true one.—2. For the apparent time of the true new moon, compute the apparent time of the new moon observed.—3. For the apparent time of the new moon seen, compute the latitude seen.—4. Thence determine the digits eclipsed.—5. Find the times of the greatest darkness, immersion, and emersion.—6. Thence determine the beginning, and ending of the eclipse.

From the foregoing problems, it is evident that all the trouble and fatigue of the calculus arises from the parallaxes of longitude and latitude, without which, the calculation of solar eclipses would be the same with that of lunar ones.

See the Construction and Calculation of Eclipses by Flamsteed in Sir Jonas Moor's System of Mathematics, and in Ferguson's Astronomy, &c.

In the Philos. Trans. N° 461 is a contrivance to represent solar eclipses, by means of the terrestrial globe, by M. Seguer, professor of Mathematics at Gottingen. And Mr. Ferguson has fitted a terrestrial globe, so as to shew the time, quantity, duration, and progress of solar eclipses, at any place of the earth where they are visible; which he calls the Eclipsareon. He has also given a large catalogue of ancient and modern eclipses, including those recorded in history, from 721 years before Christ, to A. D. 1485; also computed eclipses from 1485 to 1700, and all the eclipses visible in Europe from 1700 to 1800. See his Astron.

The Number of Eclipses, of both luminaries, in any year, cannot be less than two, nor more than seven; the most usual number is 4, and it is rare to have more than 6. The reason is obvious; because the sun passes by both the nodes but once in a year, unless he pass by one of them in the beginning of the year; in which case he will pass by the same again a little before the end of the year; because the nodes move backwards 19 1/3 degrees every year, and therefore the sun will come to either of them 173 days after the other. And if either node be within 17° of the sun at the time of new moon, the sun will be eclipsed; and at the subsequent opposition, the moon will be eclipsed in the other node, and come round to the next conjunction before the former node be 17° beyond the sun, and eclipse him again. When three eclipses happen about either node, the like number commonly happens about the opposite one; as the sun comes to it in 173 days afterward, and 6 lunations contain only 4 days more. Thus there may be two eclipses of the sun, and one of the moon, about each of the nodes. But when the moon changes in either of the nodes, she cannot be near enough the other node at the next full, to be eclipsed; and in 6 lunar months afterward she will change near the other node; in which case there cannot be more than two eclipses in a year, both of the sun.

Period of Eclipses, is the period of time in which the same eclipses return again; and as the nodes move backwards 19 1/3 degrees every year, they would shift through every point of the ecliptic in 18 years and 225 days; and this would be the regular period of their return, if any complete number of lunations were finished without a fraction; but this is not the case. However, in 223 mean lunations, after the sun, moon, and nodes have been once in a line of conjunction, they return so nearly to the same state again, as the the same node which was in conjunction with the sun and moon at the beginning of the first of these lunations, will be within 28′ 12″ of the line of conjunction with the sun and moon again, when the last of these lunations is completed; and in this period there will be a regular return of eclipses for many ages. To the mean time of any solar or lunar eclipse, by adding this period, or 18 Julian years 11 days 7 hours 43 minutes 20 seconds, when the last day of February in leap years is 4 times included, or a day less when it occurs 5 times, we shall have the mean time of the return of the same eclipse. In an interval of 6890 mean lunations, containing 557 years 21 days 18 hours 30 minutes 11 seconds, the sun and node meet so nearly, as to be distant only 11 seconds.

The Use of Eclipses. In Astronomy, eclipses of the moon determine the spherical figure of the earth; they also shew that the sun is larger than the earth, and the earth than the moon. Eclipses also, that are similar in all circumstances, and that happen at considerable intervals of time, serve to ascertain the period of the moon's motion. In Geography, eclipses discover the longitude of different places; for which purpose those of the moon are the more useful, because they are more often visible, and the same lunar eclipse is of equal magnitude and duration at all places where it is seen. In Chronology, both solar and lunar eclipses serve to determine exactly the time of any past event.

Eclipses of the Satellites. See Satellites of Jupiter.

The chief circumstances here observed, are, 1. That the satellites of Jupiter undergo two or three kinds of | eclipses; the first of which are proper, being such as happen when Jupiter's body is directly interposed between them and the sun: and these happen almost every day. Various authors have given tables for computing eclipses of the satellites of Jupiter; as Flamsteed, Cassini, &c, but the latest and best of all, are those of professor Wargentin of Upsal.

The second sort are occultations, rather than observations; when the satellites, coming too near the body of Jupiter, are lost in his light; which Riccioli calls occidere zeusiace, setting jovially. In which case, the nearest or first satellite exhibits a third kind of eclipse; being observed like a round macula, or dark spot, transiting the disc of Jupiter, with a motion contrary to that of the satellite; like as the moon's shadow projected on the earth, will appear to do, to the lunar inhabitants.

The eclipses of Jupiter's satellites furnish very good means of finding the longitude at sea. Those especially of the first satellite are much surer than the eclipses of the moon, and they also happen much oftener: the manner of applying them is also very easy. See LONGITUDE.