of an eclipse from the elements. First, from the values of the latter at a given moment to determine the point, if any, at which the shadow-axis intersects the surface of the earth, and the respective outlines of the umbra and penumbra on that surface. Within the umbral curve the eclipse is annular or total; outside of it and within the penumbral curve the eclipse is partial at the given moment. The penumbral line is marked from hour to hour on the maps given annually in the American Ephemeris. Second, a series of positions of the central point through the course of an eclipse gives us the path of the central point along the surface of the earth, and the envelopes of the penumbral and umbral curves just described are boundaries within which a total, annular or partial eclipse will be visible. In particular, we have a certain definite point on the earth’s surface on which the edge of the shadow first impinges; this impingement necessarily takes place at sunrise. Then passing from this point, we have a series of points on the surface at which the elements of the shadow-cone are in succession tangent to the earth’s surface. At all these points the eclipse begins at sunrise until a certain limit is reached, after which, following the successive elements, it ends at sunrise. At the limiting point the rim of the moon merely grazes that of the sun at sunrise, so that we may say that the eclipse both begins and ends at that time. Of course the points we have described are also found at the ending of the eclipse. There is a certain moment at which the shadow-axis leaves the earth at a certain point, and a series of moments when, the elements of the penumbral cone being tangent to the earth’s surface, the eclipse is ending at sunset. Three cases may arise in studying the passage of the outlines of the shadow over the earth. It may be that all the elements of the penumbral cone intersect the earth. In this case we shall have both a northern and a southern limit of partial eclipse. In the second case there will be no limit on the one side except that of the eclipse beginning or ending at sunrise or sunset. Or it may happen, as the third case, that the shadow-axis does not intersect the earth at all; the eclipse will then not be central at any point, but at most only partial.
The third problem is, from the same data, to find the circumstances of an eclipse at a given place—especially the times of beginning and ending, or the relative positions of the sun and moon at a given moment. Reference to the formulae for all these problems will be given in the bibliography of the subject.
Authorities.—The richest mine of information respecting eclipses of the sun and moon is T. R. von Oppolzer’s “Kanon der Finsternisse,” published by the Vienna Academy of Sciences in the 52nd volume of its Denkschriften (Vienna, 1887). It contains elements of all eclipses both of the sun and moon, from 1207 B.C. to A.D. 2161, a period of more than thirty centuries. Appended to the tables is a series of charts showing the paths of all central eclipses visible in the northern hemisphere during the period covered by the table. The points of the path at which the eclipse occurs, at sunrise, noon and sunset, are laid down with precision, but the intermediate points are frequently in error by several hundred miles, as they were not calculated, but projected simply by drawing a circle through the three points just mentioned. For this reason we cannot infer from them that an eclipse was total at any given place. The correct path can, however, be readily computed from the tables given in the work. Eduard Mahler’s memoir, “Die centralen Sonnenfinsternisse des 20. Jahrhunderts” (Denkschriften, Vienna Academy, vol. xlix.), gives more exact paths of the central eclipses of the 20th century, but no maps. General tables for computing eclipses are Oppolzer’s “Syzygientafeln für den Mond” (Publications of the Astronomische Gesellschaft, xvi.), and Newcomb’s, in Publications of the American Ephemeris, vol. i. part i. Of these, Oppolzer’s are constructed with greater numerical accuracy and detail, while Newcomb’s are founded on more recent astronomical data, and are preferable for computing ancient eclipses. F. K. Ginzel’s Spezieller Kanon der Sonnen- und Mondfinsternisse (Berlin, 1899) contains, besides the historical researches already mentioned, maps of the paths of central eclipses visible in the lands of classical antiquity from 900 B.C. to A.D. 500, but computed with imperfect astronomical data. Maguire, “Monthly Notices,” R.A.S. xlv. and xlvi., has mapped the total solar eclipses visible in the British Islands from 878 to 1724. General papers of interest on the same subject have been published by Rev. S. J. Johnson. A résumé of all the observations on the physical phenomena of total solar eclipses up to 1878, by A. C. Ranyard, is to be found in Memoirs of the Royal Astronomical Society, vol. xli. A very copious development of the computation of eclipses by Bessel’s method is found in W. Chauvenet’s Spherical and Practical Astronomy, vol. i. The Theory of Eclipses, by R. Buchanan (Philadelphia, 1904), treats the subject yet more fully. Hansen’s method is developed in the Abhandlungen of the Leipzig Academy of Sciences, vol. vi. (Math.-Phys. Classe, vol. iv.). The formulae of computation by this method are found in the introductions to Oppolzer’s two works cited above. (S. N.)
ECLIPTIC, in astronomy. The plane of the ecliptic is that plane in or near which the centre of gravity of the earth and moon revolves round the sun. The ecliptic itself is the great circle in which this plane meets the celestial sphere. It is also defined, but not with absolute rigour, as the apparent path described by the sun around the celestial sphere as the earth performs its annual revolution. Owing to the action of the moon on the earth, as it performs its monthly revolution in an orbit slightly inclined to the ecliptic, the centre of the earth itself deviates from the plane of the ecliptic in a period equal to that of the nodal revolution of the moon. The deviation is extremely slight, its maximum amount ranging between 0.5′ and 0.6″. Owing to the action of the planets, especially Venus and Jupiter, on the earth, the centre of gravity of the earth and moon deviates by a yet minuter amount, generally one or two tenths of a second, from the plane of the ecliptic proper. Owing to the action of the planets, the position of the ecliptic is subject to a slow secular variation amounting, during our time, to nearly 47″ per century. The rate of this motion is slowly diminishing.
The obliquity of the ecliptic is the angle which its plane makes with that of the equator. Its mean value is now about 23° 27′. The motion of the ecliptic produces a secular variation in the obliquity which is now diminishing by an amount nearly equal to the entire motion of the ecliptic itself. The laws of motion of the ecliptic and equator are stated in the article Precession of the Equinoxes.
Attempts have been made by Laplace and his successors to fix certain limits within which the obliquity of the ecliptic shall always be confined. The results thus derived are, however, based on imperfect formulae. When the problem is considered in a rigorous form, it is found that no absolute limits can be set. It can, however, be shown that the obliquity cannot vary more than two or three degrees within a million of years of our epoch.
The formula for the obliquity of the ecliptic, as derived from the laws of motion of it and of the equator, may be developed in a series proceeding according to the ascending powers of the time as follows: we put T, the time from 1900, reckoned in solar centuries as a unit. Then,
Obliquity＝23° 27′ 31.68″ − 46.837″ T −0.0085″ T2 +0.0017″ T3.
From this expression is derived the value of the obliquity at various epochs given in the following table. The left-hand portion of this table gives the values for intervals of 500 years from 2000 B.C. to A.D. 2500 as computed from modern data. For dates more than three or four centuries before or after 1850 the result is necessarily uncertain by one or more tenths of a minute, and is therefore only given to 0.1′.
| B.C. | 2000; | obl. | ＝23° | 55·5′ | A.D. | 1700; | obl. | ＝23° | 28′ | 41·91″ |
| 1500 | ” | ＝23 | 52·3 | 1750 | ” | ＝23 | 28 | 18·51 | ||
| 1000 | ” | ＝23 | 48·9 | 1800 | ” | ＝23 | 27 | 55·10 | ||
| 500 | ” | ＝23 | 45·4 | 1850 | ” | ＝23 | 27 | 31·68 | ||
| 0 | ” | ＝23 | 41·7 | 1900 | ” | ＝23 | 27 | 8·26 | ||
| A.D. | 500 | ” | ＝23 | 38·0 | 1950 | ” | ＝23 | 26 | 44·84 | |
| 1000 | ” | ＝23 | 34·1 | 2000 | ” | ＝23 | 26 | 21·41 | ||
| 1500 | ” | ＝23 | 30·3 | 2050 | ” | ＝23 | 25 | 57·99 | ||
| 2000 | ” | ＝23 | 26·4 | 2100 | ” | ＝23 | 25 | 34·56 | ||
| 2500 | ” | ＝23 | 22·5 | |||||||
(S. N.)
ECLOGITE (from Gr. ἐκλογή, a selection), in petrology, a typical member of a small group of metamorphic rocks of special interest on account of the variety of minerals they contain and their microscopic structures and geological relationships. Typically they consist of pale green or nearly colourless augite (omphacite), green hornblende and pink garnet. Quartz also is usually present in these rocks, but felspar is rare. The augite is mostly a variety of diopside and is only occasionally idiomorphic. The garnet sometimes forms good dodecahedra, but may occur as rounded grains, and encloses quartz, rutile, kyanite, and other minerals very frequently. The hornblende is usually pale green and feebly dichroic, but, in some eclogites which are allied to garnet-amphibolites, it is of dark brown colour. Among the commoner accessory minerals are kyanite (of blue or greyish-blue tints), rutile, biotite, epidote and zoisite, sphene, iron oxides, and
