Page:The New International Encyclopædia 1st ed. v. 06.djvu/721

* ECLIPSE. 629 ECLIPSE. necessarily has a peuuinbra, or envelope, on both sides of the central loiie. In the case before us ( Fig. 2 ), supf)ose a cone having its apex U' be- tween the sun and the earth, and enveloping each of them respectively in its opposite halves CO'C and AO'A'. It is clear that from every point in the shaded part of the cone CO'C" but without the shadow BOB', a portion of the sun will be visible — and a portion only — the portion increas- ing as the point approaches either of the lines L'B, C'B', and diminishing as it approaches the lines BO, B'O. In other words, the illumina- tion from the sun's rays is only partial within the space referred to, and diminishes from its e.xtreme boundary line toward the lines BO, B'O. When, then, the luoon is about to sutler eclipse, it first loses brightness on entering this pe- numbra ; so that when it enters the real shadow, the contrast is not between one part of it in shade and the other iu full brilliancy, but between a part in shade and a part in par- tial shade. On its emersion, the same con- trast is presented between tlic i)art in the umbra and the part in the penumbra. What we should expect ou this geometric view of the earth's shadow, actually happens. From the breadth of the penumbra, it happens that the moon may fall wholly within it before immer- sion in the umbra commences ; and so softly do the degrees of light shade into one another, that it is diliicult to tell when a remarkable point on the moon's surface leaves the penumbra to pass into the umbra, or the reverse. Prediction of Ltj>-ar Eclipses. We said that lunar eclipses only happen at full moon. They do not happen every full moon, because the moon's orbit is inclined to the ecliptic, on which the centre of the earth's shadow moves at an angle of 5° 9' nearly. Of course, if the moon moved on an ecliptic, there would be an eclipse every full moon ; but from the magnitude of the angle of inclination of her orbit to the ecliptic, an eclipse can only occur on a full moon hap- pening when the moon is at or near one of her nodes, or the points where her orbit intersects the ecliptic. An eclipse clearly can happen only when the centres of the circle of the earth's shadow and of the moon's disk apjiroach within a distance less than the sum of their apparent semi-diameters; and this sum is very small; so tnat except when near the nodes, the moon, on vrhichever side of the ecliptic she may be, may pass above or below the shadow without entering it in the least. The moon's average diameter is known to be 31' 8".2, and from the Ametican Ephemeris, or the British yautical Almanac, we may ascertain its exact amount for any hour — its variations all taking place between the values 20' 24" and 33' 32". As for the diameter of the circle of the shadow, as seen from the earth's centre, it is easily found by geometric construction and calculation and is shown to vary between 1° 10' 30" and 1° 30' 38"; and its value for any time may be found from the Ameri- can Ephemeris, or the liritish yauliral Almanac, to which value astronomers usually add about 1' 30", as a correction for their calculation, which proceeds on the assumption that the earth has no atmosphere. Starting from these elements, it is a simple problem in spherical trigonometry (which may be solved approximately by plane trigonometry by supposing the moon and the earth's shadow to move for a short time near the node in straight lines) to fix the limits within which the shadow and moon must concur to allow of an eclip.se. Recollecting that the earth's shadow on the eclii)tic is at the opposite end of the diameter from the sun, and lliat tlicreforc as it nears one node the sun must ap- proach the other — the sun and sluidow being al- ways e<]uidislant from the opposite nodes — we lind, from the .solution of the above problem: ( 1 ) That if, at the time of full moon, the dis- tance of the sun's centre from the nearest node be greater than 12° 15', there cannot be an eclipse; (2) if at that time the distance of the sun's centre from the nearest node be less than 9" 30', there will certainly be an eclipse; (3) if the distance of the sun's centre from a node be between these values, it is doulitful whether there will be an eclipse, and a detailed calculation must be resorted to, to ascertain whether there will be one or not. It may here be mentioned that before the laws of the solar and lunar motions were discovered with any- thing like accuracy, the ancients were able to predict the dates of lunar eclipses with tolerable correctness by means of the eclipse cycle or Saros (see Pehiod) of 18 Julian years and 11 days. Their power of doing so turned on this, that in 223 huiations the moon returns almost to the same position in the heavens. If she did return to exactly the same position, then, by simply observing the eclipses which occurred during the 223 lunations, we should know the order in which they would recur in all time coming. All lunar eclipses are visible in all parts of the earth which have the moon above their hori- zon, and are everywhere of the same magnitude, with the same beginning and end; and this imiversality of lunar eclipses is the reason why it is popularly thought, contrary to fact, that they are of more frequent occurrence than solar eclipses. The eastern side of the moon, or left- hand side as we look toward her from the north, is that which first immerges and emerges again. The reason of this is that the motion of the moon is swifter than that of the earth's shadow, so that she overtakes it with her east side fore- most, passes through it. and leaves it behind to the west. It will he readily understood from the explanations above given that total eclipses of the longest duration happen in the very nodes of the ecliptic. But from the circumstance of the circle of the shadow- being much greater than the moon's disk, total eclipses may happen within a small distance of the nodes, in which cases, however, their duration is less. The further the moon is from her node at the time, the smaller is the eclipse, till, in the limiting case, she just touches the shadow, and passes on unobscured. Eclipses of the Sun. These are caused, as we have stated, by the interposition of the moon between the earth and sun, through which a greater or less portion of the sun is necessarily hid from view. By a process similar to that used in ascertaining the length of the earth's shadow, it can be shown that the greatest value of the length of the moon's shadow is about (iO semi-diameters of the earth; at the same time, we know that the least distance of the niotm from the earth is about .50 semi-diameters, ft follows that when a conjunction of the sun and n.oon happens at a time when the length of the shadow and the distance of the moon from the