PREDICTION OF LUNAR 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 approach 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 whichever side of the ecliptic she may he. may pass above or below the shadow without entering it in the least. The moon's average diameter is known to he 31' 8".2, and from the American Ephemeris, or the British Yautieal Almanac, we may ascertain its exact amount for any hour —its variations all taking place between the values 29' 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 caleulation and is shown to vary between 1° 1 6' 36" and 1° 30' 38"; and its value for any time may he found from the .I merieun Ephemeris, or the BritiRh Nautical A lmanar, to which value astronomers usually add about 1' :30", as a correction for their •aleulation, which proceeds on the assumption that the earth has no atmosphere. Starting from these elements, it is a simple problem in spherical trigonometry (whieb may he solved approximately by plane trigonometry by supposing the moon and the earth's shadow to more 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 eclipse. Recollecting that the earth's shadow on the ecliptic is at the opposite end of the diameter from the sun, and that therefore as it nears one node the sun must ap proach the other—the sun and shadow being al ways (luidistant from the opposite males— We find, from the solution of the above problem: (1 ) That if, at the time of full moon, the dis tance of the still's centre from the nearest node be greater than 12° 15', there cannot lie an eclipse: (2) if at that time the distance of the sun's centre from the nearest node he less than 9° 30', there will certainly he an eclipse; -(31 if the distance of the sun's centre from a node be between these values, it is doubtful whether there will he 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 id 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 (see PERIOD) of 1S Julian years and 11 days. Their power of doing so turned on this, that in 223 lunations 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 coining.
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 universality 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 be 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 distanee 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 ease, she just touches the shadow, and passes on unobscured.