nutes, or 18 years, 11 days, 7 hours, and 43 minutes, according as there are five or four leap years in the interim, the moon returns to the same position nearly with respect to the sun, lunar nodes, and apogee, and therefore the eclipses return nearly in the same circumstances: this period was called the Chaldean Saros, being used by the Chaldeans for foretelling eclipses. 250. From the refraction of the sun's light by the atmosphere of the earth, we are enabled to see the moon in a total eclipse, when it generally appears of a dusky red colour. The moon has, it is said, entirely disappeared in some eclipses. The Penumbra makes it very difficult to observe accurately the commencement of a total eclipse of the moon; an error of above a minute of time may easily occur. Hence lunar eclipses now are of little value for finding geographical longitudes. The best method of observing an eclipse of the moon is by noting the time of the entrance of the different spots into the shadow, which may be considered as so many different observations. ECLIPSES OF THE SUN. 251. From what has been said of the earth's shadow, it is easy to see that the angle of the moon's shadow is nearly equal to the apparent diameter of the sun. Hence we compute that the length of the conical shadow of the moon varies from 60 to 55 semidiameters of the earth. The moon's distance varies from 65 semidiameters to 56. Therefore sometimes when the moon is in conjunction with the sun, and near her node, the shadow of the moon reaches the earth, and involves a small portion in total darkness, and so occasions a total eclipse of the sun. The part of the earth involved in total darkness is always very small, it being so near the vertex of the cone; but the part involved in the Penumbra extends over a considerable portion of the hemisphere turned toward the sun in these parts the sun appears partially eclipsed. 252. The length of the shadow being sometimes less than the moon's distance from the earth, no part of the earth will be involved in total darkness; but the inhabitants of those places near the axis of the cone will see an annular eclipse, that is, an annulus of the sun's disc will only be visible. Thus let HF, LU (Fig. 37) be sections of the sun and moon. axis SV of the cone, to meet the earth in B: from Produce the B draw tan- gents to the moon, intersecting the sun in I and N. of which IN is the diameter, will be invisible at B, and the annulus, of which IH is the breadth, will be visible. It has been computed that a total eclipse of the sun can never last longer, at a given place, than 7m 38, nor be annular longer than 12m 24s. The diameter of the greatest section of the shadow that can reach the earth is about 180 miles. 253. The general circumstances of a solar eclipse may be represented by a projection with considerable accuracy, and a map of its progress on the surface of the earth constructed. (Professor Vince's Astron. vol. 1.) The phænomena of a solar eclipse at a given place may be well understood by considering the apparent diameters of the sun and moon on the concave surface, and their distances as affected by parallax. When the apparent diameter of the sun is greater than that of the moon, the eclipse cannot be total, but it may be annular. From the tables we compute for the given place the time when the sun and moon are in conjunction, that is, have the same longitude. From the horizontal parallax of the moon, given by the tables, at this time, we compute its effectsa in latitude and longitude; by applying these to the latitude and longitude of the moon, computed from the tables, we get the apparent latitude and longitude, as seen on the concave surface; and a Or rather the effects of the difference of the parallaxes of the sun and moon. knowing the longitude of the sun, we compute the apparent distance of their centres, from whence we can nearly conclude the time of the beginning and ending of the eclipse, especially if we compute by the tables the apparent horary motion of the moon in latitude and longitude at the time of the conjunction. About the conjectured time of beginning, compute two or three apparent longitudes and latitudes, and from thence the apparent distances of the centres, from which the time may be computed by proportion when the apparent distance of the centres is equal to the sum of the apparent semidiameters, that is, the beginning of the eclipse. In like manner the end may be determined. The magnitude also of the eclipse at any time may be thus determined: let SE (Fig. 38) be the computed apparent difference of longitude of the centres L and S, LE the computed apparent latitude of the moon. In the triangle LSE we have therefore LE and ES to find SL the distance of the centres. Hence mn (the breadth of the eclipsed part of the sun) Ln+ Sm-SL is known. 254. The ecliptic limits of the sun (the greatest distance of the conjunction from the node when an eclipse of the sun can take place) may be found as follows: let CN and NL (Fig. 39) be the ecliptic and moon's path, and CN the distance, when greatest, of the conjunction from the node; as the angle N (the inclination of the orbit) may be considered as constant, when CN is greatest, CL, the true latitude of the moon, is greatest. The true latitude =apparent latitude ± parallax in latitude = (when an eclipse barely takes place) sum of the semidiameters + parallax in latitude. Therefore at the ecliptic limits the parallax in latitude is the greatest possible, that is, when it is equal to the horizontal parallax. Hence CL semidiameter moon + sem. diam. sun + hor. par. moon. Therefore CL (when a It is scarcely necessary to mention the horizontal parallax of the sun in this investigation. It should properly be the horizontal parallax of the moon-hor. par. sun. greatest) NC= 33' + 61′ (= 1° 34′) nearly. And because sin. cot. N x tan. LC rad. we find NC = 17° 12' nearly. An eclipse may happen within this limit; but if we take CL = 30' +54' (the least diameters and least parallax) = 1° 24′ we find NC 15° 19′ and an eclipse must happen within this limit. 255. There must be two eclipses, at least, of the sun every year, because the sun is above a month in moving through the solar ecliptic limits. But there may be no eclipse of the moon in the course of a year, because the sun is not a month in moving through the lunar ecliptic limits. When a total and central eclipse of the moon happens, there may be solar eclipses at the new moon preceding and following, because, between new and full moon, the sun moves only about 15°, and therefore the preceding and following conjunctions will be at less distances from the node than the limit for eclipses of the sun. As the same may take place at the opposite node, there may be six eclipses in a year. Also when the first eclipse happens early in January, another eclipse of the sun may take place near the end of the year, as the nodes retrograde nearly 20° in a year. Hence there may be seven eclipses in one year, five of the sun, and two of the moon.b 256. Thus more solar than lunar eclipses happen, but few solar are visible at a given place. A total eclipse of the sun, April 22, 1715, was seen in most parts of the south of England. A total eclipse of the sun had not been seen in London since the year 1140. The eclipse of 1715 was a very remarkable one; during the total darkness, which lasted in London 3m 23s, the planets Jupiter, Mercury, and Venus were seen; also the fixed stars Capella Art. 60, 83, and 132. b Or four of the sun and three of the moon.-ED. |