Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/874

]) in apogee Sun in perigee -{ at mean distance in perigee ]) in apogee Number of eclipses annually 5 Point C is 23,204 miles from j earth (fig. 38). Point C is 9038 miles from earth (fig. 38). Point C is 8187 miles beyond earth (fig. 39). Point C is 15,844 miles from {earth (fig. 38). Point C is 1678 miles from at mean distance j garth (fi<r 38) ( Point C is 15,547 miles be- 1Q I )eri e ee | yond earth (fig. 39).

These numbers correspond to the fact that the limits between which the apparent diameter of the sun varies are 32 36"-4 and 31 31" 8, while the lunar disk varies in diameter from 33 31" l to 29 21 //- 9, so that in a central solar eclipse, where the sun is in perigee and the moon in apogee, the sun s disk extends beyond the moon s by

(32 36"-4- 29 21"-9), or by 1 37" 2 ;

while the sun is in apogee and the moon in perigee, the moon s disk extends beyond the sun s by

(33 31"-1 - 31 31"-8) or by 59" G.

In the former case, or any case in which the sun s disk exceeds the moon s so that in central eclipse a ring of sun light is seen, the eclipse is called an annular solar eclipse ; while, if the moon s disk exceeds the sun s, and the whole of the sun is thus eclipsed, when the centres of the disks coincide, the eclipse is called a total solar eclipse. When only a part of the sun is hidden, and no annulus is formed, the eclipse is called a partial solar eclipse. It is clear that an eclipse which is total or annular for certain parts of the earth will be partial elsewhere ; and in cases (which occur very seldom, however) where the point C falls between E and a, fig. 38, the eclipse will be total along a certain part of the central track, and annular along the rest of that track. In a total eclipse the greatest possible breadth of the total shadow uu (fig. 39) is about 173 miles. This is the minor axis of the shadow-ellipse.

The following table, combined with the fact that the moon s greatest apparent diameter is 33 31" 8, will be suffi cient to illustrate the general conditions of lunar eclipses and the limits for totality:—

Apparent diameters of earth s shadow. tin )) in apogee 1 15 24-30 at mean distance 1 23 2 31 in perigee 1 30 40 31 ]) in apogee 1 15 56 86 at mean distance 1 23 34 87 in perigee 1 31 12 87 I Jin apogee 1 16 28 29 at mean distance 1 24 6 30 ( in perigee 1 31 44 30

It may be added that an eclipse of the sun can only occur when the moon at the time of mean conjunction with the sun is within 19 of her node, and will certainly occur if she is within 13. A lunar eclipse can only happen when she is within 13 3 of her node, at the time of mean opposition to the sun, and will certainly occur if she is within 7; but the limits are somewhat wider than those for solar eclipses, if penumbral lunar eclipses be counted. It is convenient to notice that in every period of 21,600 lunations there are, on the average, 4072 solar eclipses and 2614 lunar eclipses, besides 161 7 penumbral lunar eclipses that is, 4231 lunar eclipses including penumbral ones.

Noting that eclipse-seasons last on the average about 33 days, and that three eclipse-seasons each having three eclipses cannot occur in succession, it is easy to determine the greatest and least number of eclipses which may occur in any single year. The average interval between succes sive eclipse-seasons is 173 3 days. Two such intervals amount together to 346 - 6 days, or fall short of a year by about 1 9 days. Hence there cannot be three eclipse-seasons in a year; for each eclipse-season lasts on the average 33 days. Suppose an eclipse-season to begin with the begin ning of a year of 366 days. The middle of the season occurs at about midday on January 17; the middle of the next eclipse-season 173 3 days later, or on the evening of July 8 ; and the middle of the third occurs yet 173 3 days later, or on December 29, early in the forenoon ; so that nearly the whole of the remaining half belongs to the fol lowing year. This is clearly a favourable case for the oc currence of as many eclipses as possible during the year. If all three seasons could be of the class containing three eclipses, there would be eight eclipses in the year, because the second eclipse of the third season would occur in the middle of that season. This, however, can never happen. But there may be two seasons, each containing three eclipses, followed by a season containing two eclipses, only one of which can occur in the portion of the eclipse-season falling within the same year. In this case there would be seven eclipses in the year. So also there would be seven if in the first season there were three, in the second two, and in the third three, for then the portion of the third falling within the year, being rather more than one-half, would comprise two eclipses. So also if the three succes sive seasons comprise severally two, three, and three eclipses. The same would clearly happen if the year closed with the close of an eclipse-season.

There may then be as many as seven eclipses in a year, in which case at least four eclipses will be solar, and at least three of these partial, while of the lunar eclipses two at least will be total.

As regards the least possible number of eclipses, it is ob vious that, as there must be two eclipse-seasons in the year, and at least one eclipse in each, we cannot have less than two eclipses in the course of a year. When there are only two, each eclipse is solar and central.

As regards intermediate cases, we need make no special inquiry. Many combinations are possible. The most com mon case is that in which there are four eclipses two solar and two lunar. Further, it may be noticed that, whatever the number of eclipses, from two to seven inclusive, there must always be two solar eclipses at least in each year.

Chapter XII.—The Planet Mars.

After Venus, Mars is the planet whose orbit is nearest Mars, to the earth. His diameter is about 4400 miles, and his volume about one-sixth of the earth s; his mass, however, is little more than one-ninth of h?rs, his density being estimated at only-^ths of the earth s. His mean distance from the sun is about 139 millions of miles ; but the eccen tricity of his orbit amounting to 093262, his greatest and least distances differ considerably from this mean value, amounting to 152,304,000 and 126,318,000 miles respectively. It follows that his distance from the earth when in opposition varies largely in opposition near his perihelion his distance is about 33,800,000 miles, whereas, when he is near aphelion, his opposition-distance amounts to 61,800,000 miles. As he is also more brightly illumin ated by the sun when in perihelion, it follows that he appears much brighter when in opposition at that part of his orbit. In fact, the brightness of Mars at opposition near perihelion bears to his brightness at opposition near aphelion, the ratio

(61,800,000) 2 x (152,304,000) 2 : (33,800,000) x (126,318,000) 2 , or about 34 : 7. In other words, the planet is nearly five times as bright at

one of the favourable oppositions as at one of the unfavour-