Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/873

Solar and lunar eclipses can be considered together, so far as the general law of their sequence is concerned. From what has been already shown, it follows that, if the motions of the sun and moon could be watched continuously from the centre of the earth, the moon would be seen to pass round the star-sphere once in each sidereal month on a path inclined about 5 8 to the ecliptic, while the sun would complete the circuit of the ecliptic once in a sidereal year; and the moon would pass the sun s place once in each synodical month. The place of conjunction of the sun and moon would clearly pass round the star-sphere, advancingly, making the complete circuit of the heavens once in each year on the average; and the same would happen with the place of conjunction of the moon and the point directly opposite the sun. Moreover, as the moon at these conjunctions would, of course, be on her own apparent orbit, and that orbit is inclined to the sun s, it is clear that, supposing the moon s orbit fixed, the conjunc tions of sun and moon during one-half of the year would occur with the moon in the northern half of her apparent orbit, and those in the other half would occur with the moon in the southern half of her orbit. The same would be true of the conjunctions of the moon with the point opposite the sun, only, of course, the halves of the lunar orbit would be interchanged. At or near the time when the place of either conjunction was crossing from the northern to the southern side of the moon s orbit, or vice versa, the conjunction would occur with the moon so near to the ecliptic, that if the conjunction was one of sun and moon, she would hide the sun s disk wholly or partially, while, if the conjunction was one of the moon with that point opposite the sun towards which the earth s shadow is thrown, she would enter that shadow wholly or partially. In other words, at two seasons separated by six months there would be eclipses of the sun or moon, or both, whereas during the intervening months no eclipses would occur.

The number of eclipses which could occur in either eclipse-season would depend on the rate at which the points of successive conjunction approached and left the ecliptic, on the proximity necessary for the occurrence of an eclipse of cither sort, and also on the manner in which the lunar node happened to be passed. For example, suppose that a con junction of the sun and moon occurred when the moon was exactly at a node, so that a central eclipse of the sun occurred ; then, half a synodical month before and half a synodical month after that conjunction, there would be a conjunction of the moon with the point opposite the sun, and the moon being only half a month s journey from her node, would be at a point of her orbit not far from tha ecliptic. But the extent of the earth s shadow is such, that the moon would only be partially in the penumbra, and penumbral lunar eclipses are not considered by astronomers. There would therefore be only one eclipse in such an eclipse-season, viz., a central solar eclipse. Next, suppose that when the moon was at her node, she was exactly opposite the sun, then there would be a total lunar eclipse. Half a lunation later and earlier she would be in conjunction with the sun, and she would be at a point of her orbit not far from the ecliptic. In this case, although during half a month from nodal passage the moon supposed to be viewed from the earth s centre gets to a distance from the ecliptic exceeding the sum of her own and the sun s semidiamcters, and therefore so viewed would pass clear of the sun, yet for the earth, regarded as a whole, she would not pass quite clear of the sun. In other words, for those parts of the earth where the effect of parallax would shift the moon most towards the sun, there would be a slight partial solar eclipse at the conjunc tion following or preceding the total lunar eclipse. In this case, then, there would be three eclipses, one lunar and total, the other two solar and partial. These results would be approximated to if the conjunction of sun and moon in the first case, or of moon and sun-shadow in the second case, occurred with the moon very near a node. But otherwise there would be an eclipse either solar or lunar a few days before her nodal passage, and another either lunar or solar a few days after her nodal passage, and no other eclipse of either sort in that eclipse-season.

All this corresponds to the actual conditions except in one respect. The lunar nodes retrograde, so as to meet the advancing conjunction-points of either kind ; and thus, instead of a year being occupied in the complete circuit of the conjunctions, the actual interval has for its mean value the mean interval between the successive conjunctions of the sun with the rising node of the moon s orbit, or 34G G07 days. Accordingly, the average interval between successive eclipse-seasons is 173 - 3 days instead of half a sidereal year.

Fig. 37.

Fig. 38.

Fig. 39.

Eclipses of both sorts are illustrated in fig. 37. Here E Theory is the earth, and the moon is shown in two places at M, eclipses, directly between the earth and sun, and at the point opposite M, in the heart of the earth s shadow-cone. The true geometrical shadows of the earth and moon are shown black, the true geometrical penumbra? are shaded (of course the vertical dimensions in the figure have been enormously exaggerated). The distance EC is variable, being as great as 870,300 miles when the earth is in aphelion, and as small as 843,300 miles when the earth is in perihelion. The earth s shadow thus extends about 3 J times as far from the earth as the moon s orbit. In figs. 38 and 39 tho extremity of the moon s shadow is shown on a larger scale, in one case falling short of the earth, in the other extending beyond the earth. For the moon s conical shadow has a length which varies in the same propor tion as the earth s shadow, that is, as 8703 to 8433 ; and the absolute length thus varies from 229,780 miles (fig. 38) to 237,140 miles (fig. 39). Since the moon s greatest mean and least distances are respectively 252,984 miles, 238,818 miles, and 221.593 miles, it follows that for solar eclipses we have—