rapidly for a comparatively short time, and at other times changing the rate of its direct movement considerably in different parts of the zodiac. These effects are often increased by the considerable eccentricity of its orbit; so that before the discovery of Kepler's laws its movements were thought very perplexing, and could not well be accounted for by any theory of the Solar System that had been contrived. 346. The apparent direct motion of a superior planet cannot ordinarily be as quick as the apparent direct movement of the Sun; so that at the time of the conjunction of the planet the Sun apparently overtakes and passes it. The times of day at which any planet rises and sets during any season depend, of course, on its place at that season in the zodiac; the explanations already given with regard to the Sun and Moon will be sufficient to account for the appearances occasioned by such movements of the planets as can be observed without astronomical instruments. 347. The appearances called transits, eclipses, and occultations, still remain to be noticed. These are all due to the passage of one celestial object directly between two others, and may all be illustrated by some such comparison as the following. 348. If a man is walking past some large building, at a considerable distance from it, while carriages are occasionally passing between him and the building, they will hide more or less of it from him as they pass, according to their distance from him and their size. A small carriage passing within a few feet of him may hide the whole length of the building for a second or two; while a still larger carriage driven close by the building will appear to cover only a small part of it at If a low carriage or an open wagon passes between the observer and the building, he may be able to see the upper part of the building over the carriage, even if it passes near him. once. 349. Any particular carriage, then, will hide more of the building the nearer it passes to the observer. But it will take longer to pass in front of the building the farther it passes from the observer. Suppose two straight lines drawn from the observer, one to each end of the building. Then a carriage will begin to hide the building as soon as it begins to cross the first of these lines to which it comes, and will continue to hide some part of the building until it has entirely crossed the second line. But the space it has to cross from one line to the other is greater the farther it is from the observer. If it is not driven directly across this space, it will usually be longer between the lines than it would be if it crossed both of them equally far from the observer; but if its course carries it partly towards him, it will come to the second line at a place where the two lines are nearer together than they were at the place where it crossed the first line; so that its course between the lines may be no longer, or may .even be shorter than if it had crossed them both equally far from the observer. 350. If the observer, as we supposed at first, is himself moving along while the carriage passes, the two lines will be always shifting their places. This will make a difference in the particular time at which the carriage will cross either of them; but it will not make any difference in the two general rules that the carriage hides more of the building at a time the nearer it is to the observer, and continues to hide one part or another of the building for a longer time the farther it is from the observer. Of course, if the carriage and the observer are moving contrary ways, it will not be so long between him and the building as it would be if it moved the same way with him. 351. There is another way of looking at the same facts. Suppose it to be evening and that the building is illuminated. We may wish to inquire how much ground will be covered by the shadow of the carriage. In order to distinguish between the ends of the building, we will call them north and south ends, considering the building as facing eastwards. Then if a line is drawn from the northernmost light in the building past the northern edge of the carriage, and from the southernmost light in the building past the southern edge of the carriage, the place where these lines cross, beyond the carriage, will be as far as its shadow reaches. Anywhere between these lines, and between the place where they cross and the carriage, the carriage cuts off the view of both the northernmost and the southernmost light at once. Outside of this space, one light at least will not be behind the carriage. 352. But if we wish to know the shape of the space from which the carriage hides some of the lights in the building, we may suppose lines drawn from all the lights near the ends and top of the building, so that each line touches the carriage on the edge farthest from the light it starts from. For instance, let a line be drawn from the northernmost light to the southern edge of the carriage and from the southernmost light to the northern edge of the carriage. These lines will cross or come nearest to each other between the building and the carriage, and will get continually farther apart beyond the carriage; so that the farther off we are the more space there will be within which some of the light from the building is cut off by the carriage. 353. When a dark object, like the Moon or a planet, is considered as lighted up by the Sun on one side and casting a shadow on the other, the shadow itself is called an umbra, and the space behind the planet from which it cuts off some sunlight is called a penumbra. In this sense, the words umbra and penumbra have a very different meaning from that which they have when used with regard to the solar spots (56). 354. Since the planets are smaller than the Sun, and are globular, their umbræ are funnel-shaped. From the place where an umbra ends, the planet to which it belongs must look just as large as the Sun; from any place within the umbra the planet must look larger than the Sun; and from any place beyond the end of the umbra the Sun must look larger than the planet (267). If we take a glass funnel and fit two round flat pieces of pasteboard into it, one larger than EXPLANATION OF PLATE IX. In this plate, the dot at E represents the Earth on about the same scale as that on which the Sun is represented in Plate I., page 38. The width of the Earth's orbit, on the same scale, is about equal to the joint length of a number of lines of print, one from each page between Plates I. and IX. By taking one line from each leaf only, we shall accordingly have the distance of the Earth from the Sun. The corresponding extent of the penumbræ of Mercury and Venus, at the distance of the Earth from the Sun, is also shown in Plate IX. ERRATA. Owing to an error in the printing of this edition, Plates IX., X., XI., and XII have been placed between pages 193 and 194, instead of between pages 207 and 208. The number of pages between Plates I. and IX. should be about 170, in order to make the explanation of Plate IX. correct. |