The longitude of Mars for each date can be found from Fig. 15 by measuring the angle between the straight line _S V_ and the line drawn from the earth to Mars. Thus for October 12th we may find with the protractor that the angle between the line _S V_ and the line joining the earth to Mars is a little more than 30°, and in Fig. 14 the position of Mars for this date is shown nearly opposite the cross line corresponding to 30° on the ecliptic. Just how far below the ecliptic this position of Mars should fall can not be told from Fig. 15, which from necessity is constructed as if the orbits of Mars and the earth lay in the same plane, and Mars in this case would always appear to stand exactly on the ecliptic and to oscillate back and forth as shown in Fig. 14, but without the up-and-down motion there shown. In this way plot in Fig. 14 the longitudes of Mars as seen from the earth for other dates and observe how the forward motion of the two planets in their orbits accounts for the apparently capricious motion of Mars to and fro among the stars. [Illustration: FIG. 16.--The orbits of Jupiter and Saturn.] 28. THE ORBITS OF THE PLANETS.--Each planet, great or small, moves in its own appropriate orbit about the sun, and the exact determination of these orbits, their sizes, shapes, positions, etc., has been one of the great problems of astronomy for more than 2,000 years, in which successive generations of astronomers have striven to push to a still higher degree of accuracy the knowledge attained by their predecessors. Without attempting to enter into the details of this problem we may say, generally, that every planet moves in a plane passing through the sun, and for the six planets visible to the naked eye these planes nearly coincide, so that the six orbits may all be shown without much error as lying in the flat surface of one map. It is, however, more convenient to use two maps, such as Figs. 16 and 17, one of which shows the group of planets, Mercury, Venus, the earth, and Mars, which are near the sun, and on this account are sometimes called the inner planets, while the other shows the more distant planets, Jupiter and Saturn, together with the earth, whose orbit is thus made to serve as a connecting link between the two diagrams. These diagrams are accurately drawn to scale, and are intended to be used by the student for accurate measurement in connection with the exercises and problems which follow. In addition to the six planets shown in the figures the solar system contains two large planets and several hundred small ones, for the most part invisible to the naked eye, which are omitted in order to avoid confusing the diagrams.