Fig. 109 shows on a large scale the shape of that part of the orbit near the sun and gives the successive positions of the comet, at intervals of 2/10 of a day, on September 16th and 17th, showing that in less than 10 hours--17.0 to 17.4--the comet swung around the sun through an angle of more than 240°. When at its perihelion it was moving with a velocity of 300 miles per second! This very unusual velocity was due to the comet's extraordinarily close approach to the sun. The earth's velocity in its orbit is only 19 miles per second, and the velocity of any comet at any distance from the sun, provided its orbit is a parabola, may be found by dividing this number by the square root of half the comet's distance--e. g., 300 miles per second equals 19 ÷ √ 0.004. [Illustration: FIG. 109.--Motion of the Great Comet of 1883 in passing around the sun.] Most of the visible comets have their perihelion distances included between 1/3 and 4/3 of the earth's distance from the sun, but occasionally one is found, like the second comet of 1885, whose nearest approach to the sun lies far outside the earth's orbit, in this case halfway out to the orbit of Jupiter; but such a comet must be a very large one in order to be seen at all from the earth. There is, however, some reason for believing that the number of comets which move around the sun without ever coming inside the orbit of Jupiter, or even that of Saturn, is much larger than the number of those which come close enough to be discovered from the earth. In any case we are reminded of Kepler's saying, that comets in the sky are as plentiful as fishes in the sea, which seems to be very little exaggerated when we consider that, according to Kleiber, out of all the comets which enter the solar system probably not more than 2 or 3 per cent are ever discovered. [Illustration: FIG. 110.--The Great Comet of 1843.] 163. DIMENSIONS OF COMETS.--The comet whose orbit is shown in Figs. 108 and 109 is the finest and largest that has appeared in recent years. Its tail, which at its maximum extent would have more than bridged the space between sun and earth (100,000,000 miles), is made very much too short in Fig. 109, but when at its best was probably not inferior to that of the Great Comet of 1843, shown in Fig. 110. As we shall see later, there is a peculiar and special relationship between these two comets.