And here we reach the frontier of the Solar System, as actually known to us. In landing on the world of Neptune, which circles through the Heavens in eternal twilight at a distance of more than four milliard kilometers (2,480,000,000 miles) from the common center of attraction of the planetary orbs, we once again admire the prodigies of science. Uranus was discovered with the telescope, Neptune by calculation. In addition to the solar influence, the worlds exert a mutual attraction upon each other that slightly deranges the harmony ordered by the Sun. The stronger act upon the weaker, and the colossal Jupiter alone causes many of the perturbations in our great solar family. Now during regular observations of the position of Uranus in space, some inexplicable irregularities were soon perceived. The astronomers having full faith in the universality of the law of attraction, could not do otherwise than attribute these irregularities to the influence of some unknown planet situated even farther off. But at what distance? A very simple proportion, known as Bode's law, has been observed, which indicates approximately the relative distances of the planets from the Sun. It is as follows: Starting from 0, write the number 3, and double successively, 0 3 6 12 24 48 96 192 384. Then, add the number 4 to each of the preceding figures, which gives the following series: 4 7 10 16 28 52 100 196 388. Now it is a very curious fact that if the distance between the Earth and the Sun be represented by 10, the figure 4 represents the orbit of Mercury, 7 that of Venus, 16 of Mars; the figure 28 stands for the medium distance of the minor planets; the distances of Jupiter, Saturn, and Uranus agree with 52, 100, and 196. The immortal French mathematician Le Verrier, who pursued the solution of the Uranian problem, supposed naturally that the disturbing planet must be at the distance of 388, and made his calculations accordingly. Its direction in the Heavens was indicated by the form of the disturbances; the orbit of Uranus bulging, as it were, on the side of the disturbing factor. On August 31, 1846, Le Verrier announced the position of the ultra-Uranian planet, and on September 23d following, a German astronomer, Galle, at the Observatory of Berlin, who had just received this intelligence, pointed his telescope toward the quarter of the Heavens designated, and, in fact, attested the presence of the new orb. Without quitting his study table, Le Verrier, by the sole use of mathematics, had detected, and, as it were, touched at pen's point the mysterious stranger. Only, it is proved by observation and calculation that it is less remote than was expected from the preceding law, for it gravitates at a distance of 300, given that from the Earth to the Sun as 10.