It seems surprising that after these brilliant beginnings thirty-eight years should then have passed without the discovery of a single planet, for it was only in 1845 that the fifth, _Astræa_, was discovered by Hencke (who should not be confused with the astronomer Encke), a simple amateur astronomer, postmaster at Berlin, who amused himself by constructing charts of the stars. The principal reason for this must be attributed to the want of good star-charts, for to find these little moving points the first thing necessary is to have a very precise chart of the region of the Zodiac which we observe, in order to see whether one of the stars observed is in motion. The earliest good Zodiacal charts are those which the Academy of Berlin commenced to publish in 1830, taking as a basis the zones of Bessel continued by Argelander. Those of the Paris Observatory, which are more perfect, were only begun in 1854. These small planets are all telescopic, invisible to the naked eye, with the exception of Vesta, and sometimes Ceres, which good sight can occasionally succeed in distinguishing; they are of the seventh, eighth, ninth, tenth, and eleventh magnitudes, and even still smaller, and it was for this reason also that so long an interval of time elapsed between the fourth and fifth discoveries. It is probable that all the small planets of any importance are now known, but that a great number—several hundreds, perhaps—still remain to be discovered of which the average brightness does not exceed that of stars of the twelfth magnitude, and of which the diameter is but a few miles. The diameter of the largest, Vesta, may be estimated at 400 kilometres (248 miles). Hencke found successively the 5th and the 6th in 1845 and 1847; Hind, the English astronomer, the 7th and 8th in 1847; Graham, an English observer, the 9th in 1848; Gasparis, an Italian astronomer, the 10th and 11th in 1849 and 1850, and afterward seven others. Hind has further discovered eight others; Goldschmidt, a German painter (a naturalized Frenchman), discovered fourteen between 1852 and 1861.[27] They are now discovered by swarms; Paliser alone has found sixty-eight since 1874.