NOTES TO BOOK VII. 307 



first discovered by Bode of Berlin. The mean distances 

 from the Sun, of the planets Mercury, Venus, the Earth, 

 Mars, Jupiter, Saturn, Uranus, are respectively as the 

 numbers 4, 7, 10, 16, 52, 100, 196, which do not follow 

 any regular law. But if we suppose that there is between 

 Mars and Jupiter a planet whose mean distance is 28, we 

 have the numbers 4, 7, 10, 16, 28, 52, 100, 196. And 

 if we take the successive differences of these numbers, 

 they are 3, 3, 6, 12, 24, 48, 96; when each difference 

 after the first two is double of the preceding. On the 

 strength of this law the German astronomers wrote On 

 the long-expected Planet, and formed themselves into an 

 association for its discovery. 



(N.) p. 242. Since the publication of the First 

 Edition, and indeed very recently, another small planet 

 has been discovered, which appears undoubtedly to belong 

 to the same group as Ceres, Pallas, Juno and Vesta. It 

 has been named Astrcea by Professor Encke of Berlin, 

 who pursued it in its course after it had been first dis- 

 covered and announced by Mr. Hencke, a zealous astrono- 

 mical observer at Driesen, on the evening of Dec. 8, 1845. 

 Its orbit appears to be very near those of the other four 

 small planets ; and its intersections with the planes of the 

 orbits of the others occur in the same constellations, the 

 Virgin and the Whale, which had already been found to be 

 the places where the planes of the other orbits intersect. 

 It may appear that Astrsea ought to have been seen by 

 Olbers in his search of these regions of the heavens, men- 

 tioned in the text, p. 241. But the Star-maps, executed 

 according to the proposal mentioned in p. 295, enable 

 astronomers to execute a more rigorous scrutiny of the 

 skies than was before possible. The orbit of Astrsea has 



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