HISTORY OF SCIENCE. 



few years before the discovery of Uranus, Professor Bode of Berlin 

 published a notice of a singular numerical relation among the mean 

 distances of the planets from the sun. This relation is known by the 

 name of Bode's Law, and may be expressed in several ways, as, for 

 example, if we write down the numbers 3, 6, 12, 24, 48, 96 (each of 

 which is double its predecessor in the series), and add four to each 

 number, or, what amounts to the same thing, if we take the formula 

 3x2" +4, and calculate its values when the index has the respective 

 values o, i, 2, 3, 4, and 5, we obtain the numbers 7, 10, 16, 28, 52, 

 100. Now these numbers, leaving out the fourth, are nearly propor- 

 tional to the distances of Venus, the earth, Mars, Jupiter, and Saturn 

 respectively from the sun, as may be seen from the following table, in 

 which are included three planets unknown when Bode drew attention 

 to this relation : 



When Uranus was discovered, its distance from the sun was held 

 to conform to Bode's law; but the deficiency of a planet between Mars 

 and Jupiter constituted a gap in the series which Bode conjectured 

 would one day be filled up by the discovery of an intermediate planet. 

 Some German astronomers were confident enough to calculate from 

 analogy what would be the elements of the missing planet, and it is 

 said that these surmises guided subsequent observations to some extent 

 at least. PIAZZI (1746 1826), Astronomer Royal at Palermo, being 

 occupied with a revision of the heavens for the purpose of compiling 

 a new and more complete catalogue of fixed stars, observed on the 

 ist of January, 1801, in the constellation Taurus, a small star which, 

 having changed its position in the course of a few days, he supposed 

 to be a comet. As such he in fact drew the attention of other astro- 

 nomers to it ; but it was soon found that the orbit of the new body was 

 nearly circular, and that it was in reality a planet, whose elements re- 

 sembled closely those calculated for the imaginary planet which Bode's 

 law required. This coincidence, after that afforded by Uranus, made 

 this curious relation announced by Bode deserving of the attention of 



