THE PLANETS. 



117 



at that time with sufficient accuracy for this purpose. In 

 reahty, the distances between Jupiter, Saturn, and Uranus ap- 

 proximate very closely to the duplication ; nevertheless, since 

 the discovery of Neptune, v/hich is much too near to Uranus, 

 the defectiveness in the progression has become strikingly ev- 

 ident.* 



"What is called the law of Wurm of Leonberg, and some- 

 times distinguished from the law of Titius and Bode, is mere- 

 ly a correction' which Wurm made as to the distance of Mer- 

 cury from the Sun, and the difference between the distances 

 of Mercury and Venus. Approximating nearer to the fact, 

 he fixes the former as 387, the latter 680, and the distance 

 of the Earth 1000. f Gauss had already, on the occasion of 



* Since, according to Titius, the distance from the Sun to Saturn, 

 then the outermost planet, is taken as =100, the individual distances 

 should be, 



Mercury, Venus, Earth, Mars, Small planets, Jupiter, 



4 7 10 _1_6_ _2 8 _5 2 



107 iWo 100 100 iFO" loir 



according to the so-called progression : 4, 4+3, 4+6, 4+12, 4+24, 



4+48 ; consequently, when the distance of Saturn from the Sun is taken 



as 789-2 million geographical miles, those of the other planets, expressed 



in the 'same measure, are.: 



Distances, according to Titius, in Geographical 

 Miles. 



Mercury 31'6 millions. 



Venus 55-2 



Earth 78-8 



Mars 126-0 



Smallplanets 2208 " 



Jupiter 410 4 " 



Saturn 789-2 



Uranus 1586-8 " 



Neptune. ..3062-0 



t Wurm, in Bode^s Astron. Jakrbnch for the year 1790, 'p. 168; and 

 Bode, Von dem neuen zwischen Mars und Jupiter entdeckten achten 

 Hauptplaneten des Sonnensystems, 1802, p. 45. With the numerical cor- 

 rection of Wurm, the series, according to the distances from the Sun, is : 



Mercury 387 Parts. 



Venus 387+ 293= 680. 



Earth 387+ 2-293= 973. 



Mars 387-f 4-293= 1559. 



Smallplanets 387-1- 8-293= 2731. 



Jupiter 387+ 16-293= 5075. 



Saturn 387-f 32-293= 9763. 



Uranus 387+ 64293=19139. 



Neptune 387+128-293=37891. 



In order' that the degree of accuracy of these results may be tested, 

 the actual mean distances of the planets are given in the next table, as 

 they are acknowledged at the present time with the addition of the 



