PORTION OF THE COSMOS. THE PLANETS. 321 



Bonnet arrived at the number 4 for the orbit of Mercury. 

 Perhaps he only selected it in order to have for Saturn, 

 which was then the most distant known planet (its distance 

 is 9-5, therefore nearly lO'O), exactly 100 parts in connec- 

 tion with the easily divisible numbers 96, 48, 24, &c. This 

 is more probable than that he should have made the series 

 by beginning with the nearer planets. Even in the last 

 century, this law of doubling, beginning not from the Sun 

 but from Mercury, could not be affirmed to agree sufficiently 

 with the true distances of the planets as then known to us. 

 The distances of Jupiter, Saturn, and Uranus, do indeed in 

 reality approach very nearly to the rate of doubling ; but 

 since the discovery of Neptune, which is much too near to 

 Uranus, the defect of the progression has become strikingly 

 obvious ( 524 ). 



What has been called the law of Vicarius Wurm of 

 Leonberg, arid has been sometimes distinguished from that 

 of Titius and Bode, is a simple correction of the latter law, 

 applied by Wurm to the solar distance of Mercury and to 

 the difference between the solar distances of Mercury and 

 Venus. With a nearer approximation to the truth, he 

 makes the solar distance of Mercury 387, and that of Venus 

 680, the Earth being 1000 ( 525 ). On the occasion of the 

 discovery of Pallas by Olbers, Gauss, in a letter to Zach 

 (Oct. 1802), already passed a striking and just sentence on 

 the so-called law of distances. He says " Contrary to the 

 nature of all truths which deserve the name of laws, that 

 of Titius applies only in a very cursory manner to most of 

 the planets, and (which does not appear to have been before 

 remarked) not at all to Mercury. It is clear that the series 

 4,4 + 3, 4 + 6, 4 + 12, 4 + 24, 4 + 48, 4 + 96, 4 + L92, 



