THE PLANETS. 443 



How the translator and commentator of Bonnet obtained 

 the number 4 for the orbit of Mercury, is nowhere stated. 

 Perhaps he selected it only in order to have in combination 

 with the easily divisible numbers 96, 48, 24, &e., exactly 100 

 for Saturn, at that time the most distant planet known, whose 

 distance is 9- 5, thus very nearly = 10*0. It is less probable 

 that he constructed the order of succession by commencing 

 from the nearer planets. A sufficient correspondence of the 

 law of duplication setting out, not from the Sun, but from 

 Mercury, with the true planetary distances, could not have 

 been affirmed in the last century, as the latter were known at 

 that time with sufficient accuracy for this purpose. In reality, 

 the distances between Jupiter, Saturn, and Uranus approximate 

 very closely to the duplication ; nevertheless, since the disco- 

 very of Neptune, which is much too near to Uranus, the defec- 

 tiveness in the progression has become strikingly evident.** 



38 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, 



Too" To^o Too" To~o To"o To" 



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 : 



