688 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



■whose velocity, 14,238 miles per hour, is a mean between that 

 of Neptune, 14,238 miles, and that of Uranus, 15,730 miles per 

 hour. The distance of Pluto from the sun is 2,230 millions of 

 miles. Being 600 millions of miles from Neptune, and 400 from 

 Uranus, it could not have been made asteroidal by their influences. 

 If, therefore, a ring ever did exist in this interval, a planet is 

 moving in it now. 



Bode's Law of the Planetary Distances. 



Kepler was the first astronomer who noticed the fact that the^ 

 intervals between the planets become greater as we proceed out- 

 ward from the centre. He also noticed that the interval between 

 Jupiter and Mars, and also that between Venus and Mercury, was 

 too great for the rule. He therefore suggested, or rather pre- 

 dicted, with the bold enthusiasm that characterized him, that a 

 new planet would be discovered in each of those intervals. 



Prof. Bode, of Berlin, has expressed the idea of the increasing 

 intervals by a scheme of numbers, which is known as ^^ Bode's 

 LawJ- It is as follows : 



Mer. Ven. Earth. Mars. Ast. Jup. Sat. Uran. Nep. 



The first line of figures is a repetition of 4 ; the second line 

 begins with 0, then 3, next twice 3, then four times 3, and so on. 

 The third line is obtained by adding the figures of the two upper 

 lines together. The fourth or last line represents the actual dis- 

 tances of the planets from the sun. 



Although Prof. Bode could o-ive no reflson for the law or rela- 

 lion of the distances which he and others had observed, we can 

 now, by the light of the principles which have been explained in 

 this essay, perceive that Bode's law has its foundation in nature. 

 The primitive rings, or (which is the same thing) the planetary 

 intervals, actually did increase in width by a regular law, though 

 it Avas not identioal with that of Bode. The real cause of the 

 increase in the width of the rings with distance from the 

 primary, was the rate of the decrease of the velocities. This 

 rendered a greater difference of distance necessary to produce 

 a ring in the outer part of the system than in the interior. Had 



