PROCEEDINGS OF THE POLYTECHNIC ASSOCIATION. 689 



the decrease of the velocities been uniform, that is, so much for 

 each mile, the rings would have been of a uniform width. TIiq 

 increase in the width of the rings, therefore, was in the same ratio 

 as the departure of the decrease of the velocities from uniformity. 



Imperfect as Bode's law is, astronomers have hitherto possessed 

 no other means by which to judge, or even to conjecture, concern- 

 ing the' probable distances of undiscovered planets. When astro- 

 nomers found that the perturbations of Uranus indicated the 

 existence of an unknown planet, beyond the orbit of Uranus, they 

 had no means whatever of guessing its distance, except the mere 

 fact that from the earth to Uitmus the intervals are about doubled. 

 Leverrier and Adams, therefore, predicted that Neptune would be 

 found about eight hundred millions of miles farther from the sun 

 than he actually is. If the law of common difference of velocities 

 had then been known, this mistake would not have been committed. 

 It is a curious fact that our theory indicates that Hercules, the 

 next planet (in the table) beyond the orbit of Neptune, is very 

 nearly the same distance from the sun as Leverrier and Adams 

 supposed Neptune to be. May it not be that the calculations of 

 those two eminent astronomers were more correct than has been 

 supposed, and that Hercules, and not Neptune, was the planet for 

 which they were looking? Hansen, one of the ablest astionomers 

 in Europe, declared, bef«u-e Neptune was discovered, that the per- 

 turbations of Uranus indicated two disturbing unknown planets j 

 our theory and tables indicate more than two. Some very distin- 

 guished mathematicians have expressed doubts whether the calcu- 

 lations of Leverrier really indicated the existence of Neptune; 

 and are inclined to look upon its discovery by Dr. Galle as a for- 

 tunate accident. If this be true, it follows that the disturber or 

 disturbers of Uranus, one or more, are yet to be found. Let us 

 hope that the serial relations herein explained may contribute to 

 their discovery. 



Serial Relations of the Planets. 



The velocity of Mercury, the planet nearest to the sun, is 

 (according to Lardner,) 110,725 miles per hour, which is, of 

 course, greater than the velocity of any other planet. If a series 

 of rings originally existed that differed 1,582 miles per hour in 

 their orbital velocities, it follows that each successive ring be- 

 yond Mercury had an orbital velocity of 1,582 less than its next, 

 [Am. Inst.] KK 



