704 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



was to the centre ; consequently the rings decreased in width in 

 the same ratio as the velocities increased ; and the primitive riuo-s 

 had a common difference of velocities equal to 1,582 miles per 

 hour. 



5. The movement of the nebulous matter in spiral paths toward 

 the centre, caused a large portion to accumulate at the inner edge 

 of each ring in a globular mass ; and thus the rings became trans- 

 formed to planets. 



6. In the interior parts of each system the rings were extremely 

 narrow, and the attraction of the exterior rings prevented the 

 inward spiral movement requisite to form normal planets ; conse- 

 quently, rings of asteroids or planetettes were produced between 

 all the interior secondaries. 



7. In the outer parts of the system, where the rings were very 

 wide, and the planets not very large, no asteroids were formed ; 

 therefore I infer the existence of a planet (Pluto) between Neptune 

 ajid Uranus, and several others between Uranus and Saturn. I 

 also infer the existence of several undiscovered satellites in 

 Saturn's system. 



8. The orbital velocities of unseen planets being ascertained by 

 the theory of common difference, their distances can also be deter- 

 mined, by the rule that the orbital velocities, one to another, are 

 inversely proportional to the square roots of the mean distances. 



9. In carrying this new theory out to its consequences, an inte- 

 resting relation has been discovered between the square roots of 

 the distances, which has never before been known, and which is 

 illustrated by several tables. 



10. The more massive a primary, the narrower at a given dis- 

 tance must have been the primitive rings or intervals, and there- 

 fore more likely to purturb each other, and produce asteroids.- 



11. The less dense the nebula from which rings were formed, 

 the less massive the rings must have been, and therefore less likely 

 to produce asteroids by their mutual perturbations. 



12. The reason why Saturn's satellites are, some of them, so 

 near the primary, is because the primitive Saturnian nebula had 

 so little density. The same fact accounts for the narrow intervals 

 between Saturn's interior satellites. 



At the conclusion of Mr. Grimes' exposition, an animated dis- 

 cussion arose, in which Drs. Vanderweyde and Bradley, Messrs. 

 Miller, Walling and others took part. It was the general opinion 

 of those who adopt Laplace's theory that Mr. Grimes had not 



