682 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



TABLE 5. 

 Relative velocities of the satellites of Uranus. 



Theoretical Actual 



velocities. velocities. 



Miles per hour. Miles per hour. 



l._yelocity ofthe 1st 12,500 12,500 



Subtract 600X2= 1,200 



2._Velocity of the 2d 11,300 11,200 



Subtract 600x2= 1,200 



3._Velocity of the 3d 10.100 10,056 



Subtract 600x2= 1,200 



4._Velocity of the 4th 8,900 8,828 



Subtract 600 600 



5._Vclocity of the5th 8,300 8,178 



Su})tract 600 600 



6._Velocity of the eth 6,700 7,636 



I was led to discover the law of common difference of planetary 

 velocities in the following manner: In 1857 I printed a small 

 volume entitled " Geonomy, or the creation of the Continents." 

 In writing an introduction to a proposed new edition of that 

 work, I attempted to make a brief statement, and a plausible 

 defense of the nebular hypothesis of Laplace. Being thus led to 

 examine the subject critically, I convinced myself that the hypothe- 

 sis is erroneous. I therefore endeavored to frame a more reason- 

 able theory in its stead. After many unsuccessful experiments, I 

 at length succeeded in producing the theory, that the relative 

 magnitudes and densities of the planets are owing to the rotation 

 of the nebula in a resisting medium; and that the rings were sep- 

 arated by the antagonism between the aggregating tendency and 

 the differences of the orbital velocities. I gave the substance of 

 this theory in a public lecture, in the winter of 1860, before the 

 members of the Mercantile Library Association, in Boston. Shortly 

 afteiward, it occurred to my mind that if this theory is true, there 

 should be some evidence of it found in the actual relative veloci- 

 ties of the known planets and satellites. I proceeded at once to 

 construct tables of the orbital velocities, and was, of course, much 

 gratified to find my theory confirmed in such a remarkable manner. 

 A brief and imperfect statement of this discovery was published 

 at the time, in the Scientific American; but I have not, until now, 



