448 Scientific Intelligence. 







The computation of the paths of the fragments, immediately subse- 

 quent to the rupture, must, at present, be regarded as beyond the reach 

 of analysis ; but the mass of the planet being small, the mutual pertur- 

 bations of its fragments must soon have been quite inconsiderable. 

 When this state of things was attained, the nodes of the orbits then to 

 be described may yet have been very nearly together; viz., the nodes 

 of the orbits of the several fragments as marked upon the orbit of the 

 original planet, or the nodes of all the fragments but one, as marked 

 upon the orbit of that excepted one. At the same time the respective 

 distances of the several fragments from the sun must all have been 

 very nearly equal. 



It becomes us then to inquire, how nearly the data which we at pres- 

 ent possess, or may yet acquire, will enable us, by computation back- 

 ward, to arrive at an indication of this state of things. 



Now the masses being all insignificant, it would seem that the secular 

 motions of the nodes of the several orbits upon the ecliptic (or that of 

 the nodes of all the orbits but one counted upon the orbit of that ex- 

 cepted one) as well as the motions of the lines of apsides, might all be 

 very accurately determined. 



Should the algebraical differences of the motions of the nodes, thus 

 found, indicate a near approach of all the nodes at some former period, 

 this would itself be an indication of the common origin of the planets 

 in question; and the time at which the nearest approach was found to 

 have occurred, would also be the latest date which could be assigned to 

 the rupture of the original planet. 



All this would be confirmed, if the secular motions of the major axes 

 of the several orbits should also indicate such a position of them, that 

 the distances of the several planets from the sun should, at the date 

 thus obtained, be nearly the same. 



The orbits of all the planets being movable, it would be preferable 

 to refer the intersections of the orbits in question to a fixed plane suita- 

 bly situated, and compute the motion of the points of intersection in 

 that plane. For the suggestion of this modification I am indebted to 

 Prof. Peirce, of Harvard University, to whom, in conversation, I com- 

 municated the plan here described. 



In the close approach of the nodes, the confirmation of the hypothe- 

 sis in question does not require that all the nodes thus brought into the 

 neighborhood of each other, should be of the same description; viz., 

 all ascending, or else, all descending nodes. On the contrary the con- 

 firmation would be the greater, if the result should be different. That 

 such would prove to be the fact, if the approximation were found to 

 have occurred at all, seems to be foreshadowed by the present position 

 (on the ecliptic) of the descending node of Iris, in the region of the 

 ascending nodes of the others. 



As before remarked, the period of nearest approach in question will 

 furnish the latest date which we can fix upon for the rupture of the 

 original planet. For it is quite evident that several revolutions of the 

 nodes may have occurred since that event, if it really happened. The 

 approach to an equality of distances, as indicated at the same time, by 

 the requisite changes in the positions of the major axes of the orbits, 



would in any case, indicate the date, with great probability. 



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