* 
i ‘ my 
< Z oy 
i. 
30 B.A. Gould, Jr., on the Orbits of the Asteroids. 
Later, after Gauss had computed the secular variations of Ce- 
res and Pallas, Encke, at his suggestion, made farther inyvestiga- 
tions for the purpose of determining whether the distance of the 
two orbits at the node, were on the increase or decrease. The 
result of his computations was, that the orbits are approaching 
one another 
Encke found* the following radius-vectors. 
Year.» | Inthe QQ of Ceres on the Pallas-orbit. | In the @5 of Ceres on the Pallas-orbit. 
, Ceres. Pallas. eres. | Pallas. Diff. 
898 | 282204 ~ 270322 | —0- r i978 2-6761 : nt: —0-29832 
1898 2.92427 | 284945 | —0-07482 2:5956 ? — 0°19223 
|. 3475 2:95374 2:95743 | +0: 00369... | 2: 37987 2 49163 +0-08824 | 
“ According to this, ” to use the wordst o f Gan uss, “a section in 
the node would actually take place about the year 3397, which 
may be considered, at any rate, as an approximation to the truth. 
To be sure a section must also at some former period have occur- 
red; but from the progression of the numbers in the third and 
sixth columns, we can at least cies that this can only have 
been many thousands of years before. If we therefore adopt the 
hypothesis of Dr. Olbers concerning the origin of the new plan- 
ets, the occurrence must have taken place at an epoch, for us at 
esent immeasurably long before the times to which history 
reaches back.” 
It is also evident from the foregoing table, that the dmence be- 
tween the two orbits in the descending node upon the Pallas-or- 
bit, is at present on the decrease. 
ny rate we are justified in concluding, without any farther 
computation of the secular variations, that at the last time that a 
section of the Pallas and Ceres orbits took place, neither of the 
nodes of Juno coincided with the node of Pallas. Although the 
subsequent discovery of five more asteroids has most certainly 
confirmed the conjecture of Olbers, that still more similar bodies 
would be found, it has nevertheless almost immeasurably multi- 
ied the difficulties in our way ;—if indeed it has not rendered it 
absolutely impossible to assign a period, by computation of the 
secular variations of the apsidal and nodal lines of these eight or- 
bits, when at the same time all the nodal lines upon one of the 
orbits coincided, and all the radius vectors were equal. 
n this place belongs, perhaps, the remark, that as far as we 
yet me to determine the orbit of, Flora, the aphelion of this viegal 
falls within the perihelion distance of Ceres. 
On the other hand, it must be mentioned a all the. nodes up- 
on the Ceres-orbit fall within a single quadran 
The following table gives the distances of the several nodes 
upon the orbit of Ceres from one another. ‘These distances are 
———— 
* Monatliche Correspondenz, xxvi, 299. 1G. ,auvi, 299. 
