B. A. Gould, Jr., on the Orbits of the Asteroids. 29 
For if this supposition be true, the oes would almost exactly 
have filled the gap between Mars and Jupiter, where, according 
to an empirical formula, much in vogue at that time, an unknown 
planet had been long suspected. Indeed a society of German as- 
tronomers had:been already forined, to search for this ‘sega 
* member of our solar system. 
g As a corroboration of this hypothesis, he referred to the cir- 
* cumstance that both Pallas and Ceres seemed to vary considera- 
bly in magnitude, which he explained by the —— that these 
| bodies were not round, but of vary irregular figure 
“This idea,” he wrote to Zach,* has at least one great advan- 
tage over some other hypotheses, that it ean be soon tested. For 
f if it is true, we shall be able to find still more fragments of ‘the 
; shattered planet, and the easier stil, because a 
which describe an, elliptical orbit around the sithiaees pass the 
descending node.of Pallas upon the orbit of Ceres.”» + 
| he discovery of Juno, soon after; and net far from-the Ape 
ia rent place of this node, seemed to afford a strong confirmation 
Olbers’s hypothesis, and Zach immediately begant to ponies: it 
a tested and confirmed theory. ae. 
L A simple calculation gives however the following wesisltsl? ; 
‘True anomaly of Ceres, 
‘In % of ses on the Ceres-orbit, - “= 2209-9! 56-6» 
oe toe -  - Pv = aie = 
Ls In Q of. Repe on the Pallas-orbit, - - "D4go 32° 32! 36-0). 
“ & & Juno % is - Woe oo. i ‘9 
* It October, 1804, Olbers wrotet Zach again that the distance 
between the two nodes on the Ceres-orbit (the calculations of 
Gauss gave 24° at that time) ‘was in no wise discordant with his 
hypothesis ; that’as a necessary consequence of the very different 
inclinations to the plane of Jupiter’s orbit, the motion of their 
lines of nodes produced by Jupiter’s attraction must be very dif+ 
ferent from the motion of their apsidal lines, which would fase | 
from the same attraction ; that still farther, inasmuch as t 
bits have nearly “equal major-axes, but very unequal @icetitiiee 
ties, they must have cut one aother at some former time in their 
node upon the Ceres-orbit. Indeed if we assume according to 
the determinations of Oriani, the annual motion of the aphelion 
t fot Pallas = 1061, and for Ceres = 1209, and consider the 
nodes as sidereally ‘at rest, and the inclinations constant, it results 
that a section of the Ceres and Pallas orbits in the above men- 
| tioned node, must have taken place 7463 years before, and in 282 
| years again occur. In the descending node the same would hap- 
. pen in 925 hig s 
4 
s 
wee 
* Monto Corepondes, v8 eA 0,588 
