=, , 
’ -.. 
34 B. A. Gould, Jr., on the Orbits of the Astercids. 
In a paper like this, the influence of the perturbations is of 
course, not to be considered ;—still less the mutual action of the 
asteroids upon one another. Be it allowed me here, however, to 
express my belief that in future calculations this influence can- 
not always be neglected. 
Should, at any future time, as is by no means impossible, 1 two 
of those coupled i in the following table, approach the node at the 
same time, their mutual action must,.in spite of their excessively 
small mass, be extremely strong. 
Such an occurrence is for Ceres and Pallas nud. for similar pairs, 
where the periods of revolution are very nearly equal, not so 
probable as for such pairs as Flora‘and Astrea, whose periods of 
revolution differ by 3174 days and which revolve, ewan ab in 
planes inclined to another by a small angle. 
The following are those nodes at which the asteroid orbits are 
ata less distance from one another than one-fifth of the n 
radius-vector of the earth, and where, as before, the first erg 
tioned orbit is referred to ‘the other. 
sremonee id the orbits. 
Asc. Node, 
Pallas and Amrea, : E , 0:12 
Juno ; Fe 
Ceres ‘* . 
Flora “ al ‘ 
Hebe “ Tas; . 
Juno Co Me 0-11 
a fh 
Vesta “ & . 0- ae 
fiora sé ; e r ‘ 0-02 ‘ . 
illus = Flora, : . . : é 0-13 
Behe. 88 02 ee : 0-03 
Paltas ‘ Vesta, . : ‘ . 0-10 
Pallas “ Ceres, .. F ‘ 3 “19 
“4 Juno, - J . A 
The shortness of the iio | in which ‘Astreaa and Flora com- 
plete each an integral number of revolutions (nineteen revolutions 
of Flora are is nearly equal to fifteen of Astrea), renders 
such an appro to one another in the vicinity of the above 
mentioned 20 by no means improbable. Indeed if the ele- 
ments of both planets could at present be considered as suffi- 
istant 
= = geri it would be — easy to name a not very d 
which this must ap 
ae similar relation is “that of Iris and Hebe to Flora, 
om to Vesta, in the descending nodes. The periods of 
revolution are in the case of Iris and Vesta, very nearly eq 
on the ates hand the mutual inelinaton ‘of the two orbits is 
very sm 
gs periods of Iris and Flora are to one another, nearly as 
9 to 8, of Hebe and Floray nearly as 15 to 13. Here however 
