On the Small Planets between Mars and Jupiter. 81 
tion upon the whole group to which they belong. This is what 
we propose here to examine. 
The small planets revolve in a zone which begins at the 
mean distance of 2°20 from the sun and extends to the distance 
of 3-16; unity being here the mean distance of the earth from 
the sun. 
The excentricities of the orbits are quite considerable; their 
mean rising to 0-155, The amount of excentricity in each one 
seems to bear no relation to the mean distance from the sun, or 
to the longitude of the perihelion. 
The inclinations of the orbits, both with reference to each 
other and to the ecliptic, are also quite large. 'The mean of the 
sines of the inclination to the ecliptic is 0:155. The amount of 
the inclination in each one does not appear to depend either upon 
the mean distance from the sun, or upon the direction of the 
ascending node. 
The perihelia and the ascending nodes present some special 
peculiarities. The perihelia of teventy of them, having their 
longitudes between 4° and 184°, are embraced in an extent of 
the heavens less than a semi-circumference. The ascending 
nodes of the orbits of twenty-two, whose longitudes are between 
36° and 216°, are also comprised within less than half of the 
circumference of the heavens, and nearly coincident with the 
Space occupied by their perihelia. Possibly we may trace a regu- 
lar difference between the mean direction of the ascending nodes 
of the planets nearest to the sun and of those more remote, and 
so have ground for the conjecture that these asteroids belon 
really to two distinct groups. But we pass this by for the present. 
What has been said suffices for our present purpose; viz., the de- 
termination of a superior limit of the total mass of matter that can 
exist in the zone of the heavens which we are considering. _ 
_ Such an investigation can be based only upon a close examina- 
tion of the nature and amount of the influences exerted by this 
Matter upon the nearer planets, Mars and the Earth. The differ- 
ent terms into which we commonly resolve these influences are 
hot equally well suited to our object. The periodic terms, de- 
Pending upon the relative situation of the planets influenced and 
the small masses which act upon them, neutralize each other, if 
there are a great number of asteroids situated at each instant in 
every part of the heavens: so that the sum total of the disturb- 
h 
long ude of the perihelia and nodes, may however present analo- 
Stoonp Senrms, Vol. XVII, No. 52.—July, 1854. il 
