On the Smali Planets between Mars and Jupiter. 83 
terms are respectively proportional to the excentricities of the 
terrestrial orbit and the orbits of the small planets, and as the 
excentricities of these last are at the mean nine times greater 
than that of the earth. | 
The perihelion of Mars is situated much more favorably in re- 
lation to the mean direction of the perihelia of the asteroids; and 
besides the excentricity of its orbit is greater. Asa result of these 
two conditions united, the second term which enters into the ex- 
pression of the motion of the perihelion is only one fourth of the 
rst. Now this superiority of the first term may be expected to 
continue after the discovery of a great number of new asteroids, 
whether this predominance of the perihelia in the mean direction 
of the summer solstice shall be confirmed, as it probably will be, 
or whether we shall be obliged fo return to the idea of a uniform 
distribution of them through every part of the heavens. 
n accordance with these remarks I have found that if the 
mass of the whole group of asteroids was equal to the mass of 
the earth, it would produce in the heliocentric longitude of the 
perihelion of Mars an inequality which in a century will amount 
to eleven seconds. Such an inequality, supposing it to exist, 
surely could not have escaped the notice of astronomers. If we 
reflect that this inequality will become strikingly sensible at the 
moment of the opposition of Mars, we must believe that at pres- 
ent and although the orbit of Mars has not been determined wit 
perfect accuracy it cannot nevertheless admit of an error in lon- 
gitude greater than one-fourth of the inequality which we have 
Pointed out. Hence we conclude that the sum total of the mat- 
ter constituting the small planets situated between the mean dis- 
lances 220 and 3:16 cannot exceed about one-fourth of the mass 
of the Earth. : , 
~ Similar conelusions may be reached by considering the motion 
of the plane of the ecliptic; the result will depend however in 
that case upon the hypothesis that the ascending nodes of more 
than three-fourths of the orbits are situated in a semi-circumfer- 
nee. The limit moreover which we should reach in this way 
Mare by the discovery of new asteroids. Such as it ls, it 
ms fitted to throw some light upon a subject in regard to 
the 0} lowj Pi 
ere ing propositions. : , 
suffe The excentricities of the orbits of the known asteroids can 
euist only very small changes as the effect of perturbation. 
® Compt. Rend., t. xxvii, p. 965. 
