226 LeVerrier on the constitution of the Solar System. 
the earth. This group of asteroids would accelerate the motion of 
the perihelion of Mars just as an addition of a tenth to the mass of 
the earth would do. If it is situated very nearly in the ecliptic, 
it will produce the same effect upon the orbit of Venus. It wil 
have, moreover, no influence upon the periodic terms of the 
perturbations of Venus and Mars. Finally the relation existing 
between the mass of the earth, gravity and parallax of the sun 
will not be altered.* 
At the beginning, we had hoped that it would be possible to 
derive the true mass of the earth from the periodical perturba- 
tions of Mars, and from its secular perturbations, some knowl- 
edge of the total mass of the asteroids situated between Mars 
and Jupiter. 
The first part of this attempt has only half succeeded, on — 
er 
account of the peculiar circumstances of the observations. 
was simply reason to believe it unnecessary to increase the mass 
of the earth. We see at once what high interest attaches to the 
direct determination of the velocity of light, and, in consequence, 
of the amount of the solar parallax. We should thus solvea 
nice question. 
The estimation of the total mass of the small planets situated 
between Mars and Jupiter, becomes impossible if the group 0 
asteroids which is found at the same distance from the sun as the 
earth is admitted to have any influence. There being no means 
of separating completely the effects of these two groups, it 1S 
only possible to assign the superior limits of their masses, b 
attributing to each of the groups successively the whole excess 
not exceed about one-third of the mass of the earth. 
The constitution of the inferior (or intra-Jovial) portion of our 
planetary system, deduced from a discussion of observations, 
may then be summed up as follows: 
Ist. Besides the planets, Mercury, Venus, Earth and Mars, there 
exists between the sun and Mercury a ring of asteroids whose mass 
ts comparable with the mass of Mercury itself. : 
2d. At the distance of the earth from the sun, is found a second 
ring of asteroids whose mass is not greater than the tenth part of the 
mass of the earth. 
8d. The total mass of the group of small planets situated between 
Mars and Jupiter is not greater than the third part of the mass of x 
the earth. ‘ 
* Tt is true, that from the determ 
have found that both the earth’s mass and the solar parallax should be 
But this result depends on so small a fraction of the lunar equation that we 
be fully justified in disregarding it. The final data discussed a 
d above have far 
inati th tion of the earth, We 
ination of the Junar equati pe eased. 
