PLA 
PLA 
effect of the attraction of the Earth at a 
distance equal to the mean radius of its 
164 
orbit, is equal to multiplied by 
19614040 
the cube of the tangent of the solar parallax 
= . Hence the masses ot the 
10-“' 
Sun and Earth are to each other as the 
numbers ,1479560.5 and 4.486113; there- 
fore the mass of the Earth is 
of the Sun being unity. M. de la Place 
calculated the ma-sses of Mars and Venus 
from the secular diminution of the obliquity 
of the ecliptic, and from the mean accelera- 
tion of the Moon’s motion. The mass of 
Mercury he obtained from its volume, sup- 
posing the densities of that planet and of 
the Earth reciprocally as their mean dis- 
tance from the Sun, a rule which liolds- 
•with respect to the Earth, Jupiter, and 
Saturn. The following table exhibits the 
masses of the ditFerent planets, that of tiie 
Sun being unity : 
ioio 
Venus 
oo'oloj 
- 
184608a 
i0^9 
eJm 
1^4 
The densities of bodies are proportional 
4o their masses divided by their bulks; and 
when bodies are nearly spherical, their 
bulks are as the cubes of their semi-dia- 
meters, of course the densities in that case 
are as the masses divided by the cubes of 
tire semi-diameters. ' 
Planets, motion of the. Each of the 
primary planets bend their course about 
tbe centre of the Sun, and are accelerated 
in their motions as they approach to liim, 
and retarded as they recede from him; so 
that a ray, drawn from any one of them to 
the Sun, always describes equal spaces, or 
areas, in equal times :■ whence it follows 
that tbe power which bends their way into 
a curve line, must be directed to the Sun. 
This power is no other than that of gravi- 
tation, which we have already proved to in- 
crease, as the square of the planet’s distance 
from the Sun decreases. See Gravita- 
tion, &c. But the univemality of this law 
still further appears, by comparing the mo- 
tions of the different planets: for the power 
which acts on a planet near the Sun, is 
manifestly greater than that which acts on 
a planet more remote ; both because it 
moves with greater velocity, and because it 
moves in a lesser orbit, which has more cur- 
vature, and separates furtiier from its tan- 
gent, in arcs of the same length, than in a 
greater orbit. By comparing the motion 
of the planets, the velocity of a nearer 
planet is found to be greater than that of 
one more remote, in the proportion of ibe 
square-root of tbe number which expresses 
the greater distance, to the square root of 
that which expresses tbe lesser distance ; so 
that if one planet was four times further from 
tlie San than another, the velocity of the first 
would be half the velocity of the latter; and 
the nearer planet would describe an arc in 
one minute, equal to the arc described by the 
otl>er planet in two minutes : and though 
the curvature of the orbits were the same, 
the nearer planet would describe, by its 
gravity, four times as much space as the 
other would describe in the same time ; so 
that the gravity of the nearer planet would 
appear to be quadruple, from the conside- 
ration of its greater velocity only. But be- 
sides this, as tlie radius of the lesser orbit 
is supposed to be four times less than the 
radius of the other, the lesser orbit must be 
four times more curved ; and the extremity of 
a small arc of tbe same length, will be four 
times further below tbe tangent, drawn at 
the other extremity, in the lesser orbit tiian 
in the greater ; so that, tliough the veloci- 
ties were equal, the gravity of llie nearer 
planet would, on this account only, be found 
to be quadruple. Hence, <m both these 
accounts together, the greater velocity of 
the nearer planet, and the greater curvature 
of its orbit, its gravity towards the Sun must 
be supposed .sixteen times greater, though 
its distance from the Sun is only four times 
less than that of the other ; that is, when 
the distances are as 1 to 4, the gravities are 
reciprocally as the squares of these num- 
bers, or as 16 to 1. And in the same man- 
ner as this principle governs the motions of 
the primary planets of the great solar sys- 
tem, acts at their surfaces, and keeps their 
parts together ; so it governs also the mo- 
tions of the satellites, or secondary planets, 
in tlie lesser systems of which the greater is 
composed, and' is extended around them, 
decreasing in the same manner as the squares 
ef the distances increase, Tlie comets are 
c 
