NEWTONIAN PHILOSOPHY. 
diameter of their orbits directly, and as the 
squares of the periodical times inversely ; 
and the weights at any distance from the 
centre of the planet are greater or less in a 
duplicate ratio of their distances inversely. 
And since the quantities of matter in the 
planets are as their powers at equal dis- 
tances from tlieir centres : and, lastly, since 
the weights of equal and homogeneous bo- 
dies towards homogeneous spheres are, at 
the surfaces of the spheres, as the diameters 
of those spheres ; and consequently, the 
densities of heterogeneous bodies are as the 
weights at the diameters of the spheres. 
VI. The common centre of gravity of the 
Sun, and all the planets is at rest ; and the 
Sun, though always in motion, yet never 
recedes far from the common centre of all 
the planets. 
For the matter in the Sun being to that 
in Jupiter as 1033 to 1 j and Jupiter’s dis- 
tance from the Sun to the semi-diameter of 
the Sun in a ratio somewhat bigger; the com- 
mon centre of gravity of Jupiter and the 
Sun will be a point a little without the Sun’s 
surface ; and by the same means, the com- 
mon centre of Saturn and the Sun will be a 
point a little within the Sun’s surface ; and 
the common centre of the Earth, and all the 
planets, will be scarce one diameter of the 
Sun distant from the centre thereof ; but the 
centre is always at rest ; therefore, though 
the Sun will have a motion this and that 
way, according to the various situations of 
the planets, yet it can never recede far 
from the centre ; so that the common centre 
of gravity of the Earth, Sun, and Planets, 
may be esteemed the centre of the whole 
world. See Planet. 
VII. The planets move in ellipses that have 
their foci in the centre of the Sun ; and de- 
scribe areas proportionable to their times. 
This we have already laid down d posteriori 
as a phenomenon ; and now that the prin- 
ciple of the heavenly motions is shewn, we 
deduce it therefrom d priori. Thus, since 
the weights of the planets towards the Sun 
are reciprocally as the squares of their dis- 
tances from the centre of the Sun ; if the 
Sun were at rest, and the other planets did 
not act on each other, their orbits would be 
elliptical, having the Sun in the common 
umbilicus, and would describe areas propor- 
tionable to the times ; but the mutual actions 
of the planets are very small, and may be 
well thrown aside. 
Indeed, the action of Jupiter on Saturn is 
of some consequence ; and hence, accord- 
ing to the different situation and distances 
of those two planets, their orbits will be a 
little disturbed. The Earth’s orbit too is 
sensibly disturbed by the action of the 
Moon 5 and the common centre of the two 
describes an ellipsis round the Sun placed in 
the umbilicus ; and, with a radius drawn to 
the centre of the Sun, describes areas pro- 
portionable to the times. See Earth, &c. 
VIII. The aphelia and nodes of the planets 
are at rest, excepting for some inconsider- 
able irregularities arising from the action of 
the revolving planets and comets. Conse- 
quently, as the fixed stars retain their posi- 
tion to the aphelia and nodes, they too are 
at rest. 
IX. The axis, or polar diameter, of the 
planets is less than the equatorial diameter. 
The planets, had they no diurnal rotation, 
would be spheres, as having an equal gra- 
vity on every side : but by this rotation the 
parts receding from the axis endeavour to 
rise towards the equator, which, if the mat- 
ter they consist of be fluid, will be affected 
veiy sensibly. Accordingly, Jupiter, whose 
density is found not much to exceed tliat of 
water on our globe, is observed by astrono- 
mers to be considerably less between the 
two poles than from east to west. And, on 
the same principle, unless our Earth were 
higher at the equator than towards the 
poles, the sea would rise under the equator, 
and overflow all near it. But this figure of 
the Earth Sir Isaac Newton proves likewise 
i posteriori, from the oscillations of pendu- 
lums being slower and smaller in the equi- 
noctial, than in the polar parts of the globe. 
See Earth. 
X. All the Moon’s motions, and all the 
inequalities of these motions, follow from 
these principles, e. gr. her unequal velocity, 
and that of her nodes and apogee in the 
syzygies and quadratures; the differences 
in her excentricity and her variation. See 
Moon. 
XI. From the inequalities of the lunar 
motions, we can deduce the several inequa- 
lities in the motions of the satellites. 
XII. From these principles, particularly 
the action of the Sun and Moon upon the 
Earth, it follows, that we must have tides, or 
that the sea must sw'ell and subside twice 
every day. See Tides. 
XIII. Hence, likewise, follows the whole 
theory of comets, as that they are above' the 
region of the Moon, and in the planetary 
spaces ; that they shine by the Sun’s light, 
reflected from them; that they move in 
conic sections, whose umbilici are in the 
centre of the Sun ; and, by radii drawn to 
