. NEWTONIAN PHILOSOPHY. 
primary planets ; and of the primary planets, 
with respect to the Sun. 
As to the Moon, the proposition is tlius 
proved: the Moon’s mean distance is 60 
semidiameters of the Earth ; her period, 
with r egard to the fixed stars, is 27 days, 
7 hours, 43 minutes; and the Earth’s cir- 
cumference 123,249,600 Paris feet. Now, 
supposing the Moon to have lost all her 
motion, and to be let drop to the Earth, 
with the power which retains her in her 
orbit, in the space of one minute she will 
fall 15^5 Paris feet; the arch she describes 
in her mean motion, at the distance of 60 
diameters of the Earth, being the versed 
sign of 15^ Paris feet. Hence, as the 
power, as it approaches the Earth, increases 
in a duplicate ratio of the distance in- 
versely ; so as at the surface of the Ear th 
it is 60 X 60 greater than at the Moon; a 
body falling with that force in our region 
must, in a nrinute’s time, describe the 
space of 60 X 60 X 15^ Paris feet, or 
15j‘j Paris feet in the space of one second. 
Birt this is the rate at which bodies fall 
by their gravity at the snrface of ortr Earth ; 
as Huygens has demonstrated by experi- 
ments with pendulums. Consequently, the 
power whereby the Moon is retained in 
her orbit, is tire very same we call gravity ; 
for, if they wer-e different, a body, falling 
with both powers together, would descend 
with double the velocity, and in a second 
of lime describe 30 a feet. 
As to the other secondary planets, their 
phenometra, with respect to their primary 
ones, being of the same kind with those of 
the Moon about the Earth, it is argued by 
analogy, that they depend on the same 
causes ; it being a rule or axiotrr all philoso- 
phers agree to, that effects of the same kind 
have the same cairses. Again, attraction 
is alw'ays mutual, i. e. the reaction is equal 
to the action : consequently the primary 
planets gravitate towards their secondary 
ones, the Earth towards the Moon, and the 
Sun towards them all. And this gravity, 
with regard to each several planet, is re- 
ciprocally as the square of its distance from 
the centre of gravity. See Attraction, 
&c. 
IV. All bodies gravitate towards all the 
planets ; and their weight towards any one 
planet, at equal distances from the centre 
of the planet, is proportional to the quantity 
of matter in each. 
Eor the law of the descent of heavy bodies 
towards the Earth, setting aside tlieir un- 
equal retardation from the resistance of the 
air, is this, tliat all bodies fall equal spaces 
in equal times ; but the nature of gravity or 
weight, no doubt, is the same on the other 
planets as on the Earth. 
Suppose, e. gr. such bodies raised to the 
surface of the Moon, and together with the 
Moon deprived at once of all progressive 
motion, and dropped towards the Earth : 
it is shewn, that in equal times they will 
describe equal spaces with the Moon ; and 
therefore, that their quantity of matter is 
to that of the Moon, as their weights to its 
weight. 
Add, that since Jupiter’s satellites re- 
volve in times that are in a sesquiplicate 
ratio of their distances from the centre of 
Jupiter, and consequently at equal distances 
from Jupiter, their accelerating gravities 
are equal ; therefore, falling equal altitudes 
in equal times, they will describe equal 
spaces ; just as in heavy bodies on our Earth. 
And the same argument will hold of the pri- 
mary planets with regard to the Sun, and 
the powers whereby unequal bodies are 
equally accelerated are as the bodies, i. e. 
the weights are as the quantities of matter 
in the planets, and the weight of the primary 
and secondary planets towards the Sun, are 
as the quantities of matter in the planets 
and satellites. 
And hence are several corollaries drawn 
relating to the weights of bodies on the sur- 
face of the Earth, magnetism, and the exist- 
ence of a vacuum. 
V. Gravity extends itself towards all bo- 
dies, and is in proportion to the quantity of 
matter in each. 
That all planets gravitate towards each 
other has been already shewn; likewise, 
that the gravity towards any one, consider- 
ed apart, is reciprocally as the squares of 
its distance from the centre of the planet ; 
consequently, gravity is proportionable to 
the matter therein. Further, as all the parts 
of any planet. A, gravitate towards another 
planet, B ; and the gravity of any part is to 
the gravity of the wdiole, as the matter of 
the part to the matter of the whole ; and as 
reaction is equal to action : the planet B will 
gravitate towards all the parts of the planet 
A ; and its gravity towards any part will be 
to its gravity towards the whole, as the 
matter of the part. to the matter of the 
whole. Hence we derive the methods of 
finding and comparing weights of bodies to- 
wards different planets ; of finding the quan- 
tity of matter in the several planets, and 
their densities ; since tlie weights of equal 
bodies, revolving about planets, are as the 
