Archimedes Texts

414
the Moon and Sun; neer, in a word, at the time of its conjun
ction and change; remote, in its Full and Opposition; and the
greatest vicinity differ the quantity of the Diameter of the Lu
nar Orb. Now if it be true that the virtue which moveth the
Earth and Moon, about the Sun, be alwayes maintained in
the same vigour; and if it be true that the same moveable
moved by the same virtue, but in circles unequal, do in shorter
times passe like arches of lesser circles, it must needs be granted,
that the Moon when it is at a lesse distance from the Sun, that is
in the time of conjunction, passeth greater arches of the Grand
Orb, than when it is at a greater distance, that is in its Opppsition
and Full. And this Lunar inequality must of necessity be imparted
to the Earth also; for if we shall suppose a right line produced from
the centre of the Sun by the centre of the Terrestrial Globe, and
prolonged as far as the Orb of the Moon, this shall be the semi
diameter of the Grand Orb, in which the Earth, in case it were
alone, would move uniformly, but if in the same semidiameter we
should place another body to be carried about, placing it one
while between the Earth and Sun, and another while beyond
the Earth, at a greater distance from the Sun, it is necessary,
that in this second case the motion common to both, according
to the circumference of the great Orb by means of the distance
of the Moon, do prove a little slower than in the other case,
when the Moon is between the Earth and Sun, that is at a lesser
distance. So that in this businesse the very same happeneth that
befals in the time of the clock; that lead which is placed one
while farther srom the centre, to make the vibrations of the
staffe or ballance lesse frequent, and another while nearer, to
make them thicker, representing the Moon. Hence it may be
manifest, that the annual motion of the Earth in the Grand
Orb, and under the Ecliptick, is not uniform, and that its ir
regularity proceedeth from the Moon, and hath its Monethly
Periods and Returns. And because it hath been concluded, that
the Monethly and Annual Periodick alterations of the ebbings
and flowings, cannot be deduced from any other cause than
from the altered proportion between the annual motion and the
additions and substractions of the diurnal conversion; and that
those alterations might be made two wayes, that is by altering
the annual motion, keeping the quantity of the additions un
altered, or by changing of the bignesse of these, reteining the
uniformity of annual motion. We have already found the first
of these, depending on the irregularity of the annual motion
occasioned by the Moon, and which hath its Monethly Periods.
It is therefore necessary, that upon that account the ebbings
and flowings have a Monethly Period in which they do grow