1the 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
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
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
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
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
ction and change; remote, in its Full and Oppoſition; and the
greateſt vicinity differ the quantity of the Diameter of the
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
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
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
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