1would have you conſider three Places, which
I call Points; the two Ends, that is the Steel
and the Peathers, and the third is the Loop in
the Middle for throwing the Dart by; and the
two Spaces between the two Ends and the
Loop, I ſhall call the Radii. I ſhall not diſ
pute about the Reaſons of theſe Names, which
will appear better from the Conſideration of
the Thing itſelf. If the Loop be placed ex
actly in the Middle of the Dart, and the Fea
ther End be juſt equal in Weight to the Steel,
both Ends of the Dart will certainly hang even
and be equally poiſed; if the ſteel End be the
Heavieſt, the Feather will be thrown up, but
yet there will be a certain Point in the Dart
further towards the heavy End, to which if
you ſlip the Loop, the Weight will be imme
diately brought to an equal Poiſe again; and
this will be the Point by which the larger Ra
dius exceeds the ſmaller juſt as much as the
ſmaller Weight is exceeded by the larger. For
thoſe who apply themſelves to the Study of
theſe Matters, tell us, that unequal Radii may
be made equal to unequal Weights, provided
the Number of the Parts of the Radius and
Weight of the right Side, multiplied together,
be equal to the Number of thoſe Parts on the
oppoſite left Side: Thus if the Steel be three
Parts, and the Feather two, the Radius be
tween the Loop and the Steel muſt be two, and
the other Radius between the Loop and the
Feather muſt be three. By which Means, as
this Number five will anſwer to the five on the
oppoſite Side, the Radii and the Weights an
ſwering equally to one another, they will hang
even and be equally poiſed. If the Number
on each Side do not anſwer to one another,
that Side will overcome on which that Inequa
lity of Numbers lies. I will not omit one Ob
ſervation, namely, that if equal Radii run out
from both Sides of the Loop, and you give the
Ends a twirl round in the Air they will de
ſeribe equal Circles; but if the Radii be un
equal, the Circles which they deſcribe, will be
unequal alſo. We have already ſaid that a
Wheel is made up of a Number of Circles:
Whence it is evident, that if two Wheels let
into the ſame Axis be turned by one and the
ſame Motion, ſo as when one moves the
other cannot ſtand ſtill, or when one ſtands
ſtill the other cannot move; from the Length
of the Radii or Spokes in each Wheel we may
come at the Knowledge of the Force which is
in that Wheel, remembring always to take the
Length of the Radius ſrom the very Center of
the Axis. If theſe Principles are ſufficiently
underſtood, the whole Secret of all theſe En
gines of which we are here treating, will be
maniſeſt; eſpecially with Relation to Wheels
and Leavers. In Pullies indeed we may con
ſider ſome ſurther Particulars: For both the
Rope which runs in the Pully and the little
Wheel in the Pully are as the Plain, whereon
the Weight is to be carried with the middle
Motion, which we obſerved in the laſt Chapter
was between the moſt Eaſy and the moſt Dif
ficult, inaſmuch as it is neither to be raiſed up
nor let down, but to be drawn along upon the
Plain keeping always to one Center. But that
you may underſtand the Reaſon of the Thing
more clearly, take a Statue of a thouſand
Weight; if you hang this to the Trunk of a
Tree by one ſingle Rope, it is evident this Rope
muſt bear the whole thouſand Weight. Faſten
a Pully to the Statue, and into this Pully let
the Rope by which the Statute hangs, and bring
this Rope up again to the Trunk of the Tree,
ſo as the Statue may hang upon the double
Rope, it is plain the Weight of the Statue is
then divided between two Ropes, and that the
Pully in the Middle divides the Weight equal
ly between them. Let us go on yet further,
and to the Trunk of the Tree faſten another
Pully and bring the Rope up through this
likewiſe. I ask you what Weight this Part of
the Rope thus brought up and put through
the Pully will take upon itſelf: You will ſay
five hundred; do you not perceive from hence
that no greater Weight can be thrown upon
this ſecond Pully by the Rope, than what the
Rope has itſelf; and that is five hundred. I
ſhall therefore go no farther, having, I think,
demonſtrated that a Weight is divided by Pul
lies, by which means a greater Weight may be
moved by a ſmaller; and the more Pullies
there are, the more ſtill the Weight is divided;
from whence it follows that the more Wheels
there are in them, ſo many more Parts the
Weight is ſplit into and may ſo much the more
eaſily be managed.
I call Points; the two Ends, that is the Steel
and the Peathers, and the third is the Loop in
the Middle for throwing the Dart by; and the
two Spaces between the two Ends and the
Loop, I ſhall call the Radii. I ſhall not diſ
pute about the Reaſons of theſe Names, which
will appear better from the Conſideration of
the Thing itſelf. If the Loop be placed ex
actly in the Middle of the Dart, and the Fea
ther End be juſt equal in Weight to the Steel,
both Ends of the Dart will certainly hang even
and be equally poiſed; if the ſteel End be the
Heavieſt, the Feather will be thrown up, but
yet there will be a certain Point in the Dart
further towards the heavy End, to which if
you ſlip the Loop, the Weight will be imme
diately brought to an equal Poiſe again; and
this will be the Point by which the larger Ra
dius exceeds the ſmaller juſt as much as the
ſmaller Weight is exceeded by the larger. For
thoſe who apply themſelves to the Study of
theſe Matters, tell us, that unequal Radii may
be made equal to unequal Weights, provided
the Number of the Parts of the Radius and
Weight of the right Side, multiplied together,
be equal to the Number of thoſe Parts on the
oppoſite left Side: Thus if the Steel be three
Parts, and the Feather two, the Radius be
tween the Loop and the Steel muſt be two, and
the other Radius between the Loop and the
Feather muſt be three. By which Means, as
this Number five will anſwer to the five on the
oppoſite Side, the Radii and the Weights an
ſwering equally to one another, they will hang
even and be equally poiſed. If the Number
on each Side do not anſwer to one another,
that Side will overcome on which that Inequa
lity of Numbers lies. I will not omit one Ob
ſervation, namely, that if equal Radii run out
from both Sides of the Loop, and you give the
Ends a twirl round in the Air they will de
ſeribe equal Circles; but if the Radii be un
equal, the Circles which they deſcribe, will be
unequal alſo. We have already ſaid that a
Wheel is made up of a Number of Circles:
Whence it is evident, that if two Wheels let
into the ſame Axis be turned by one and the
ſame Motion, ſo as when one moves the
other cannot ſtand ſtill, or when one ſtands
ſtill the other cannot move; from the Length
of the Radii or Spokes in each Wheel we may
come at the Knowledge of the Force which is
in that Wheel, remembring always to take the
Length of the Radius ſrom the very Center of
the Axis. If theſe Principles are ſufficiently
underſtood, the whole Secret of all theſe En
gines of which we are here treating, will be
maniſeſt; eſpecially with Relation to Wheels
and Leavers. In Pullies indeed we may con
ſider ſome ſurther Particulars: For both the
Rope which runs in the Pully and the little
Wheel in the Pully are as the Plain, whereon
the Weight is to be carried with the middle
Motion, which we obſerved in the laſt Chapter
was between the moſt Eaſy and the moſt Dif
ficult, inaſmuch as it is neither to be raiſed up
nor let down, but to be drawn along upon the
Plain keeping always to one Center. But that
you may underſtand the Reaſon of the Thing
more clearly, take a Statue of a thouſand
Weight; if you hang this to the Trunk of a
Tree by one ſingle Rope, it is evident this Rope
muſt bear the whole thouſand Weight. Faſten
a Pully to the Statue, and into this Pully let
the Rope by which the Statute hangs, and bring
this Rope up again to the Trunk of the Tree,
ſo as the Statue may hang upon the double
Rope, it is plain the Weight of the Statue is
then divided between two Ropes, and that the
Pully in the Middle divides the Weight equal
ly between them. Let us go on yet further,
and to the Trunk of the Tree faſten another
Pully and bring the Rope up through this
likewiſe. I ask you what Weight this Part of
the Rope thus brought up and put through
the Pully will take upon itſelf: You will ſay
five hundred; do you not perceive from hence
that no greater Weight can be thrown upon
this ſecond Pully by the Rope, than what the
Rope has itſelf; and that is five hundred. I
ſhall therefore go no farther, having, I think,
demonſtrated that a Weight is divided by Pul
lies, by which means a greater Weight may be
moved by a ſmaller; and the more Pullies
there are, the more ſtill the Weight is divided;
from whence it follows that the more Wheels
there are in them, ſo many more Parts the
Weight is ſplit into and may ſo much the more
eaſily be managed.