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Fro the given Celerityr of the Body moved, the Height of
the Liquid Cylinder is found, as alfo the Weight of it from the
known fpecific Gravity of the Liquid, and Diameter of the Bo-
dy.-_Lec a Ball, for Inlance, of three Inches Diameter be mo-
ved in Water with a Celerity wherewith it would go fixreen
Foot in a Second: FromExperiments on falling Bodies and o-
thers made on Pendulums, it has been found that this is the
Celerity which a Body acquires in falling from a Height of four
Foot; therefore the Weight of a Cylinder of Water, of three
Inches Diameter, and two Foot high, that is, a Weight of a-
bout fix Pound and three Ounces, is equal to the Reft~ence of
the aforefaid Ball. See DESCENT.
Let the ReJflence fo discovered be divided by the Weight of
the Body, which determines its Quantity of Matter, and you will
have the Retardation.
RESISTENCE of fluid Mediums to the Motion of Pendulums.
The Arch defcribed by a Pendulum ofcillating in vacua, with
the Celerity it has acquir'd in descending, is equal to the Arch
described by the Defcent; but the fame does not happen in a Fluid,
and there is a greater Difference between thofe Arches the greater
the Refilence is; that is, the greater the Arch is which is defcrib'd
in the Defcent.
Let the ReJif/lexe of the Liquid be in Proportion to the Ve-
locity; and let two Pendulums, entirely alike, ofcillating in a Cy-
cloid, perform unequal Vibrations, and begin to fall the fame
Moment; they here begin to move by Forces that are as the Arches
to be deferibed. If thofe Impreffions alone, which are made the
fir't Moment, be considered; after a given Time the Celerities
will be in the fame Ratio, as in the Beginning; for the Retarda-
tions which are as the Velozities themselves, cannot change their
Proportions, the Ratio between Quantities not being changed by
the Addition and Subitradion of Quantities in the fame Ratio.
Therefore in equal Times, however the Celerities of Bodies are
changed in their Motion by the Re/ftence, the Spaces gone
through, are as the Forces in the Beginning; that is, as the Arches
to be defcribed by the Defcent i therefore after any time the
Bodies are in the correspondent Point of thofe Arches. But in thefe
Points the Forces generated are in the fame Ratio as in the Be-
ginning, and the Proportion of the Celerities, which is not vari-
ed by the Rejflence, fuffers no Change from the Gravity. In the
Afcent, Gravity retards the Motion of the Body; but in corref-
pondent Points, its Adtions are in the fame Ratio as in Defeents.
And therefore every where in correfpondent Points, the Celerities
are in the fame Ratio. But as in the fame Moment# the Bodies
are in their correfpondent Points, it follows that the Motion of
both is deftroy'd in the fame Moment, that is, they finiffi their
Vibrations in the fame Time.  The Spaces run through in the
Time of one Vibration, are as the Forces by which they are run
thro'; that is, the Arches of the whole Vibrations are as the Arches
defcribed by the Defcent, the doubles whereof are the Arches to
be described in Vacuo. The DetetLs of the Arches to be defcri-
bed in Liquids from the Arches to be defcribed in Vacuo, are the
Differences of Quantities in the fame Rario, and are as the
Arches defcrib'd by the Defcent. See PENDULUM1.
RESISTENCE of Fuid' MediUms to the Motion of falling Bodies.
The Rejqflences are as the Squares of the Celerities, and
therefore every where in correfpondent Points, as the Squares of
the Arches defcribed by the Defcent, in which Ratio alfo, the
Retardations are; but as each of them keep the fame Proporti-
on in correfponding Poinrs, the Sums of them all will be in the
fame Proportion; that is, the whole Retardations, which are the
Defedts of the Arches described in the Liquid, from the Arches
to be described in Vacuo, or which is the fame, the Difference
between the Arches described in the Defcent, and the next Af-
t cent. Therefore thefe Differences, if the Vibrations are not ve-
ry unequal, are nearly as the Squares of the Arches defcribed by
the Defcent: Which is alfo confirm'd by Experiments in greater
Vibrations; for in thefe the Proportion of Refflence, here confi-
dered, obtains.
A Body freely descending in a Fluid is accelerated by the re-
fpedive Gravity of the Body, which continually ads upon it,
yet not equably, as in a Vacuum: the Rejijience of the Liquid oc-
cafions a Retardation, that is, a Diminution of Acceleration,
which Diminution increafes with the Velocity of the Body. Now
there is a certain Velocity, which is the greateft a Body can
acquire by falling; for if its Velocity be fuch that the Ref/iflce
anifing from it becomes equal to the refpective Weight of the
Body, its Motion can be no longer accelerated; for the Motion
here continually generated by the refpedcive Gravity, will be
diftroy'd by the Refifience, and the Body forced to go on equably.
A Body continually cories nearer and nearer to this greateft
Celerity, but can never attain to it.
When the Denfities of a Liquid Body are given, the re-
fptf&ive Weight of the Body may be known; and by knowing
the Diameter of the Body, it may be found     from what
Height a Body falling in Vacuo, can acquire fuch a Velocity, as that
th Reiftence in a Liquid fhall be equal to that refpediveWeight,


which will be that greateft Velocity above mentioned.-If the
Body be a Sphere. it is known that a Sphere is equal to a Cylin-'
der of the fame Diameter, 'vhofe Height is two third Parts of
that Diameter ; which Height is to be increafed in the Ratio where-
in the refipedlive weight of the Body exceeds the weight of
the Liquid, in order to have the Height of a Cylinder of the
Liquid, whofe weight is equal to the refpecfive weight of the
Body ; but if you double this Height, you will have a Height
from which a Body falling in Vacuo, acquires fuch a Velocity as
generates a ReJijience equal to this refpedive weight, and which
therefore is the greateft Velocity which a Body can acquire fall-
ing in a Liquid from an infinite Height. Lead is eleven times
heavier than Water, wherefore its refpedive weight is as to the
weight of Water as Io to I; therefore a leaden Ball, as it ape
pears from what has been faid, cannot acquire a greater Velocity
in falling in Water, than it would acquire in falling in Vacuo,
from an Height of 'I3 -3- of its Diameters.
A Body lighter than a Liquid, and afcending in it by the Adti-
on of the Liquid, is moved exadtly by the fame Laws as an hea-
vier Body falling in the Liquid. Wherever you place the Body,
it is fuftained by the Liquid, and carried up with a Force equal
to the Difference of the weight of the Quantity of the Liquid,
of the fame Bulk as the Body, from the weight of the Body.
Therefore you have a Force that continually adls equably up-
on the Body, by which not only the A6tion of the Gravity of
the Body is deftroyed fo as that it is not to be confidered in
this Cafe, but the Body is alfo carried upwards by a Moti-
on equably accelerated, in the fame manner as a Body heavier
than a Liquid defcends by its refpecive Gravity; but the equabi-
lity of the Acceleration is deftroyed in the fatre Manner by the
efiJience, in the Afcent of a Body lighter than the Liquid, as it
is deftroyed in the Defcent of a Body heavier.
When a Body fpecifically heavier than a Fluid is thrown up
in it, it is retarded upon a double Account; on Account of the
Gravity of the Body, and on Account of the ReJfexzce oi the
Liquid; con fequently, a Body rifes to a lefs Height than it would
rife in Vacuo with the fame Celerity.  But the Defeds of the
Height in a Liquid from the Heights to which a Body would
rife in Vacuo with the fame Celerities, .have a greater Proporti-
on to each other than the Heights themfelves; and in lefs Heights
the Defedts are nearly as the Squares of the Heights in Vacuo.
RESISTENCE of the Air, in Pneumaticks, is the Force where.
with the Motion of Bodies, particularly Projedtiles, is retarded by
the RefifJence of the Air or Atmofphere.  See AIR and PIlio.
JECTILE.
The Air being a Fluid, the general Laws of the Reiflence of
Fluids obtain therein; only the different Degrees of Denfiry in
the different Stages or Regions of the Atmofphere, occafion fome
irregularity. See ATMOSPHERL
The diff*rent RESISTENCE of thejfame Mediums to Bodies of difi-
rent Figures.
Sir Jfaac Newton fhews, That if a Globe and a Cylinder of
equal Diameters. be moved with equal Velocity in a thin Me-,
dium, confiting of equal Particles, difpofed at equal Diftances,
according to the Diredtion of the Axis of the Cylinder; the Re-
fijence of the Globe will be lefs by half than that of the Cy-
linder.
Solid of the leaj1 RESISTENcE.-From the laft Propofition the
fame Author deduces the Figure of a Solid, which Shall have the
leaft RefJilence of any containing the fame Quantity of Matter
and Surface. See SOLID.
The Figure is this.-Suppofe DNFB (Tab. Mechanickf, Fig.
57.) to be fuch a Curve, as, that if from any Point N, be let
fall a Perpendicular NM, to the Axis AB, and from a given Point
G, be drawn a right Line GR, parallel to a Tangent to the Fi-
gure in N, and cut the Axis when continued, in R : A Solid
described by the Revolution of this Figure about its Axis AB,
moving in a Medium from A towards B, is leis reffled than in
any other circular Solid of the fame Area, &c. Newt. Princ. p. 327.
The Refiftence of a Globe, perfedly hard and in a Medium,
whofe Particles are fo too; is to the Force wherewith the Whole
Motion may be either deftroy'd or generated which it his when
at the time, when it has described four thirds of its Diameter;
as the Denfity 6f the Medium to the Denfity of the Globe.-
Hence alib, the fame Author infers that the Rerzj7ence of a Globe,
is, cateris paribus, in a duplicate Ratio of its Velocity.  Or its
Refiflence is ceteris paribus, in a duplicate Ratio of its Diameter.
Or, ceeris paribus, as the Den ity of the Medium. Laffly, that
the adtual Re/jiene of a Globe is in a Ratio compounded of the
duplicate Ratio of the Velocity, and of the duplicate Ratio of
the Diameter, and of the Ratio of the Dentity of the Me-
dium.
In they: Articles the Medium is fuppofed to be difcontinuous,
as Air probably is: If the Medium be continuous, as Water,
Mercury, &c. where the Globe does not ftrike immediate-
ly on all the Particles of the Fluid generating the Re/y~exce,
but only on thofe next it, and thofe again on othersi
e. the' Rejilence will be lefs by half  And a Globe in
fuch a Medium undergoes a RefJience which is to the Force
where-


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