An Explication of the Sixth PLATE.
Figure 1. Is an Instrument to shew the various Parabola's that are made by
Projectils, and particularly the Truth of the several Rules in the Art of
Gunnery. Wherein A B is a Tunnel full of Quicksilver, D K is a Glass Tube,
let into a Groove or Frame of Wood for its Support, and at K is a fine
Stem, accommodated to the Arch of a Quadrant L M, and turning upon its
Center, to direct the projected Quicksilver to any Angle; while the Tube's
perpendicular Altitude, or the Force that produces the Projection, is
either the same, or altered by a different Inclination at Pleasure,
according to the Nature of the several Experiments.
_Fig. 2._ Is a Cycloid with its equal Sides A B, A C, and pendulous Body
E, oscillating therein. And, _Note_, That by the Make of the Figure, the
Line B C is equal to the Circumference of the Circle D G F, by which it
was describ'd; that the Length of the Cycloid it self is four times that
Circle's Diameter; that every Part of it from F the _Vertex_ is still
double to the Chord of the Correspondent circular Arch G F; that its
included Area B D C F, is Three times the Area of the former Circle; that
the Force upon the Pendulum at any Point E, is exactly proportional to the
Distance along the Cycloid of the Point from the _Vertex_, as E F; and
that therefore the Time of every Oscillation, in all Angles whatsoever, is
always equal.
_Fig. 3._ A C B is a Syphon with Quicksilver from A to C, and a Pendulum
of half that Length; to shew here also that the Force is as the Line to be
describ'd, and that by Consequence the Vibrations in the Syphon are all
equal: as also to shew that they are equal to those of a Pendulum, of half
the same Length: As is plain from the former Case of the Cycloid, where
the Length of the Pendulum is half that of the Cycloid in which the Body
moves.
_Fig. 4._ A B are two Spheres, to denote the several Laws of Motion in the
Collision of Bodies, whether Elastical or not Elastical, to be tried in
the Cycloid, or in a Circle, with proper Corrections: Which Experiments
yet are most of them too difficult for such a Course as this is.
_Fig. 5._ Is an Instrument to explain muscular Motion; supposing the
Muscles to be some way like a String of Bladders; by shewing that a
smaller Quantity of an elastical Fluid may equally raise equal Weights
with a larger; and to shew exactly what Quantity is necessary for any
particular Effect. For thus will the lesser Quantity of Air, (measured in
both Cases by the Gage C A K, as condens'd by the Syringe H A) equally
raise an equal Weight to the same Height by the lesser three Bladders,
that the greater Quantity raises the same by the one larger Bladder.
_Fig. 6._ Are several Pendulums of several Sorts of Matter, heavy and
light; where the Centers of Suspension and Oscillation are equally
distant, and the Times of those Oscillations are all equal. This also
hints the other remarkable Phænomena of Pendulums; _viz._ that the
Semicircular and Cycloidal Times of Oscillation are to each other as 34 to
29: That in both the Length of the Strings of Pendulums are in a duplicate
Proportion to their Times of Oscillation; and that the Heights of Roofs,
_&c._ may be found from the Times of the Oscillations of Pendulous Bodies
fixed to them, on the known Hypothesis that a Pendulum of 39.2 Inches
vibrates in one Second of Time.
_Fig. 7._ Is a Fountain running on Wheels, and made by Air condens'd on
the Surface of Quicksilver, and so forcing the Quicksilver to ascend
through the Pipe G: And is to shew that the Lines of Projectils, or other
Bodies, are not alter'd by the common Motion of the whole Instrument or
Floor on which they are plac'd; and that all Motions on the Earth, if it
move, will be the same as if it stand still.
_Fig. 8._ Is a Parabola with the several Lines belonging to it, in order
to demonstrate the Doctrine of Projectils; and particularly the Art of
Gunnery.
_Fig. 9._ Is an Engine moving on Wheels, that lets a Ball fall down from a
Groove through a Hole, as it is in Motion; to shew that it will then fall
on the same Point of the Frame that it falls upon when it is at rest; as
does a Stone let fall from the Top of the Mast of a Ship under Sail: and
that all respective Motions on the Earth must be the very same, while it
self moves as if it were at rest.
_Fig. 10._ Is a Cylindrical Iron A B, swinging on a Pin E F, in the very
same time that a pendulous Body D of two thirds of its Length C D does; to
shew that two thirds is the Center of Oscillation or Percussion in all
such prismatick or cylindrical Bodies.
[[Opticks Plate I. ― Sutton Nicholls sculp:]]
7
OPTICKS.
An Explication of the First PLATE.
Figure 1. Represents the Foundation of Vision, and of all Opticks
whatsoever, by exhibiting to the Eye a Specimen how the Rays of Light do
as well originally, as after Reflection or Refraction, spread themselves
in right Lines from each Point in every visible Object, as P, to each
other Point, as R, R, R, R, R, every way, to be receiv'd by the Eye in any
direct Position whatsoever.
_Fig. 2._ Represents the known Law of Reflection; that the Angle of
Incidence C P D, is equal to that of Reflection C P E, or that the Angle
of Inclination D P A is equal to the other E P B.
_Fig. 3._ Shews the Reason why a plain Looking-Glass, as A E F B, exhibits
the Object C D by the Image _c d_, which is equal to C D, and equidistant
from the Glass A _c_ = A C: And in an erect Posture; all depending only on
the Equality of the Triangles, whose Vertices are C _c_ : D _d_, and have
their common Bases below E and above F, which Glass by forming the same
Image _c d_, so to the Eye, as if the real Object C D was at _c d_, must
needs shew that Picture in the Place assign'd, without any Inequality of
Distance or Magnitude, or any Inversion.
_Fig. 4._ Shews the Reason why the same or equal Object, as A B, C D, E F,
appears larger when it is nearer, and smaller when farther off: _viz._ on
account of the Inequality of the Angles A G B, or M G N, and C G D, or
K G L, and E G F or H G I, and the consequent Inequality of the Pictures
made by the Rays at the Bottom of the Eye.
_Fig. 5._ Shews the Reason why a Convex Looking-Glass, as A E F B,
exhibits Object C D by the Image _c d_, both nearer to the Glass, and
lesser than it self; but still in an erect Posture. All depending only on
the different Bend of the Circle between E and its lower Point, between F
and its upper Point; which cannot make the Angles of Reflection or
Inclination equal, as they must needs be in all such Reflections, without
making the Vertices of the Angles, as _c_ and _d_, nearer the Glass than C
and D: And so the apparent Picture or Diameter _c d_ lesser than that of
the Object C D, though without any Inversion.
_Fig. 6._ Shews the Reason why a Concave Glass, as A E F B, exhibits an
Object plac'd nearer the Glass than the Center, as C D by the Image _c d_,
remoter from the Glass, and larger than it self, _viz._ for Reasons just
contrary to those under the fifth Figure foregoing.
_Fig. 7._ Shews the Reason why a Concave Glass, as C D E F, exhibits an
Object, if it be plac'd remoter than the Center, as A B, inverted, and at
different Distances between the Eye and the Glass; according to the Length
or Shortness of its own Distance, as B C or A D, _viz._ Because the Rays
from the same Point still cross one another, as at G and H, before they
fall upon the Eye; and so by forming an inverted Image make it impossible
for the Eye to see the Object in any other Position than that the Image
has; which Image indeed it self is the only proper Object of the Eye, in
all such Cases whatsoever.
_Fig. 8._ Is a Picture in Confusion; but rectified by a Convex Cylinder,
and thereby brought into exact Order again.
_Fig. 9._ Represents an Image in a Cylindrical Concave Surface, when the
Eye is in a Plain perpendicular to its Axis; so that lengthways it is as a
Plain, and breadthways as a Concave _Speculum_: Which therefore makes the
Picture longer, but not wider. The contrary will happen in a Convex
_Speculum_, which will make it shorter but not narrower, for the like
Reason.
[[Plate II. ― Sutton Nicholls sculp.]]