PENITENTIARY HOUSE. See Prison.
PENSTOCK, in engineering, a gate employed for pond-ing back-water ; it works, up vertically in a grooved frame.
PENTADORON, a Roman brick, whose length measuresfive palms. See Brick .
PENTAGON (from the Greek irevrayovoc, quinquangu-lus, compounded of ttev-e, five, and ywvia, an angle ) in geo-metry, a figure of five sides and five angles.
If the five sides are equal, the angles are so too ; and thefigure is called a regular pentagon. Most citadels are regu-lar pentagons.
The most considerable property of a pentagon is, that oneof its sides, for example, de, is equal in power to thesides of a hexagon and a decagon inscribed in the same circle,abode; that is, the square of the side d e is equal to the sumof the squares of the sides Da and d b.
A pentagon, and also a decagon, may be inscribed in acircle, by drawing the two diameters, AFi«i», perpendicu-lar to each other, and bisecting the radius o n at q. Withthe centre q, and distance q a, describe the arc a r ; and withthe centre a, and radius A r, describe the arc r b ; then a bis one-fifth of the circumference ; and a b, carried five timesover, will form the pentagon ; and the arc a b bisected in s,will give a s, the tenth-part of the circumference, or the sideof the decagon.
If tangents be drawn through the angular points, theywill form the circumscribing pentagon, or decagon. SeePolygon , and Regular Figure.
Pappus has also demonstrated, that twelve regular penta-gons contain more than twenty triangles inscribed in thesame circle, lib. v. probl. 43.
The dodecahedron, which is the fourth regular body, con-sists of twelve pentagons.
PENTAGRAPH, or more correctly Pantagraph, orParallelogram, an instrument for copying plans, maps,designs, &c., with expedition, even by a person unskilled inthe art of drawing.
This instrument consists of four brass or wooden rulers, inthe form of a parallelogram, with moveable joints at theangles ; two of the rulers are extended beyond the parallelo-gram, one for the purpose of carrying a fixed socket, called
c, with a metal tracer, in order to trace over the outlines ofthe original drawing or print ; and the other, called b, forcarrying a moveable socket; also called b, with a pencil, inorder to trace out a drawing similar to the original. Theparts, b and c, of the rulers thus extended, being upon thesame side of one of the diagonals, the side of the parallelo-gram, called d, which adjoins the ruler with the moveablesocket, has another moveable socket, also called d, in orderto insert a vertical pin, which is fixed in a flat piece of lead;both of the moveable sockets, b and d, are clamped by meansof a screw. As the metal tracer, c, the pin in the socket
d, and the pencil in the socket b, are cylindrical, in fixingthe instrument, the axes of the three cylinders must be setall in the same plane, and they will remain so throughoutevery movement of the instrument.
The pins which fasten the parallelogram at the anglesbeing also vertical cylinders to the plane of the instrument,the axis of the metal tracing point, in the socket C, and thoseof the two pins in the sockets of b and d, must be in thesame plane; also, the axis of the pin, in the socket d, andthose of the ruler d at the joints, must also be in a plane.In order to make the movement of the instrument easy, it isprovided with casters, or rollers, each of which turns on anaxis in the same line with the axis at the joints or angles.
The extended part of the ruler b, on which the socket andpencil are carried, has several graduations, or divisions, which
show the proportion of the drawing to be made to theoil ^and thus calling the centre of the joint connecting theded bars, the apex of the instrument , the first division ( j lt ;extended part, b, is equally distant from the apex w^ a[)( Jaxis of the tracing point on the other extended part, ’ jjagthe ruler, d, which has the steel pin, has a corresp ^division, exactly opposite the vertex, when the erulers, b and c, are brought into a straight line, an , ^ u! >lquently, the instrument is divided thereby into twoparts ; and thus it becomes necessary to have the t ' v0 j, e( j Pisite sides of the parallelogram, which has the side th elonger than the other two sides, one of whichextended part b.
ali
lenaea parr b. . u pi
The divisions upon the extended part, b, being n% ^ a t
iflPi
is,
,o®
and numbered from 1-1, 1-2, 1-3, 1-4, to I-if 3 up 11, J, £, &c., towards the vertex, the other < h v ’ S1 ° e3 pofl < bthe side of the parallelogram, d, are marked with c0 .L t wli e0ing figures, 1-1, 1-2, 1-3, &c., in such a manner, ^ thethe extended sides are brought into a straightdivision marked 1-2, on the side D, divides the in ^ iQ theinto three equal parts, from the division 1-2 ° npoint c, on the axis of the tracing point on the other ^ J- 1leg, c ; and thus the distance from 1-2, on the side > ^ theon the side b, will be half the distance betweenside d and the point c, on the extended part c. s ;Ie p ’
fro 0the
3iuc ±s aim tuc £juiui/ vjj uu cailiiiugu * - , gjv* v
In like manner, the division marked 1-3, ondivides the instrument into four equal parts, fro® 1 t f"’ 1to the tracer on c; and thus 1-3 on d will l )e “ lS p to1-3 on b, and one-third of the distance from 1-3 0axis of the tracer on c. n er- *
The other proportions are found in a similar m®' go®® 6
The fiducial edges of the clamps, which carr ^ nC il, cT °‘for the steel pin, and the socket for holding the p igg »®
_..... . . ■ , _ _. . .. ,.;<rht ang !j;et
the rulers, to which they are attached, at rig— g0C ,would, if produced, cut the axis of the cylindr 10 ®
would, it produced, cut tne axis ot tne cynm**-— .-.jri®* 1each of the said rulers. The upper part of the of co®'case, which holds the pencil, is provided with a ® U P’ re i*tain shot, or a small weight, in order to make the p eI ..gV' 1 ''sufficiently, so as to mark the paper. In order
the pencil from tracing the same path it has already etl ci >
’ wth the
passes through an eye at the vertex, returns to the ia j ie pap e1 ’
- ! {roto , t
f tW
tne pencil iro m tracino- „
a s >ih thread, or catL] ?aui n lma - , .Passes through an evo , string, connected with the I
operator, andbeino- . e , vert ex, returns to the hand
To use the instrum Vn f tlg ‘ t,laises t!le P encilii,onl * ^
be one-half of t i 1P ' * u PPose the drawing req““ e (be
clamp b upon 1-2 In 7 P na ’ set the fiducial edge , ,;al
®dge of the clam p n ext . e ”ded part b, and the d
socket d upon the nin« UP j n - 1 ~ 2 oP tfie ruier V! S hflW®^adjusted the original n ^ Jnto t)le J ead weight, then 1 ^the paper under th* rawi p& or print, under the tra loriginal, and the n« ^ enft d< tr ace over all the fine®
out a similar figure. ’ C tIie remote extrem, ' V * „
required to^eone^ - a j! ot, ' er example : suppose theof the clamp B M ?>* original; set the &
hducial edo-e of ln the extended part n, g j 0e
the socket d umnti ° amp D upon U3 of the ru ' e -J,t’ ^proceed as before he T pm fixed into the leaden wet
be reduced to i f* J n manner the dra^ „
the graduations-’ of tlie linea l dimensions, as 0 jte«>
0DS: . b . ut ’fany intermediate proportion t*rf d" ' ’ the fiduend." 0 • -
as between a 11,— _ x
the clamp n to thu 3 fourth ; bring the tiau e Jg 0
the P-ot, and the
P a contrary s nnu [ ght then P r0Ceed 'the ^w g> it is onlv /l ld U be required to enlarge tl ® ( 0 r
tube of the damnTj t0 f a " ge the pendl “ £ ® nd ‘Paper for the nfrf P for tbat of the metal tracer,
gmal, and proceed as before.