Page:Cyclopaedia, Chambers - Volume 2.djvu/429

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Pi A i K Figure, in Geometry, is an uniform Surface, from every Point of whofe Perunierera, right Lines may be drawn to every other Point in the fame. See Figure ; fee alio Plane and Surface.

Plain Angle is an Angle contained under two Lines, or Surfaces. See Angle.

It is fo call'd in contradiftinction to a fold Angle. See Solid.

Plain Triangle is a Triangle included under three right Lines, or Surfaces-, in oppofition to a fpherical, and amixt Triangle. See Triangle.

Plain Trigonometry is the Doctrine of plain Triangles, their Meafures, Proportions, d"r. See Trigonometry.

Plain Glafs, Mirror,Sic. in Optics, is a Glafs or Mirror, whole Surface is flat or even. See the Phenomena Laws of plain Mirrors, under the Article Mirror.

Plain Mirrors are what we popularly call Looking-Glaffes ; fee the manner of grinding, polilhing, and preparing them, under the Article Looking-Glafs Grinding.

P l a i n Tyle. See Tyle.

Plain Scale, is a thin Fuller, whereon are graduated the Lines of Chords, Sines, Tangents, Secants, Leagues, Rhumbs, &c. of ready life in moil Parts of the Mathematics, chief- ly in Navigation. See Line, ei-c.

See its Defcription and Ofe under the Article Scale.

Plain Chart, in Navigation, is a Sea-Chart, wherein the Meridians and Parallels are reprefented by parallel ftrait Lines ; and where, of Confequence, the Degrees are the fame in all the Parallels of Latitude.

See the Properties, ConftruSion, Sic. of thisChart under the Article Chart.

Plain Sailing, in Navigation, is the Art of working the fcveral Cafes and Varieties in a Ship's Motion, on a plain Chart. See plain Chart.

Plain Sailing is founded on the Supposition of the Earth being a Plane or flat ; which, tho' notorioufly falfe, yet Places beinglaid down accordingly, and a long Voyage broke into many Sort ones ; the Voyage may be tolerably perform'd by it, near the fame Meridian.

In Plain Sailing it is imagined, that by the Rhumb- Line, Meridian, and Parallel of Latitude, there always will be formed a Right-angled Triangle; and that Co pofited, as that the Perpendicular may reprefent Part of the Meridian, or North and South Line, containing the Difference of Lati- tude : The Bate of the Triangle, reprefents the Departure;

and the Hypothenufe the Diftance failed The Angle at the

Top is the Courfe, and the Angle at the Bafe the Comple- ment of the Courfe; any two of which, with the Right- Angle being given, the Triangle may be protracted, and the other three Parts found. See Triangle.

For the Doctrine of 'Plain Sailing, fee Sailing.

Plain Table, in Geometry, Ore. an Inftrument ufed in the Surveying of Land -, whereby the Draught, or Plan, is taken on the Spot, without any future Protraction or plot- ting. See Surveying, Plotting, &c.

The Plain Table, reprefented Tab. Surveying, Fig. 31. con- fifts of a Parallelogram of Wood, about 15 Inches long and i2broad; round this goes a Boxen jointed Frame, by means whereof a Sheet of Paper isfaften'd tight to the Table, fo as Lines may be conveniently drawn upon it.

On each fide the Frame, which may be put on either fide upwards, towards the inward Edge, are Scales of Indies, fubdivided, for the ready drawing of Parallel Lines.— Befide which, on one fide are projected the 360 Degrees of a Cir- cle, from a Brafs Center in the middle of the Table, (each Degree halved) with two Numbers to every loth Degree, the one expreliing the Degree, the other its Complement to 360, to fave Subtraction : On the other fide are projected the 180 Degrees of a Semicircle, from a Brafs Center in the middle of the Table's Length, and at ^ of its Breadth ; each Degree halv'd, and every Tenth noted with two Numbers, viz.. the Degree and its Complement to 180.

To one fide of the Table is fitted a Compafs, for placing the Inftrument by, and the whole is fix'd by a Socket, up- on a three legg'd Staff for a Stand, on which it is turn'd round, or faften'd by a Screw, as occafion requires. — Laftly, to the Table belongs an Index, which is a Ruler at leaft 16 Inches long, and 2 broad; and ufually graduated with Scales, &c. and having two Sights perpendicularly placed on its Ex- tremities. See Sight, Staff, Ball, and Socket, &c.

Vfe ofthePLM a-Table.

To tale an Angle hy the Plain Table : Or to find the Di- stance of two Places acccffible from the fame third. — Suppofe DA, DS(Tab. Surveying, Jig. 32.) the fides of the Angle requi- red; or AB the Diftance required.^ Place the Inftrument horizontally as near the Angle as poifible; and affume a Point in the Paper on the Table, v. g. C. To this Point apply the Edge of the Index, turning it about this and that way, 'till thro' the Sights you fee the Point B, and in this Situation of the Ruler, draw by its Edge the Line C E

indefinitely. After the fame manner turn about the Index i on the fame Point, 'till thro' the Sights you fee the Point A -

and draw the right Line c d indefinitely. Thus have you

the Quantity of the Angle laid down.

Meafure the Lines c A, c B, with a Chain ; (fee Chain.) and from a Scale, fet off the Meafures thus found, (fee Scale) on the refpeftive Lines ; which fuppofe to reach from c tob

and from c to a. Thus will cb and ca be proportional to

cB and cA.

Transfer the Diftance ab to the fame Scale, and find its Length ; the Length thus found, will be the Length, or Di- ftance, of A B required.

2° To find the Diftance of two Places, one whereof is inac-

cefjible, by the Plain Table -Suppofe the Diftance required

AB; {Fig. 33.) and A the accellible Point i° Place the Plain Table in C ; look thro' the Sights 'till you fee A and B; and draw ac and cb. Meafure the Diftance from your Station to A; and fet it off from the Scale, upon c a. 2° Remove the Table to A, where place it fo,as that the Point a reprefenting A, and the Index laid along the Line ac, you fee, backwards, the former Station C. {Note, m this fix- ing the Inftrument, lies the Ufe of the Compafs; for the Needle will hang over the fame Degree of the Card in the firft and the fecond Cafe ; fo that Ibme fet the Inftrument by the Needle alone ; others only ufe it to fhorten the Trouble, by bringing the Inftrument nearly to its due Por- tion by means thereof; and then fixing for good by the Back-Sight.) 3 The Inftrument fix'd, turn the Sights to B ; and draw the Line a b. a, On the Scale, meafure the In- terval ab; which will be the Diftance of A B required.

1° To find the Diftance of two inacct-JJible Places by the Plain Table.— Suppofe the Diftance of A B {Cab. Surveying, Fig. 34.) required. i u Chufing two Stations in C and D; in the rirft C, place the Plain Table ; and thro' the Sights look to D, B and A; drawing by the Edge of the Index, the Lines cd, cb, ca.—z° Meafure the Diftance of the Stations CD; and fet this off, from a Scale, on e d.—%° Removing the Table from C, fix it in D; fo as the Point d hanging over the Place D, and the Index lying along the Line cd, thro' the Sights you fee the former Station C. The Inftrument thus fix'd, direct the Sights to A and B, and draw the right Lines d a and d b. Laftly, find the Diftance of a b, on the Scale; this will be the Diftance of A B required.

Alter the fame Manner, may the Diftance of any Num- ber of Places be found from two Stations ; and thus may a Field, part of a Country, &c. be ftirvey'd.

4° To take the Plot of a Field from one Station, whence all

the Angles" may befecn; with the Plain Table. Placing the

Inftrument in the Station, affume a Point in the Paper, to reprefent the fame, v.g.C. {Fig.21.) Laying the Edge of the Index to this Point ; direct it to the feveral Angles of the Field, A B C D E F, &l. and draw indefinite Lines by its Edge, to- wards every Angle, ,Wt. Ca, Cb, Cc, Sic. meafure the Di- ftance of each Angle from the Station, viz.. GA; CB, CC, CD, &c. and from a Scale fet it off from C on its corre- (ponding Line; the Extremities hereof will give Points, which being connected by Lines will reprefent the Field.

5" To take the Plot of a Field, Wood, or the like, by going round the fame; with the Plain Table Place the Inftru- ment horizontally at the firft Angle, v.g. A. The Needle on the Meridian of the Card ; and affuming a Point on the Paper, to reprefent it, to that Point lay the Index, direct- ing it 'till thro' the Sights you fee a Mark in the Angle B. And draw an indefinite Line along it ; meafure the Diltanca of A and B, and from a Scale fet it off on the Line this drawn ; the Extremity of this Diftance will reprefent the Point B. Remove the Inftrument to B, where fet it fo as that the Needle hang over the Meridian of the Card; and foas the Index lying along the Line laft drawn, you Tee the for- mer Station A thro' the Sights: here fallen it, lay the In- dex to the Point B, and turn it, 'till thro' the Sights you fee the next Angle C; in this Situation draw a Line asbe- fore, meafure the Diftance BC, and fet it off from, a Scale on the Line. — -Remove the Inftrument to C, where, fixing it by the Needle, and the Back-Sight, as before, turn the Index on the Point C, 'till you fee the next Angle D; draw the Line, meafui-e, and fet off the Diftance C D as before, and remove the Plain Table to E ; where fix it, as before, look to the next Angle F, draw the Line, meafure, and fet off the Diftance, &c.

In this manner having compafs'd the whole Field, you'll have its whole Perimeter plotted on the Table; which nnv be now caft up and its Contents found, as in the Article of Surveying.

Manner offliifting Paper on the Plain Table.

When in large Parcels of Ground, the Plot is found' W exceed the Dimenfions of the Plain Table, and to run off from the Paper; the Sheet mult be taken off the Table, and a trefh one put on, The way of managing which fhifring,is as follows.— -Suppofe H, K, M, Z, {Fig. 35.) the Limits of the

Plain