PAR
(748)
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The Axis of the Earth in its annual Morion defcribes a Kind of Cylinder, which being prolong 'd to the Heaven of the fix'd Stars, there forms a circular Circumference; each Point whereof is the Pole of the World for itsrefpe&iveDay : fo that the Situation of the apparent Pole, with regard to any of the fix'd Stars changes very confiderably in the Courfeof a Tear.
Could this be found by Obfervation, it wou'd irrefragably evince the annual Motion of the Earth round the Sun, and re- move that only Objection which lies againft ir, urg'd by Ric- cicins, from no fuch 'Parallax being obferv'd. See Earth.
Accordingly Dr. Hook attempted to find it by obferving the various Diftance of a fix'd Star from the Zenith, in different Partsot the Earth's Orbit; and Mr. Flamjtead, from the Ac- cefs and Recefs of a fix'd Star from the Equator at different Times of the Year, and with Succefs : The Refult of his Ob- fervations being, that the Diftance of a fix'd Star, near the Pole, was found 4.0 or 4.5 Seconds nearer it at the Winter Solitice than at the Summer one, for feven Years fucceflively.
M. CaJJiui the lounger allows the Obfervations o't'Flamfead to agree with thofe made at the Royal Obfervatory ; but he denies the Confequences : he fays the Variations in the Di- ftance of the Pole Star are not fuch as they Ihou'd be, fuppo- fing the Motion of the Earth; and accounts for them from a Supposition that the Stars, like the Sun, turn or revolve on their Centres, and that fbme of 'em have their Hcmifpheres une- qually luminous : Whence, when the more ftiining Hemifphere is turn'd towards us,the Stars appears bigger, confequently more remote than when the darker is towards us. See Star.
Parallax is alfoufedin levelling, for the Angle contain'd between the Line of true Level, and that of apparent Level. See Levelling.
PARALLEL,in Geometry,from the Greek au^'msao;, equi- diftant; is a Term applied to Lines, Figures and Bodies, which, being prolong'd, are (till at equal Diftance from one another.
Parallel Right Xims, are thofe which, tho' infinitely produced, would never meet.
Thus, the Line OP, Tab- Geometry, Fig. 3d. is parallel to Q^R. See Line.
^PaTsllelXAnt is ufed inOppofiiion to Lines converging and diverging. See Converging.
Some define an inclining or converging Line, that which will meet another at a finite Diftance ; And a. 'Parallel that which wou'd only meet at an infinite 'Diftance.
Others define a Perpendicular the morteft of all Lines that can be drawn to another ; and a Parallel the longeft. For the Orthodoxy of thefe Definitions of Parallelifm we don't under- take.
Geometricians demonttrate, that two Lines, parallel to the fame third Line, are alfo parallel to one another ; and that if two Parallels O P and QR, Tab. Geometry Fig. 91J. be cut by a tranfverfe Line ST. in A and B, 1. The alternate Angles * and y are equal, a. The external Angle u is equal to the internal oppofite onci> ; and thirdly, That the two internal oppofite ones & a.ndy are alfo equal to two right ones.
It is fhewn on the Principles of Opticks, that if the Eye be placed between two Parallel Lines, they will appear to con- verge towards a Point oppofite to the Eve. And if they run to fuch a Length, as that the Diftance between them be but as a Point thereto, they will there appear to co-incide.
Parallel Fines are defcribed by letting fall equal Per- pendiculars, and drawing Lines through their Extremes, by Hiding the Compafles open to the defir'd Width along a Line, g$& or by a
Parallel Rukr,ca]]'d alfo Parallelifm, an Inftrument con- fiding of two wooden, brafs, or fteei Rulers A B, and CD ; Fig. %i. equally broad every-where, and fo join'd together by the Crofs-blades EF and GH, as to open to different Inter- vals, accede and recede, yet ftill retain their Parallelifm.
The life of this Inftrument is obvious; for one of the Rulers being applied to P S, and the other drawn to a given Point V ; aright LineAB,drawnbyitsEdge, thro'V, is a parallel to KS.
Parallel Rays, in Opticks, are thofe which keep at an equal Diftance to each other, from the vifible Object to the Eye, which isfuppofed to be infinitely remote from the Object. See Ray.
Parallel Planes are thofe Planes, which have all the Per- pendiculars drawn betwixt them equal to each other. See Plane.
Parai.li.ls. or Pahallt.i Qrcks, in Geograpny,caUM alfo Pa- rallels of Latitude, and Circles of Latitude, are letter Circles of the Sphere, conceived to be drawn from Weft to Eafl- thro' all the the Points of Meridian ; commencing from theEq uator,ro which they are parallel, and ending with the poles. See Circle.
They are call'd Parallels of Latitude, $$ c . becaufe all Places lying under the fame Parallel, have the fame Latitude. See Latitude.
Pabjkueuo/ Latitude, in Aftronomy,arelefler Circles of the Sphere parallel to the Ecliptic, imagined to paTs thro' every Degree and Minute of the Colures. See Latitude.
They are reprefenred on the Globe by the Divifions of the Quadrant of Altitude, in its Motion round the Globe, when fcrew'd over the Poles of the Ecliptic. See Glob b.
Parallels of Altitude or Mmacanten, are Circles parallel to the Horizon, imagined to pais thro' every Degree and Mi- nute of the Meridian between the Horizon, and Zenith; having their Poles in the Zenith. See Altitude.
On the Globes they are reprefented by ;he Divifions on the Quadrant of Altitude, in its Motion about the Body of the Globe, when fcrew'd to the Zenith. See Globe.
PMtM.LLLsofZ)eclination, in Aftronomy, are the fame with Parallels of Latitude in Aftronomy. See Declination .
Parallel Sphere, that Situation of the Sphere, wherein the Equator co-incides with the Horizon, and the Poles with the Zenith and Nadir. See Sphere.
In thisSphere all the Parallels of the Equator become Pa- rallels of the Horizon, confequently no Scars ever rife or fer ■ but all turn round in Circles parallel to the Horizon ; and the Sun, when in the Equinoctial, wheels round the Horizon the whole Day. After his rifing to the elevated Pole, he never fets for fix Months; and, after his retiring again to the other Side of the Line, never rifes for fix Months longer.
This Pofition of the Sphere is theirs who live under the Poles ; ifanyfuch there be. Their Sun is never above 2 3 . jp'.higK'.
Pakallll Sailing, in Navigation, is the Sailing under a Pa- rallel of Latitude. SeeSAiLiNG.
Of this there are but three Cafes. 1. Given, the Departure, and Diftance ; required the Latitude. The Canon is, As Diffe- rence of Longitude is to Radius : : So is Diftance, to Co-fine of the Latitude.
2.. Given Diff of Longitude between two Places under the fame Parallel, required their Diftance. The Canon is, As Rad. to Diff. of Longitude : : So is Co- fine of Latitude to Di- ftance.
3. Given the Diftance between two Places in the fame La- titude ; required their Difference of Longitude. The Canon is, As the Co-fine of Lat. to Diftance : ; So is Rad. to Diff". of Longitude.
PARALLELOPIPED,in Geometry,one of the regular Bo- dies, or Solids, comprehended under fix. Rectangular" and Pa- rallel Surfaces, the oppofite ones whereof are equal : As in the Figure Tab. Geometry Fig. 38. See Recular.
Two Cubes, laid together,Side by Side,conftitute a Parallelo- piped : And the fame may be faid of a fquare Beam, whofe two Extremes are fquare, and Sides long Squares.
Properties of the Parallelipiped.
All Parallelepipeds, Prifms, and Cylinders, whofe Bafcs and Heights are equal, are, themfelves, equal.
A diagonal Plane divides the Parallelepiped into two equal Prifms : A Triangular Prifm, therefore, is half a Parallelo- piped upon the fame Bafe and of the fame Altitude. Sec Prism.
All Parallelepipeds, Prifms, Cylinders, $$& are in a Ratio compounded of their Bafes and Altitudes : Wherefore, if their Bafes be equal, they are in Proportion to their Altitudes 5 and converfly.
All Parallelepipeds, Cylinders, Cones, &c, are in a tripli- cate Ratio of their homologous Sides ; and alfo of their Alti- tudes.
Equal Parallelepipeds, Prifms, Cones, Cylinders, ggfo re- ciprocate their Bafes and Altitudes.
To meafnre the Surface and Solidity of a Parallelopiped.
Find the Areas of the Parallelograms I L M K, LMON. See Parallelogram. Add thefe into one Sum, and mul- tiply that Sum by 2 : The fafhim will be the Surface of the Parallelopiped. If then the Bafe ILMK be multiplied by the A Ititude L N, the Produft will be the Solidity.
Suppofe<y.g. LM — jtfMK = 15 MO-12. Then,
LM --<jLM~3<rMK = i 5 MK = iy-MO=wM'0=M
180 5*
7* 3 tf
3" i" *)
LIKM54O LMON432 MOKPl8o
LIKM 540 MOKP180
2304 MO 12
2304
1152
2304 Superficies.
27648 Solidity.
PAR ALLELISM, the Quality of a Parallel ; or that which denominates it fuch : Or it is that whereby two Things, v.g. Lines, or Rays become equi-diftant from one another. See Parallel.
Thus, we fay remote Objects are fcarce perceptible, by reafon of the Parallelifm of the Rays.
Paral : sm of 'the Earth's Axis, in Aftronomy, or, Motion of Parallelifm; is that Situation or Motion of the Earth's
Axis,
