Page:Cyclopaedia, Chambers - Volume 2.djvu/240

 MOT

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MOT

on its Centre, and a Point in the fame Radius is at the fame time fuppofed impell'd ftrait along it.

Corol. All Curvilinear Motion, therefore, is Compound. [Cor. I. of Axiom i.)

Teeoi-.XVIU. If a moving Body A (Pig.gi.Jbeactedon by a double Power ; the one according to the Direction A B, the other according to A C 5 with the Motion compounded thereof, it will delcribe the Diagonal of a Parallelogram N D j whofe Sides A B and A C it would have defcribed in the fame time with each ot the refpectivc Powers apart.

Dcm. If the Body A were only acted on by the Force imprefs'd along A B 5 in the firit inflant of Time it would be in iome Point of the right Line A B as in H, and fo in the Line H L parallel toACj if it were only acted on by the Power A imprefs'd in the Direction A C, it would in the fame lnttant of time be in fume Point of the Line A C as in 1, and fo in the Line I L parallel to A B, But fince the Di- rections of the Powers are not oppofite to each other, nei- ther of 'em can impede the other ; and therefore the Body in the fame iniiant of Time wilt arrive both at the Point H L and at I L j and will confequently be in the Point L, where the two meet. In the fame manner it appears that if KM and MG be drawn parallel to A B and A C, the Body in the fecond Intlant ot Time will be in M, and at length in D. Q^E. D.

Cor. 1. Since about every right Line as AD, a Parallelogram as A B D C, may be coniiructed by making two equal Triangles A C D and A B D, on one common Bale A D j every rellilinear Motion, when it may be of fervice for the Demembration, mayberelolved into a compound one.

Cor. 2. But as the Proportion of the Sides A C and C D may be various, fo alfo may the right Line A D be de- fcribed by a Motion compounded various ways 3 and there- fore the fame rectilinear Motion may be refolved into va- rious compound Motions.

Cor. 3. Hence if a moveable Body be drawn by three feveral Powers according to the Directions B A, AD, and A C, (-f/g'350 ' wo °f wn i cn taken together are equiva- lent to the third ; they will be to each other as the right Lines B D, D A, D C, parallel to their Directions ; that is, reciprocally as the Sinesof the Angles included between the Lines of their Directions, and the Line ot Direction of the third : D B being to A D as the Sine of the Angle BAD to the Sine of the Angle A B D.

Theor. XIX. In an equable compound Motion, the Ve- locity produced by the confpiring Powers, is to the Velocity of each of the two apart, as the Diagonal A D (Fig. penult.) of the Parallelogram A B D C, in the Direction of whofe Sides they act, to either of thole Sides AB or A C.

Bern. For in the fame time that one of the Powers would carry it over the Side of the Parallelogram A B, and the other over A C feparately, join'd together they carry it over the Diagonal AD. The Diagonal AD therefore is the Space defcribed by the confpiring Powers in the fame Time : but in an equable Motion the Velocities in the fame Time are as the Spaces ; the Velocities therefore ariiing from the confpiring Forces are to the Velocity ariiing from either Force, as A D to A B or A C. Q^E.D.

Cor. I. The confpiring Forces therefore being given ; *'. e. the Ratio of the Velocities being given, by the Lines A B and A C given in magnitude, and the Direction thro' thole Lines being given in Pofition, or by the Angle of Di- rection 5 the Celerity and Direction of the oblique Motion is given j becaufe the Diagonal is given both in Magnitude and Pofition. .

Cor. 2. The oblique Motion however being given, the fimple ones are not, vice verfa, given ; becaufe the fame oblique Motion may be compounded of various Ample oner.

Theor. XX. In a compound Motion produced by the fame Forces, the Velocity is greater if the Angle of Di- rection be lefs 5 and lefs, if this be greater.

Dem. Let the greater Angle of Direction be BAC, (Hg.54.) the lefs FAC ; fince the Powers are fuppofed the fame, AC will be common to each Parallelogram AF C E and BAC D and befides AB= A E. Now 'tis evident that on the footing of the greater Angle, the Diagonal AD is defcribed ; and on the footing of the lefs Angle, A E ; and both in the fame time, by re'afon A B = A^. The Velocities there- fore are as A D to A E ; Wherefore fince A D is lefs than A E, the Velocity on the foot of the greater Angle is lefs than on that of the lefs Angle. Q^E.D.

Cor. Since the Legs A C and C E, with the included Angle, being given', the Angle CEA, and thence, alfo, A E is found ; the Velocity of the confpiring Powers, and the Angle of Direction, in any particular Cafe, being given ; the Velocity of the compound Motion, and confequently the Ratio of the Velocities produced by the fame Powers under different Angles of Direftions, maybe determined.

For the particular Laws of Motion cinjinx from the Colhpon of Bodes both Elaflic and Unelaitic, and that where the Direc- tions arc both perpendicular and oblique, fee Percussion.

^ For Circular Motion, and the Laws of Projectiles, fee Central Force*, and Projectile.

tor the Motion of Pen.iU10.1s, and the Laws o/"Ofcillation, fee Pendulum and Oscillation.

Perpetual Motion. See 1'erpetual Motion.

The celebrated Problem of a perpetual Motion* confifis in the inventing of a Machine ; which has the Principle of its Motion withm itfelf. M. de Li Hire has demonllrated the ImpoJTibility of any fuch Machine, and finds that it amounts toih.s, viz. to find a Body which is both heavier, and lighter at the fame time; or a Body which is heavier than itfelf. See Machine.

Animal MofiQit, is that whereby the Situation, Figure, Magnitude, %£c. of the Parts, Members, {$c. of Animals are changed.

Under thefe Motions come all the Animal Functions, as Rejpir.ition, Circulation of the Blood, Excretion, Walking S$c. See Function.

Ammal Motions are ufually divided into two Species, viz* Spontaneous, and Natural.

Spontaneous, or Mufcular Motion, is that perform'd by means of the Mufeles, at the Command of the Will; hence alfo call'd Voluntary Motion. SteMufcular Motion.

Natural, or Involuntary Motion, is that effected with- out iuch Command of the Will ; by the mere Mechanlfm of the Parts.

Such is the Motion of the Heart, and Pulfe ; the Periftal- tic Motion of the Intcttines, cjfc Sjc Heart, &c.

Intejune Motion, an Agitation of the Particles, whereof a Body confilts. See Intestine; fee alfo Fermenta- tion, Effervescence, &c.

Some Philofophers will have every Body, and every Particle of a Body, in continual Motion. For Fluids, 'tis the Definition they give of fuch Bodies, viz. that their Parts are in continual Motion. See Fluidity.

And as to Solids they infer the like Motion from the Effluvia continually emitted thro their Pores. See Ef- fluvia.

Hence they defcrihe bitejline Motion, to be a Motion of the internal, and f mailer Parts of Matter, continually ex- cited by fome externa], latent Agent, which of itfelf fa infenfible, and only difcovers itfelf by its Effects ; appoin- ted by Nature for the great Instrument of the Changes iri JBodies.

Motion, in Aflronomy, is peculiarly apply'd to the or- derly Courfcs of the heavenly Bodies. See Sun, Planet, Comet, iSc.

The Motion of the Earth, from Weft to Eait, is now ge- nerally granted among Aitronomers : See it proved under the Article Earth.

The Motions of the Celeflial Luminaries are of two Kinds, Diurnal ot Common'-, and Secondary or Proper.

Diurnal or Primary Motion, is that wherewith all the heavenly Bodies, and the whole mundane Sphere, appears to revolve every day round the Earth, from Eait. to Weft* See Diurnal.

This is alfo "call'd the Motion of the Primum Mobile, and the Common Motion ; to diftinguith it from that proper to each Planet, £j>c 'Tis about the various Phenomena refulting from this Mono?:, that Allronomy is chiefly employ'd. See Astronomy.

Suundary or Proper Motion, is that wherewith a Star, Planet, or the like, advances a certain Space every day from Well towards Eart. See Moihle.

See the feveral Motions of each Luminary, with the Irregula- rities, &c. thereof, under its proper Article ; Earth, Moon, Star, &c.

Motion of Trepidation. See Trepidation and Li- bration.

Motion, in Mufic, is the manner of beating the Mea- fure, to haften or flacken the Time of the Pronunciation of the Words, or Notes. Sea Measure and Time.

The Motion, in Songs compos'd in double Time, differs from thofe in triple Time. 'Tis the Motion that diftin- guifhes Courants and Sarabands, from Gavots, Borees, Cha- cones, t$c.

Motion is alfo ufed among Mechanics, for the Infide of a Watch, fiy<r. more commonly call'd Movement. See Movement.

Motions, in War, are the Marches, Counter-marches, £f?c. an Army makes in the changing of its Poft.

The great Skill of a General confifts in difcovering the Enemies Motions, and concealing his own. Nothing is more dangerous, than to make great Motions before a powerful Enemy, ready to come to Blows.

Motion, or Emotion, in Rhetoric, &c. See Passion.

MOTORII, Motory Nerves, the third Pair of Nerves, ferving for the Motion of the Eye. SeeNERVE.

This Pair is united into one near their Infertion into the Brain ; by which means, when one Eye is moved towards any Object, the other is directed towards the fame.

See Eye.

MOTOS,