Page:Cyclopaedia, Chambers - Volume 2.djvu/389

 PER

(784)

PER.

XII. If a Bbdy ftrike directly on an immoveable Obftacle, cither one, or both of 'em being Elaftic; the Body will be reflected with the fame "Velocity wherewith it Itruck, and in the fame Line.

For if the Elafticity were away, the whole force of the Body wou'd be fpent in breaking the Obftacle, and its Mo- tion wou'd be ftopp'd : The whole Force therefore is fpent in eompreffing the Elaftic Body ; by which means it acquires an Elaftic Force equal thereto: fince then, the Elasticity, when the eompreffing Force is fpent, reduces the Body into its former ftate ; it repells the other with the fame Force wherewith it {trucks confequently it will rebound with the fame "Velocity. And becauie an Elaftic Body reftores itfelf in the fame Direction wherein it was comprefs'd ; (there being no renfon why it ftiou'd change its Direction,} the Body wilt rebound in the fame right Line.

XIII. If an Elaftic Body ftrike obliquely on an inmoveable Obftacle, it will rebound in fuch manner as to make the Angle of Reflexion equal to the Angle of Incidence. See Reflexion.

XIV. If an Elaflic Body A, ftrike directly againft another at reft 2 ; after t PercuJJ:on > ^will remain at relt, and B pro- ceed with the fame Velocity which A had before the Shock, and in the fame Direction.

For it" the Bodies were not Elaftic, each wou'd proceed after the Stroke in the fame Direction, and with half the Ve- locity; but fince the Elaine Force acts in the fame Direction wherein the Compreffion is made, and is equal to the eom- preffing Force ; it repells A with half its Velocity, and there- tore flops its Motion 5 but it drives B further, with half its Ve- locity, and therefore accelerates its Motion. Tis therefore car- ried after the Shock with the whole Celerity wherewith v^was carried before it, and A remains at reft.

Hence, fince ^(Tab Mechanicks Fig, 41. ) transfers all its force to B ; B in like manner will transfer it toC; C again to 2), and to E. Wherefore, if there be feveral equal Elaftic Bodies, mutually touching each other; and A be itruck againft B ; all the intermediate ones remaining at reft, the laft alone, E will be mov'd ; and that with the Velocity where- with ^ftruck againft B,

XV. If two equal Elaftic Bodies A and B meet di- rectly, and with equal Velocity ; each will rebound with the fame Velocity wherewith it itruck, and in the fame Di- rection.

Forfeiting afide the Elafticity, both wou'd remain at reft: Their whole Force therefore is {pent in the Compreffion; but their Elaftic Force whereby they rebound in the former Di- rection, is equal thereto: This >orce therefore acting equally on each Bod) ^andS will produce the fame Celerity in each; and that, equal to the former. So that they will rebound with the Celerity wherewith they Itruck.

XVI. If two equal Elaftic Bodies ^and B ftrike directly againft each other with unequal Velocities ; after the Shock they will rebound with interchanged Velocities.

For fuppofe the Bodies to concur with the Velocities C -h c and C: If they meet with the fame Velocity C; after the Shock, they wou'd both move with the Velocity C. If 2? were at reft, and A ftiou'd ftrike upon it with the Celerity c ; after the Shock, A wou'd remain at reft, and B be mov'd with the Celerity c. Therefore the Excefs of Celerity c, wherewith A is carried, is transfcrr'd wholly by the Conflict to B : ^therefore is mov'd with the Celerity 6', and B with the Celerity C-\~c.

Hence, after <Percii(fion, they recede from each other with the fame Velocity as, before, they concurr'd.

XVII. If an Elaftic Body A, ftrike on another equal one, indued with alefs Degrceof Motion, 2?; after 'percitffiou, both will proceed in the fame, viz. the former, Direction, and with interchanged Velocities.

For fuppofe A to ftrike with the Velocity C -\~ c, upon B moving with the Velocity C. Since by reafon of the equal Velocities C and C, there arifes no Impulfe; 'tis the fame thing as if ^ftruck on B with the fole Celerity c, on B at reft. But in that cafe A wou'd remain at reft, and B move with the Velocity c: Therefore, after Tercufjicn, A will move with the fole Celerity C; and B with the Celerity C + c, both according to the former Direction, there being nothing to change that Direction. '

XVIII. If a Body A ftrike on another S, the Stroke is the fame as wou'd be made by the Body ^ftriking on B at reft, with the Difference of their Velocities.

Hence, fince the Elaftic Force is equal to the <Percnffion ; it acts on the Bodies AstViA B with the Difference of the' Veloci- ties they had before the Congrefs.

A

ties.

XIX. 1g determine the Velocities of any two Elaftic Bodies and B, firiking direEHy on each other with any Velcci-

If the Elaftic Body A ftrike on B, either at reft, or moving flower than A 5 the Velocity v. g, of A after c PercnfJion, is found thus: as the Sum of the Weights is to double of either of 'em, fuppofe, in this Cafe, of B ;fo is the Difference of the Ve- locities before the Congrefs, to a Velocity, which fubtracted

from the Velocity of A before the Impulfe (in the other* Cafe added to itj leaves the Velocity of A after the Con- grefs.

lfthe two Elaftic Bodies A and S meet each other; the Velocity of A after the Impulfe is found thus : As the Sum of the Weights, is to the double of either of 'em, fuppofe of B ; fo is the Sum of the Velocities before Collifion, to a Velocity which fubtracted from the Velocity of A before Collifion, leaves its Celerity after Collifion.

XX. If an Elaftic Body ^ftrike directly on another at reft B ; its Velocity after Tercuffwn will be to its Velocity be- fore it, as the Difference of Weights is to their Sum : But the Velocity it communicates to B is the fame, as double the Weight of A to the Sum of the Weights.

After tPercujfion, therefore, the Velocity of A is to the Ve- locity of B, as the difference of Weights, to the double of A.

XXI. Jf two Elaftic Bodies, A and B, ftrike directly on each other with Velocities that are reciprocally proportional to their Weights; after Collifion, they will rebound with the fame Velocity wherewith they met.

XXII. In the direct Collifion of Bodies, the fame re- fpective Velocity is preferv'd, i. e. in a direct Concurrence, the Difference of Velocities is the fame before and after the Shock ; and in a direct mutual Encounter, the difference of Velocities after the Shock is the fame with their Sum before it.

Hence they retire from each other after the Impulfe, with th e fame Velocity wherewith they mer,

XXIII. In the Collifion of Elaftic Bodies, there is not al- ways preferv'd the fame Momentum, or as the Carrefians ex- prefs it, the fame Quantity of Motion 5 but it is fometimes increas'd, and fometimes diminifh'd.

'Tis a Mrftake, therefore of Cartes and his Followers, that the fame Quantity of Motion is ftill preferv'd in the World. See Cartesian.

XXIV. If two Elaftic Bodies, ^and B, meet, or overtake each other directly ; the Sum of theFactums of the Maffesinto the Squares of the Velocities, remains the fame before and after the Congrefs.

Hence the fame Quantity of Force is likewife preferv'd in the Congrefs.

XXV. %h determine the Motion of two Bodies A and B, (Fig. 42 .J firiking obliquely againft each other \ whether they be Elaftic, or not Elaftic.

The Motion of the Body A, along AC, is refoluble into two others, in the Directions A E and A 2) ; and the Motion of B along B C into two others according to B F and B G ; and the Velocities thro' A 2) and B F are to the Velocities thro'A G and B C as the right Lines A&, B F,AC,BC; now, fine© the right Lines A M and B G are parallel, the Forces acting according to thefe Directions are not mutually oppofite, and muft ther etore be confider'd in the Congrefs. But fince the Lines A 2) and 3 F, or which is the fame, IT C and G C con- ftitute the fame right Line perpendicular to 2) C; 'tis the fame as if the Bodies A and B ftiou'd meet directly with Velocities that are as E C and G C. Find therefore theVe- locity of A and B according to the Rules above laid down.

Suppofe E. gr. the Velocity of the rebounding Body A to beast 1 H -j fince the Motion along AE is not char.g'd by the Congrefs, make C K-~A E, and compleac the Parallelo- gram HC KTj the Diagonal C /will reprefent the Motion of A after Congrefs: for after Ttrcujjicn, the Body will move according to the Direction C I, and with a Velocity as C J. In the fame manner it will be found that the rebounding Body B will move along the Diagonal of the Parcllelogram, C M; in which L M=.&G. "The Velocities therefore af- ter -Fercuffion are as C I to C M.

Centre of Percussion that Point wherein the Shock or Impulfe of the percutient Bodies is the greattft. See Centre.

The Centre of 'Percufficn is the fame with the Centre of Ofclllation, if the percutient Body revolve round a fix'd Axis. See Oscillation.

If all the Parts of the percutient Body be carried with a parallel Motion, or with the fame Velocity; the Centre of '■Percuffton is the fame with the Centre of Gravity. See Gra- vity.

PERDONATIO Urlegar'ue, in Law, a Pardon for one who is out-law'd. See Pardon and Out-lawry,

PERDUE, a Soldier placed in a dangerous, and almoft defperate Poft.

The Word is French, and litterally fignifles loft.

Thus we fay Enjans c Perdues, for the Forlorn Hope of an Army. See Forlorn.

To lie Terdue, is to lie flat on the Belly, to lie clof ely in wait.

PEREMPTORY, in Law, an Epithet applied to an Ac- tion, Exception, ££?c. fignifying 'em to be abfolute, final, and determinate ; not to be alter'd, renew'd, or reftrain'd

Thus in our Law-Books we find Peremptory Atlton, 3>£" remptory Nonft/ir, 'Peremptory E-cemption, Sic.

PERENNIAL, in Botany, is applied to Ever-greens, of Plants, which preferve their Leaves and Verdure all the Year. See Ever-£TO. a PEREGRINE,