V E L
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V E L
Velocity is conceiv'd either as abfolute, or relative : The Velocity we have have hitherto confider'd, ifjimflc, or ab- solute, with refpect to a certain Space mov'd in a certain Time.
Relative, or respective Velocity, is that wherewith two distant Bodies approach each other, and come to meet in a longer or a lefs time : Whether, only one of 'em moves to- wards the other at reft, or whether they both move ; which may happen two ways ; either by two Bodies mutually ap- proaching each other in the fame right Line, or by two Bo- dies moving the fame way in the fame Line, only the Foremoft ilower than the other ; for by this means, this will overtake that. And, as they come to meet in a greater or lefs Time, the relative Velocity is greater or lefs.
Thus, if two Bodies come nearer each other by two Foot, in one Second of Time ; their refpeftive Velocity is double that of two others, which only approach one Foot in the fame Time.
Velocities of Bodies moving in Curves.
According to Galileo's Syftem of the Fall of heavy Bodies, now admitted by all Philofophers, the Velocities of a Body falling vertically, are, each Moment of its Fall, as the Roots of the Heights from whence it has fallen 5 reckoning from the beginning thereof.
Hence that Author gather'd, that if a Body fall along an inclined Plane, the Velocities it has at the different Times, will be in the fame Ratio: For fince its Velocity is all owing to its Fall, and it only falls as much as there is perpendi- cular height in the inclined Plane ; the Velocity fhould be meafur'd by that height, as much as if it were vertical.
The fame Principle likewife led him to conclude, That if a Body fall thro' two contiguous inclined Planes, making an Angle between them, much like a Stick when broke, the Velocity would be regulated after the fame manner, fay the vertical Height of the two Planes taken together : For 'tis only this height it falls ; and from its Fall it has all its Velocity.
The Conclusion was univerfally admitted, till the Tear 1693, when M. Varignon demonftrated it to be falfe : From his Demonftration, it should feem to follow, that the Velo- cities of a Body falling along the Cavity of a Curve, for inftance, of a Cycloid ; ought not to be as the Roots of the Height ; fince a Curve is only a Series of an Infinity of in- finitely little contiguous Planes, inclined towards one another. So that Galileo's Proposition would feem to fail in this Cafe too, and yet it holds good ; only with fome Restriction.
All this Mixture of Truths and Errors, fo near a-kin to each other, ihew'd that they had not got hold of the firft Principles; M. Varignon, therefore, undertook to clear what related to the Velocities of falling Bodies ; and to fet the whole Matter in a new light : He ftill fuppofes Galileo's firft Syftem, that the Velocities at the different times of a vertical Fall, are as the Roots of rhe correfpondent Heights. The great Principle he makes ufe of to attain his End, is that of Compound Motion. See Compound Motion.
If a Body falls along two contiguous inclined Planes, making an obtufe Angle, or a kind of Concavity between 'em ; M. Varignon fhews, from the Comfofition of thofe Motions, that the Body, as it meets the fecond Plane, lofes fomewhat of its Velocity - and of conference that it is not the fame at the end of the Fall, as it would be, had it fell thro' the firft Plane prolonged : So that the Propor- tion of the Roots of the Heights afferted by Galileo, does not here obtain.
The Reafon of the lofs of Velocity, is, that the Motion, which was parallel to the firft Plane, becomes oblique to the fecond, fince they make an Angle : This Motion, which is oblique to the fecond Plane, being conceived as com- pounded, that Part perpendicular to the Plane, is loft by the opposition thereof, and part of the Velocity along with it : Confequently, the lefs of the perpendicular there is in the oblique Motion, or, which is the fame thing, the lefs the two Planes are from being one, 2. e. the more obtufe the Angle is, the lefs Velocity does the Body lofe.
Kow, all the infinitely little, contiguous, inclined Planes, whereof a Curve confifts, making infinitely obtufe Angles among themfelves, a Body falling along the Concavity of a Curve, rhe lofs of Velocity it undergoes each inftant is infi- nitely little : But a finite Portion ot any Curve, how little foever, confifting of an Infinity of infinitely little Planes, a Body moving thro' it, lofes an infinite Number of infinitely little Parts of its Velocity : and an Infinity of infinitely little Parts, makes an Infinity of a higher Order, i. e. an Infinity of infinitely little Parts, makes a finite Magnitude, if they k on r.i.»j:.an.j .. — v:~i __j -- -.-/v- ., ,. ; ~ J
Body falling along a Curve be of the firft Order, they amount to a finite Quantity, in any finite Part of the Curve, %$c. See Curve.
The Nat»re of every Curve is abundantly determin'd by the Ratio of the Differences of the Ordinates to the corre- fpondent Portions of the Axis j and the Effcnce of Curves in general, may be conceiv'd as confifting in this Ratio, which is variable a thoufand ways. Now this fame Ratio will be likewife that of two fimple Velocities, by whofe Con- currence a Body will defcribe any Curve : And of conse- quence, the Effence of all Curves in rhe general, is the fame thing as the Concourfe or Combination of all the For- ces, which taken two by two, may move the fame Body. Thus we have a moft fimple and general Equation of all pof- fible Curves, and all pofllble Velocities. See Curve.
By means of this Equation, as foon as the two fimple Ve- locities of a Body are known, the Curve refulring from 'em is immediately determin'd. It is obfetvable, that on the Foot of this Equation, an uniform Velocity, and a Velocity that always varies accotding to the Roots of the Heights, produce a Parabola, independent of the Angle made by the two projeffile Forces that give the Velocities : Confequently, a Cannon Ball, fhot either horizontally or obliquely to the Hotizon, mull always defcribe a Parabola. The beft Mathe- maticians, till then, had much ado to prove, that oblique Projeaions form'd Parabolas, as well as horizontal ones. See Projectile, and Parabola.
To have fome meafure of Velocity, the Space is to be di- vided into as many equal Parts, as the Time is conceiv'd to be divided into : For rhe quantity of Space correfponding to that Divifion of Time, is the Meafure of the Velocity.
For an Inftance ; Suppofe the Moveable A, (Tab. Mccha- nicks. Fig. 45.) travel a Space of 80 Feer in 40 Seconds of Time ; dividing 80 by 40, the Quotient 1 fhews the Velo- city of the Moveable to be fuch, as that it paffes over an Interval of two Feet in one Minute : The Velocity, there- fore, is rightly exprefs'd by JJ ; that is, by a.
Suppofe, again, another Moveable, B, which in 30 Se- conds of Time travels 90 Feet ; the Index of its Celerity will be 3. Wherefore, fince in each Cafe the meafure of the Space is a Foot, which is fuppofed every where of the fame length; and the meafure of Time a Second, which is conceiv'd every where of the fame Duration : the Indices of the Velocities 1 and 3, are homogencal : And therefore, the Velocity of A is to the Velocity of B, as 2 to 3 .
Hence, if the Space be = f, and the Time =f, the Velocity may be exprefs'd by/: t ; the Space being in a Ra- tio of the Time and the Velocity. See Motion.
VELOM, a kind of Parchmenr, finer, evener, and whi- ter than the common Parchment. See Parchment.
The Word is form'd from the French Velin, of the Latin Vitellinus, belonging to a Calf.
VELVET, a rich kind of Stuff, all Silk, cover 'd on the outfide with a clofe, fhorr, fine, foft Shag ; the other fide being a very ftrong, clofe Tilfue, or Web.
The Nap or Shag, call'd alfo the Velveting, of this Stuff, is form'd of part of the Threads of the Watp, which the Workman puts on a long narrow channel'd Ruler, or Nee- dle ; and which he afterwards cuts, by drawing a ftiarp fteel Tool along the Channel of the Needle, to the Ends of the Warp.
- The principal and beft Manufaftories of Velvet are in France : there are others in Italy, particularly at Venice, Milan, Florence, Genoa, and Lucca : others in Holland, fet up by the French Refugees ; whereof that at Haerlem is the moft considerable : But they all come (hort of the Beau- ty of thofe of France ; and accordingly are fold for io or 1 5 per Cent. lefs. There are even fome brought from China, but they are the worft of all.
The Word Velvet is form'd of the French Velours, which fignifies the fame thing ; and which comes from Velu, a thing cover'd with Hair.
There are Velvets of various Kinds ; as, 'Plain, that is, uniform and fmoorh, without either Figures or Stripes : Fi- gured, that is, adorn'd and work'd with divers Figures; tho the Ground be the fame with the Figures; that is, the whole Surface velveted. See Figured.
Ramage, or branch'd Velvet, representing long Rinds, Branches, £?>c. on a Satin Ground, which is fometimes of the fame Colour with the Velvet, but more usually of a different one. Sometimes, inftead of Satin, they make the Ground of Gold and Silver ; whence the Denominations of Velvets with Gold ground, &c.
Shorn Velvet, is that wherein the Threads that make the Velveting, have been rang'd in the channell'd Ruler, but not cut there.
Strip'd Velvet, is rhat wherein there are Stripes of divers Colours, running along the Warp ; wherher thole Stripes be partly Velvet and partly Satin, or all velveted.
Laftly, Flower a Velvet, is that wherein the Gtound is a kind of Taffety, and rhe Figures Velvet.
Velvets are likewife diftinguilh'd, with regard to their dif- ferent Degrees of Srrength and Goodnefs, into Velvets of four Threads, three Threads, two Threads, and a Thread
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