FRI
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FRI
Xaws of Friction. i° As the Weight of a Body moving on another., is hi- ereafed, Jo is the Friction.
This wo lee experimentally in a Balance ; which when only charged with a fmall Weight, eafily turns; but with a greater, a greater Force is required.
Hence, if the Line of Direction of a moving Body be oblique to the Surface moved on; the FriBion is the greater; this having the fame Effect as an Increafe of Weight.
And hence, again, as a perpendicular Stroke, or I m pref- fion is to an oblique one as the whole Sine, to the Sine of the Angle of Incidence ; and the Sine of the greater Angle is greater, and that of the leffer, left: The FriBion is the greater, as the Line of Direction approaches nearer to a Perpendicular.
This is eafily obfervable, and efpecially in the Teeth of Wheels, which are frequently broke on this very account. The FriBion, therefore, is taken away, if the Line of Di- rection of the moving Body be parallel to the Surface.
i° I'he Friction is lefs in a Body that rolls, than it would be were the fame Body to fide, as is eafily demonstrated.
For fuppofe a dented Ruler, A B, 'Tab. Mechanicks, Fig. 38. and fuppofe a Wheel D E to move along it, with its Teeth perpendicular to the Circumference. If now the Body were to Hide; the Tooth F, when it touch'd the Ruler, would defcribe a Right Line on the Surface there- of: And, as the Tooth of the Ruler, H, refifts the fame ; it could not proceed without removing, or breaking either the Tooth H s or that F. And the fame will hold in the Aiding of any rough Surface upon another; where all the FriBion will take place, than can any way arife from the Roughnefs of the Surface. But if the Wheel E D roll along the Ruler, then the Tooth H will no longer refitt its Motion, only as it is to be hoisted out of the Cavity F over the Eminence of the Tooth H : And the fame holds in the robbing of any rough Body over the Surface of another.
Hence, in Machines, left the FriBion .mould employ a good Part of the Power; Care is to betaken, that no Part of the Machine flide along another ; if it can be avoided : But rather that they roll, or turn upon each other. With this View it may be proper to lay the Axes of Cylinders, not, as is ufually done, in a Groove, or Concave Matrix ; but between little Wheels, AB CD Fig. $9. moveable on their refpective Axes. This was long ago recommended by 'P. Cafams ; and Experience confirms, that we fave a deal of Force by it. Hence alfo it is that a Pally moveable on its Axis refills lefs than if it were fix'd. And the fame may be obferv'd of the Wheels of Coaches, and other Carriages.
From thefe Principles, with a little further Help from the higher Geometry, Olaus Roemer determined the Fi- gure of the Teeth of Wheels, that mould make the leafl Refinance poffible ; and which fhould be epicycloidal. And the fame was afterwards demonstrated by de la Hire . tho*, which is to be lamented, the Thing is not yet taken into Pra- ctice.
Hence in Sawing-Milis, the Sides cf the wooden Reel- angle the Saws are fitted into, fhould be furnifh'd with Rottllf, or little Wheels ; which would greatly lefTen the FriBion ; and the like in other Cafes. Add, that as Winches, or curved Axes prevent all FriBion ; thofe mould be ufed in lieu of Wheels, as often as it is possible. See Winch.
Calculation of the Quantity or Value cf Friction.
The FriBion is a Point of the utmoft Importance in Ma- chines ; and by all means to be confider'd, in calculating the Force thereof: Yet it is generally overlcok'd in fuch Calculations : But this, principally, by reafon its precife Va- lue is not known.
It is not yet redue'd to certain, and infallible Rules: The common Method is, barely to compute the Advantage, which a moving Power has from the Machine; either on account of its Distance from a fix'd Point; or of the Dire- ction in which it acts. And in 'all the Demonstrations it is fuppos'dthattheSurfaccs of Bodies are perfectly fmooth and polifh'd. Indeed theEngineers expect, that in the Practice they fhould lofe part of the Advantage of their Force, by the FriBion : But how much, it is fuppos'd nothing but the Pra- ctice can determine. M. Amontons> indeed, has made an Attempt to fettle, by Experiment, a Foundation for a precife Calculation of the Quantity of FriBion ; and M. ^Parent has confirm'd it from Reafoning, and Geometry : But their Theory, however warranted, is not generally, and fully re- ceived.
M. Amontons Principle, is, that the FriBion of two Bo- dies depends on the Weight, or Force wherewith they bear on each other ; and only increafes as the Bodies are more itrongly prefs'd, or applied against each other; or are charged with a greater Weight: And that it is a vulgar Error, that the Quantity of. FriBion has any Dependance on the Bignefs of the Surfaces rub'd againfl: each other - or that the FriBion increafes as the Surfaces do.
Upon the first Propofal of this Paradox, M. de la tiire had Recourfe to Experiments, which fucceeded much in favour of the new Syftem. He laid feveral Pieces of rough Wood, on a rough Table : Their Sizes were unequal ; but he laid Weights on them, fo as to render them all equally heavy. And he found, that the fame precife Force, or Weight, applied to them by a little Puliy, was requir'd to put each in Motion; notwithstanding all the Inequality of the Surfaces. The Experiment fucceeded in the fame man- ner in Pieces of Marble, laid on a Marble Table.
Upon this, M. de la Hire betook himfelf to the Rationale of the Thing ; and has given us a Physical Solution of the Effect : And M. Amontons fettled a Calculus of the Value of FriBion, and the Lofg futtain'd thereby in Machines, on the footing of the New Principle.
In Wood, Iron, Lead, and Bra fs, which are the principal Materials us'd in Machines, he finds the Resistance cauled by FriBion, to be nearly the fame; when thofe Materials are anointed with Oil, or other fatty Matter: And this Re- sistance, independant of the Quantity of Surface, he makes to be nearly equal to a third Part of the Force wherewith the Bodies are prefs'd againfl: each other.
Befidc the Preffion, the Magnitude whereof determine* that of the FriBion ; there is another Circumstance to be consider 'd, viz., the Velocity. The FriBion is the greater ; and the more difficult to funnount, as the Parts are rub'd against each other with the greater Swiftnels : So that this Velocity mult be compared with that of the Power necef- fary to move the Machine, and overcome the FriBion. If the Velocity of the Power be double tfo&t of the Parts rub'd 5 it acquires, by that means, an Advantage that makes it double; or, which amounts to the fame, dimi nifties the contrary Force of FriBion by one half; and reduces it to a sixth Part of the Weight or Preffion. But this Velocity M. Amontons only considers as a Circumstance that augments or diminiitics the Effect of the Preffion, i; e. the Difficulty of the Motion : So that the FriBion still follows the Propor- tion of the Weight. Only, we are hereby directed to dif- pofe the Parts of Machines that rub against each other, in fuch manner as that they may have the leaft Velocity poffible: And thus the Diameter of the Axis of a Wheel fhould be as fmall as poifible, witftregard to that of the Wheel ; in that the leffer the Axis, the flower will be the Motion of the Surfaces rubbing against each other : fince the Velocity of a circular Motion always goes diminifhing from the Circumference to the Centre. And for the fame Reafon the Teeth of dented Wheels fhould be as fmall and thin as poffible : For a Tooth catching on a Notch, $$c. rubs one oi" its Sides againfl a Sur- face equal to its own; and is to diiengage it felf in a cer- tain time by pasting over a Space equal to the Surface : Confequently, the lefs the Surface, the lefs Space it has to move ; the littlenefs of the Surface diminifhing the Rest- ftance of the FriBion $ not as it is a lefs Surface that rubs, but as there is a lefs Space to move.
But notwithstanding all the Confirmations and Illustra- tions of this Theory of FriBion ; the Publick, nor even the Academy it felf where it was propofed, could not be brought fully to acquiefce in it. 'Tis granted, the Preffion has a great Effect ; and is, in many Cafes, the only Thing to be confider'd in FriBions : But 'twill be hard to perfuade us ab- folutely to exclude the Consideration of the Surface. In ef- fect, the Contrary feems capable of a Metaphysical Demon- stration.
If two Bodies with plain Surfaces, fuppofed infinitely hard, and polifh'd, be moved along each other; the FriBion will be none, or infinitely fmall : But, if in lieu of fuch Suppo- sition, which has no Place in Nature, we fuppofe two Bo- dies with rough, uneven Surfaces; the Difficulty of mov- ing one of them on the other, mult either arife from this, that the first is to be rais'd, in order to difengage the Parts catch'd or lock'd in the fecond ; or that the Parts mutt be broke and wore off; or both.
In the firft Cafe, the Difficulty of raifing one of the Bo- dies, makes that of the Motion ; and of confequence, the FriBion arifes wholly from the Weight, or Preffion ; and the Surface has nothing to do.
In the fecond Cafe, the Magnitude of the Surface would be all ; were it poffible this fecond Cafe could be abiblutely abstracted from the first; i.e. could the Pans of one Body be rub'd and wore againfl thofe of the other, without rail- ing one of them ; it being visible that a greater Number of Parts to be broke would make a greater Resistance, than a lefs. But as in Practice we never rub, or grind without raifing the Body ; the Resistance arifing from the Greatnefs of the Surface is always combined in the fecond Caufe with that from the Preffion : Whereas in the former Cafe that arifing from the Preffion, may be alone, and uncompounded.
Add, that what is wore off a Body, is ordinarily very lit* tie; with regard to the great Number of times the Body muft have been raifed during the FriBion ; and all the lit- tle Heights added together, which the Body mutt have been raifed to,
Hence z
