RES
( P99 )
RES
RESISTENCE, or Resisting-Foto, in PhyGcks, any Force which acts contrarily to another, fo as to deftroy or diminifli its Effect See Force.
Of Refflence, there are various Kinds, arifing from the various Natures and Properties of the reffling Bodies ; and govern'd by various Laws : As the Riffence of Solijs, the Refflence of fluids, the Refijlence of the Air, &c. The Doctrine of each whereof will be feen under the following Articles.
Resistence of Solids, in Mecbanicks, is the force wherewith the quielcent Parts of folid Bodies oppofe the Motion of others contiguous therewith. See Solidity, &c.
Of this there are two Kinds.— The firft, where the reefing and refilled Parts, i. e. the moving and quiefcent Parts, are only con- tiguous, and don't cohere; i. e. where they conftitute feparate Bodies or Maffes.
This Refflence is what M. Leibnitz calls Refflence of the Sur- face : and we, properly, Friclion ; the Coniideration whereof, being of the laft Importance in the Doctrine of Machines, iee its Laws under the Article Fraction.
The fecond Cafe of Ref fence is where the reffli?ig and reffled Parts are not only contiguous but cohere, /. e. are Parts of the fame continued Body or Mafs. — This Refflence is what we may properly call Renitency ; and was firft coniidcred by Galileo.
Theory of the Resistence or Renitency of the Tibres of folid Bodies.
To conceive an Idea of this Refflence or Renitency of the Parts, fuppofe a cylindrical Body lufpended vertically by one End. — Here, all its Parts being heavy, draw downwards; and tend to feparate the two contiguous Planes, where the Body is the weak- eft : But all the Planes refft this Separation by the Force where- with they cohere, or are bound together : Here then are two op- pofite Powers, the Weight of the Cylinder which tends to break it, and the Force of Cohseiion of the Parts which reffs the Fracture.
If the Bale of the Cylinder be increas'd, without increafing its Length ; 'tis evident the Fracture will be increas'd in the fame Ratio as the Bale : but the Weight alfo increafes in the fame Ratio; whence it is evident that all Cylinders of the fame Matter and Length, whatever their Bafes be, have an equal Refflence, when vertically fufpended.
If the Length of the Cylinder be increas'd without iacreafing the Bafe, its Weight is increafed without increafing its Reffl- ence ; confequently the lengthening it weakens it. — To find the greateft Lengch a Cylinder of any Matter may have without breaking, there needs nothing but to take any Cylinder of the fame Matter, and fallen to it the greateft Weight it will fuftain e're it break ; and then fee how much it muff, be lengthened by the Ad- dition of its Weight, 'till it equals its former Weight with the Ad- dition of the foreign Weight. — By this means Galileo found a Cop- per- Wiar, and of confequence any other Cylinder of Copper, might be lengthened to 4801 Braccios, or Fathoms of fix Foot each.
If one end of the Cylinder were fix'd horizontally into a Wall, and the reft fuipended thence, its Weight and Refflence would then ait in a different Manner; and it it broke by the Action of its Weight, the Rupture would be at the End fix'd into the Wall. A Circle or Piaue contiguous to the Wall, and parallel to the Bafe, and confequently vertical, would be detach'd from the contiguous Circle within the Plane of the Wall, and would de- fcend. All the Motion is made on the loweft extremity of the Diameter, which remains immoveable, while the upper extremi- ty defcribes a quadrant of a Citcle, and till the Circlejwhich be- fore was vertical is now horizontal ; i. e. till the Cylinder be entirely broken.
In this Fracture of the Cylinder 'tis vifible two Forces have acted, and the one has overcome the other : The Weight of the Cylinder, which atoie from its whole Mafs, has overcome the Refflence which arofe from the largenefs of the Bafe; and as the Centres of Gravity are Points wherein all the Forces ariling from the Weights of the feveral Parts of the fame Bodies, are conceiv'd to be united, one may conceive the Weight of the whole Cylinder applied in the Centre of Gravity of its Mafs, i. e. in a Point in the Middle of its Axis; and the Refflence of the Cylinder applied in the Centre of Gravity of its Bafe, i. e. in the Centre of the Bafe : It being the Bafe which reflfls the Fracture. _
When the Cylinder breaks by its own Weight, all the Motion is on an immoveable Extremity of a Diameter of rhe Bafe. — > This Extremity, therefore is the fix'd Point of a Lever, whofe two Arms are the Radius of the Bafe, and half the Axis; and of confequence the two oppofite Forces don't only act of them- fetves, and by their abfolute Force, but alfo by the relative Force they derive from their Diftance with regard to the fixed Point of the Lever.
Hence it evidently follows, that a Cylinder, e. gr. of Cop- per, which, vertically fufpended, will not break by its own Weight if lefs than 480 Fathom long, will break with a lefs Length in a horizontal Situation; in regard the Length in this latter Cafe con- tributes two Ways to the Frafture ; both as it makes it of fuch
a Weight, and as it is an Arm of a Lever to which the WeWic K applied— Hence, alfo, the (mailer die Bafe is, the lefs Length or Weight will fuffice to break it; both becaufe the Refftence is really lels, and becaufe it afts by a lefs Arm of a Leverf
If two Cylinders of the lame Matter, having their Bafes and Lengths in the fame Proportion, be fufpended horizontally; 'tis evident that the greater has more Weight than the leffer, both on Account of its Length, and of its Bafe. But it has lefs Re- fflence on Account of its Length, confidered as a longer Arm of
a Lever, and has only more Refflence on Account of its Bafe.
Therefore it exceeds the leffer in its Bulk and Weight, more than in Refflence- and confequently muft break more eafily.
Hence, we fee why upon making Alodels of Machines in imall, People are apt to be miftaken as to the Reffence and Strength of certain horizontal Pieces, when they come to exe- cute their Deiigns in large; by obfetving the fame Proportion as in the fmall— Galikus's Doctrine of Refflence therefore is no idle Speculation, but becomes applicable in Architecture and other Arts.
The Weight required to break a Body placed horizontally, be- ing always lefs than that required to break it in a vettical Situati- on; and this Weight being to be greater or lefs according to the Ratio of the two Arms of the Lever: 1 he whole Theory is al- ways reducible to this; viz. to find what Part of the abfolute Weight the relative Weight is to be, fuppofing the Figure of the Body known ; which indeed is neceffary, becaufe 'tis the Figure that determines the two Centres of Gravity, or the two Arms of the Lever.— For if the Body, e. gr. were a Cone, its Centre of Gravity would not be in the Middle of its Axis, as in the Cy- linder; and -if it were a Semi- parabolical Solid, neither its Centre of Gravity would be in the Middle of its Length or Axis ; not the Centre of Gravity of irs Bafe in the Middle of the Axis of its Bile. But flill, wherefoever thefe Centres fall in the leveral Figures, 'tis thefe that regulate the two Arms of the Lever.
It may be here obferved, that if the Bale whereby the Body is faftened into the Wall be not circular, but, e. gr. parabolical, and the Vertex of the Parabola a-top, the Motion of the Fracture will not be on an immoveable Point, but on a whole immovea- ble Line; which may be call'u the Axis of Equilibrium, and 'tis with regard to this, that the Diflances of the Centres of Gra- vity are to be determined.
Now a Body horizontally fufpended, being fuppofed fuch, as mat the fmallell addition of Weight would break it ; there is an Equilibrium between its pofitive and relative Weight; and of Confequence thofe two oppofite Powers are to each other reci- procally as the Arms of the Lever to which they are applied.— On the other Hand, the Refflence of a Body is always "equal to the greateft Weight which it will fuftain in a vertical Situation, without breaking, i. e. is equal to its abfolute Weight. There- fore, fubftituting the abfolute Weight for the Refflence, it ap- pears that the abfolute Weight of a Body fufpended horizontally, is to its relative Weight as the Diftance of its Centre of Gravi- ty from the Axis of Equilibrium, is to the Diftance of the Cen- tre of Gravity of its Bafe from the fame Axis.
The Difcovery of this important Truth, at lead of an equiva- lent hereto, and to which this is reducible, we owe to Galileo.— From this fundamental Propofition are eaffly deduced feveral Confequences.— As, for Inftance, that if the Diftance of the Centre of Gravity of the Bafe from the Axis of Equilibrium, be half the Diftance of the Centre of Gravity of the Body ; the relative Weight will only be half the abfolute Weight : And that a Cylinder of Copper horizontally fufpended, whofe Length is double the Diameter, will break, provided it weigh half what a Cylinder of the fame Bafe, 4801 Fathoms long, weighs. See Weight.
On this Syftem of Refflence of Galileo, M. Mariotte made a very fubtile Remark, which gave Birth to a new Syftem.— Gali- leo fuppofes that where the Body breaks, all the Fibres break at once; fothat the Body nhvuys reffts with its wholoabfoluteForce ■ i. e. with the whole Force all its Fibres have in the Place where it is to be broke.- But M. Mariotte finding that all Bodies, even Glafs it felf, bends before it breaks, Ihews that Fibres are to be confidered as fo many little bent Springs, which never exert their whole Force till ftretch'd to a certain Point ; and never break till entirely unbent. Hence, (hole nearett the Axis of Equi- librium, which is an immoveable Line, are ftretch'd lels than thofe further off; and of Confequence employ a lefs Part of their Force.
This Confideration only takes Place in the horizontal Situation of the Body : In the vertical the Fibres of the Bafe all break at once; fo that the abfolute Weight of the Body muft exceed the united Refflence of all its Fibres : A greater Weight is therefora required here, than in the horizontal Situation ; i. e. a gteater Weight is required to overcome their united Refflence, than to ovetcome their feveral Ref fences one after another. — The Diffe- rence between the two Situations arifes hence, that in the Hori- zontal there is an immoveable Point or Line, a Centre of Moti- on, which is not in the Horizontal.
M. Varigmn has improved on the Syftem of M. Mariotte:, and
fhewn that to Galileo's Syftem, it adds the Confideration of
the Centre of Percuffion.— The Comparifon of the Centres of
11 X Gravity,
