W H E
The ufe of thefe is very corfpicuous in Clocks, Jacks, ($ See Clockwork, Watchwork, &c.
The Power of the 'Dented Wheel depends on the iame Principle as that of the Simple one.— Tis only that to the fimple Axis in Peritrochio, which a compound Lever is to a fimple Lever. See Lever.
Its Doftrine is compriz'd in the following Canon, viz. — the Ratio of the 'Power to the Weight, in order for that to be equivalent to this, mitjl be a Ratio compounded of the Rams of the Diameter of the Axis of the laft Wheel, to the Diameter of the firft ; and of the Ratio of the Revolu- tions of the laft Wheel to thefe of the firft, in the Jam time. —But this Doctrine will deferve a more particular Expli-
W H E
l°, Then, If the Weight be multiply'd into the lrodua of the Radii of the Axis, and th.it Produa be divided by the Produa of the Radii of the Wheels, the Power rcquir'd
to fuftain the Weight will be found. Suppofe, e.g. the Spent in raijinfri
Weight A, (Tab. Mechanicks, Fig. tfi.J = tfoco Pounds, BC=d Inches, C D = 34 Inches, E F = 5 Inches, E G — = 5 Inches, HI=4 Inches, HK= 27 Inches. Then will BC.EF, HI=i20 S andCD, EG, I K= 311 30.— Hence the Power rcquir'd to fuftain the Weight, will be the Quo- tient of 6oco— iso divided by 31139, viz. 22J of a Pound, very nearly 5 a fmall Addition to which will raife it.
2 , If the Power be multiply'd into the Product of the Radii of the Wheels, and the Failnm be divided by the Pro- dud of the Radii of the Axes ; the Quotient will be the Weight which the Power is able to Curtain.— Thus, if the Power be %i\ of Pound, the Weight will be 6000 Pound.
3°, A Power and a Weight being given, to find the Num- ber of Wheels, and ill each Wheel the Ratio of the Radius of the Axis to the Radius of the Wheel : fo, as that the Power being applied perpendicularly to the 'Periphery of the laft Wheel, may fuftain the given Weight.
Divide the Weight by the Power : Refolve the Quotient into the Faaors which produce ir.— Then will the Number of FaBors be the Number of Wheels ; and the Radii of the Axis will be to the Radii of the Wheels, as Unity to thefeve- tal Wheels.— Suppofe, e. g. a Weight of ;coo Pound and a Power of 60, which refolves into thefe Faaors, 4555. Four Wheels are to be made, in one of which the Radius of the Axis is to the Radius of the J Vheel as 1 to 4. — In the reft,
C ^4 1
9 , the Ratio of the Peripheries of the fwifteft Wheel, and of the Axis of the Jloweft ; together -with the Ratio of their Revolutions, and the Weight, being given : to find the 'Power able to fuftain it.
Multiply borh the Antecedents and the Confequcnts of the given Ratio, into each other : and to the Produft of the Antecedents, the Produa of the Conlequents, and the given Weight, find a fourth Proportional. That will be the Power rcquir'd. — 'Suppofe, e.g. the Ratio of the Peripheries 8:13. That of the Revolutions 7:2; and the Weight 2000 : The Power will be found 2i4v- — 'After the fame manner may the Weight be found ; the Power and rhc Ratio of the Periphe- ries, "g?c. being given.
10°, 'the Revolutions the fwifteft Wheel is to perform while the floweft makes one Revolution, being given 2 toge- ther with the Space the Weight is to be rais'd, and the Pe- riphery of the Jin-weft Wheel ; to find the time that will be
as 1 to 5:
4 Q , If a Power move a Weight by means of two WheeiS, the Revolutions of the flower Wheel are to thofe of the fwifter, as the Periphery of the fwifter Axis is to the Peri- phery of the Wheel that catches on it. . . Hence, i°, the Revolutions are as the Radius of the Axis FE, to the Radius of the Wheel DC— 2°, Since the Num- ber of Teeth in the Axis F D, is to the Number of Teeth in the Circumference of the Wheel M as the Circumference of that, to the Circumference of this : The Revolutions of the flower Wheel M, are to the Revolution-, of the fwifter N, as the Number of Teeth in the Axis, to the Number of Teeth in the Wheel M it catches into.
5°, If the F.-Mum of the Radii of the Wheels GD, DC be multiply'd into the Number of Revolutions of the llowcrt Wheel M ; and the Produa be divided by the Fa Sum ot the Radii of the Axes which catch into them, G H, D E, £$c. The Quotient will be the Number of Revolutions of the fwifteft Wheel O. E. g. If GE = 8,DC = u, GH = 4 , D E = 3, and the Revolution of the Wheel M be one ; the Number of Revolutions of the Wheel O will be 8.
6", If a Power move a Weight by means of divers Wheels, the Space pafs'd over by the Weight is to the Space of the
Power, as the Power to the Weight. Hence, the greater
the Power, the farter is the Weight mov'd ; and vice verfa. 7°, The Spaces pafs'd over by the Weight and the Power, are in a Ratio compounded of the Revolutions of the ilovvert Wheel, to the Revolutions of the fwiftert ; and of the Peri- phery of rhe Axis of that, to the Periphery of this.— Hence, fmce' the Space of the Weight and the Power arc reciprocal- ly as the fultaining Power to the Weight , the Power that fiiflains a Weight, will be to the Weight, in a Ratio com- pounded of the Revolutions of the flowcrt Wheel to thofe of the fwifteft, and of the Periphery of the Axis of that, to the Periphery of this.
8°, the Periphery of the Axis of the floweft Wheel, with the Periphery of the fwifteft Wheel, given ; as alfo, the Ratio of the Revolutions of the one, to thofe of the other : to find the Space which the Power is to pafs over, while the Weight goes any given length.
Multiply the Periphery of the Axis of the flowed Wheel, into the antecedent Term of the Ratio, and the Periphery of the fwiftert Wheel into the confequent Term ; and to thefe two ProduBs, and the given Space of the Weight, find a fourth Proportional : This will be the Space of the Power. Suppofe, e. g. the Ratio of the Revolutions of the Howell Wheel to thofe of the fwiftert to be as 2 to 7 ; and the Sp.ce of the Weight 30 Feet : And let the Periphery of the Axis of the flowert Wheel be to that of the fwifteft as 3 to 8. The Space of the Power will be found 280.
Say, as the Periphery of the Axis of the flowed Wheel is to the Space of the Weight given ; fo is the given Num- ber of Revolutions of the fwiftert Wheel to a fourth Propor- tional • which will be the Number of Revolutions perform'd while the Weight reaches the given Height. — Then, by Ex- periment, determine the Number of Revolutions the Cwife- eft Wheel performs in an Hour ; and by this divide the fourth Proportional found before. — The Quotient will be the Time Cpent in railing the Weight.
Wheels of a Ciock, &c. are the Crown Wheel, Contrat Wheel, Great Wheel, Second Wheel, third Wheel, Striking- Wheel, Detent-Wheel, &c. See Clock, and Watch.
Wheels of Coaches, Waggons, &c. — In the Philosophical tranfatlwns, we have Come Experiments (hewing the Ad- vantages of high Wheels in Carriages of all Kinds ; the Re- fults of the Experiments amount to this :
1°, That, four Wheels of 5! Inches high, via. one half of the ordinary Height of the Wheels of a Waggon, draw a, Weight of 5c//. Averdupoife up an inclined Plane with lels Weight by fix Ounces, than two of them match'd with two fmalier ones of 4J Inches height.
2°, That any Vehicle might be much more eafily drawa in rough ways, if the fore Wheels were as high as the bind- Wheels, and the Thills fix'd under the Axis.
•° That fuch a Vehicle would likewiCe be drawn more eafily where the Wheels cut in Clay, Sand, (gc.
4 , That high Wheels would not cut fo deep as low Wheels.
5°, That low Wheels are indeed beft for turning in a nar- row Compais.
potter's Wheel. See Pottery.
Ariftotle's Wheel. See Rota Ariftotelica.
Meafuring Wheel. SeePEDoMETER, Perambulator, Waywiser, ci?c.
Wheel is alfo a kind of Punilhment which great Cri- minals are put to in divets Countries. See Punishment.
In France, their Affaffins, Parricides, and Robbers on the Highway, are condemn'd to the Wheel, i. e. having their Bones firft broke with an Iron Bar on a Scaffold, they^ are cxpos'd and left to expire on the Circumference of a Wheel. —In Germany, they break their Eones on the Wheel it felt
This cruel Punilhment was unknown to the Antients ; as is obferv'd by Cujas. — 'Tis not certain who was the Inven- tor.— Its firft Introduaion was in Germany. 'Twas but rare- ly praais'd any where elCe, till the Time of Francis I. of France ; who by an Edia of the Year 1 5 54. appointed it to be inffiaed on Robbers on rhe Highway. Richclet dates rhe Edia of the Year 1538, and quotes Srcdetis.
Wheel, in the Military Art, is the Word of Command when a Battalion is to alter its Front, either one way or the other. See Evolution. ...
To Wheel to the right, the Man in the right Angle is to turn very llowly, and every one to wheel from thelelt toihe right, regarding him as their Centre ; and vice verfa, wnen they are to wheel to the left.
When a Divlfion of Men are on the March, if the Word be Wheel to the right, or to the left, then the right or lerr- hand Man keeps his Ground, turning only on his Hee , and the reft of the Rank move about quick, till they make an even Line with the faid right or left-hand Man.
Squadrons of Horfe wheel much after the fame manner.
WiiEEL-p'/rc, among Chymifts, a Fire uCed For fufing of Metals ; properly called Ignis Rot<£. See Fusion, Me.-
It'is a Fire which covers or incompafles the Crucible, Coppel, or Melting-Pot quite over ; a-top, as well as around the Sides. S'-eFiRE. _
WHFRLICO TES, a fort of open Chatiots, uled by rer- uns of Quality before rhe Invention of Coaches. See Coach, Chariot, $5c.
WHF.RRI. See Vessel, Boat, (So.
WHETSTONE, a St, ne for the whetting or iharpening Knives, and other Tools upon. See Stone, and Hone.
WHEY, the Serum or watery Part ot Milk.
See Milk.
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