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colour : thefe he executed with rapidity, and, as he always 

 fold them, he acquired fufScient money to indulge a natural 

 propenfity to the pleafures of the table. Hence he became 

 a martyr to the gout, and died of that difeafein 1801, at the 

 age of 54. He was elefted an academician in 1791. 



WHEE, Whey, Whie, or Qui, in Rural Economy, a 

 term ufed to fignify a young heifer, or heifer-calf, in differ- 

 ent places and parts of the country. 



WHEEANG, or Whang, a provincial term made ufe 

 of to fignify a thong or itrap of leather for the harnefs 

 or geer of farm-teams, or other domeflic purpofes. 



WHEEL, Rota, in Mechanics, a fimple machine, confift- 

 ing of a round piece of wood, metal, or other matter, which 

 revolves on an axis. 



For an account of the wheel and axle, as a mechani- 

 cal power, fee Axis in Perttrochio, and Mechanical 

 Powers. 



The wheel is one of the principal mechanic powers. It 

 has place in moft engines : in effeft, it is of an aflemblage of 

 wheels that mod of our chief engines are compofed. Wit- 

 nefs clocks, mills, &c. 



Its form is various, according to the motion it is to have, 

 and the ufe it is to anfwer. By this it is diilinguifhed into 

 fimple and dented. 



Wheels, Simple, are thofe whofe circumference and axis 

 are uniform, and which are ufed fingly, and not combined. 

 Such are the wheels of carriages, which are to ha.ve a double 

 motion ; the one circular about their axis ; the other refti- 

 linear, by which they advance along the road, &c. which 

 two motions they appear to have ; though, in effeft, they 

 have but one : it being impofTible the fame thing fhould 

 move, or be agitated, two different ways at the fame 

 time. 



This one is a fpiral motion ; as is eafily feen, by fixing a 

 piece of chalk on the face of a wheel, fo as that it may 

 draw a line on a wall, as the wheel moves. The line it 

 here traces is a juft fpiral, and flill the more curve, as the 

 chalk is fixed nearer the axis. 



The faft, however, has been difputed ; and it has been 

 alleged, that nothing is more eafy than for any one, who 

 will take the trouble to make the experiment, to prove its 

 falfehood. Place the chalk on the face of the wheel, as 

 direfted, and you will find that, fo far from its defcribing 

 a jufl fpiral, and that flill the more curve as the chalk is 

 fixed nearer the axis, the chalk, if placed on the periphery of 

 the wheel, will defcribe a cycloid, and the nearer it is placed 

 to the axis, the nearer will the line it defcribes approach to 

 the flraight line which is defcribed by the axis itfelf. More- 

 over, it is not true, nor pretended to be fo, that the fame 

 thing moves two ways at once in the reftilinear and circular 

 motion of wheels. The local motion, or motion of the 

 whole wheel, is reftilinear only ; that of the parts of the 

 wheel circulan. Nor can this latter motion with any pro- 

 priety be called that of the wheel, unlefs the fame thing 

 could alfo move quick and flow at the fame time, which the 

 different parts of the wheel, in revolving round its axis, 

 evidently do. Jacob's Obf. on the Strufture and Draught 

 of Wheel-Carriages, 1773, p. 28, &c. 



For a very nice phenomenon, in the motion of thefe 

 wheels, fee Rota Ariflotelica. 



We fhall add, that, in wheels of this kind, the height 

 fhould always be proportioned to the flature of the animal 

 that draws or moves them. The rule is, that the load and 

 the axis of the wheels be of the fame height with the power 

 that moves them ; otherwife the axis being higher than the 

 beafl, part of the load will lie upon him ; or, if it be lower, 

 he pulls to difadvantage, and muft exert a greater force. 

 Though Stevinus, Dr. Wallis, &c. fhew, that, to draw a 

 lot 



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vehicle, &c. over wafte uneven places, it were befl to fix the 

 traces to the wheels fomewhat lower than the horfe's breaft. 

 See Wheels of Coaches, &c. 



The power of thefe wheels refults from the differences of 

 the radii of the axis, and circumference. The canon is 

 this : " As the radius of the axis is to that of the circum- 

 ference, fo is any power to the weight it can fuftain 

 hereb)f." 



This is alfo the rule in the axis in peritrochio ; and, in 

 effeft, the wheel, and the axis in peritrochio, are the fame 

 thing ; only, in theory, it is ufually called by the latter 

 name, and in praftice by the former. 



Wheels, Dented, are thofe either whofe circumference, 

 or axis, is cut into teeth, by which they are capable of 

 moving and afting on one another, and of being combined 

 together. 



The ufe of thefe is very confpicuous in clocks, jacks, 

 &c. 



The pov?er of the dented wheel depends on the fame 

 principle as that of the fimple one. It is only that to the 

 fimple axis in peritrochio, which a compound lever is to a 

 fimple lever. 



Its doftrine is comprifed in the following canon ; vi%. 

 " The ratio of the power to the weight," in order for that 

 to be equivalent to this, " mufl be compounded of the ra- 

 tios of the diameter of the axis of the lafl wheel to the dia- 

 meter of the firfl ; and of the ratio of the number of revo- 

 lutions of the lafl wheel, to thofe of the firfl, in the fame 

 time." But this doftrine will deferve a more particular 

 explanation, 



1. Then, if the weight be multipled into the produft of 

 the radii of the axes, and that produft be divided by the 

 produft of the radii of the wheels, the power required to 

 fuflain the weight will be found. Suppofe, e. gr. the wright 

 A {PlaieXL.fg. 83. Mechanics,) — 6000 pounds, B C = 

 6 inches, C D = 34 inches, E F = 5 inches, E G = 35 

 inches, H I = 4 inches, H K = 27 inches : then will 

 BCxEFxHI = i2o;andCD x EG x HK 

 =: 32130. Hence the power required to fuflain the weight, 

 will be 6000 x 120 -f- 32130 = 22^ very nearly ; afmall 

 addition to which will raife it. 



2. If the power be multiplied into the produft of the 

 radii of the wheels, and the faftum be divided by the pro- 

 duft of the radii of the axes ; the quotient will be the 

 weight which the power is able to fuflain. Thus, if 

 the power be 224 pounds ; the weight will be 6000 

 pounds. 



3. A power and weight being given, to find the number 

 of wheels, and in 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 lafl 

 wheel, may fuflain the given weight. 



Divide the weight by the power ; refolve the quotient 

 into the faftors which produce it. Then will the num- 

 ber of faftors be the number of wheels ; and the radii of 

 the axes will be to the radii of the wheels, as unity to the 

 feveral wheels. Suppofe, e.gr. a weight of 3000 pounds, 

 and a power of 60, the quotient of the former by the latter 

 is 500, which refolves into thefe faftors, 4. 5. 5. 5. Four 

 wheels are, therefore, to be made ; in one of which, the ra- 

 dius of the axis is to the radius of the wheel, as i to 4 ; in 

 the refl, as i to 5. 



4. If a power move a weight by means of two wheels, 

 the revolutions of the flower wheel are to thofe of the fwifter, 

 as the periphery of the fwifter axis is to the periphery of the 

 wheel that catches on it. 



Hence, i. The revolutions are as the radius of the axis 

 F E to the radius of the wheel D C. 2. Since the »um. 



ber 



