W HE

860

WHE

powers by the imaginary lines MO and ON. As the length ofOM, therefore, is to that of ON ; so is the proportion required tothe weight to balance it on the obstacle, when rising over it; andin tliis case the arms are equal, it is plaii) that the powers must beso likewise. Every obstacle, therefore, exceeding this height,which is as 7-03 to 4S, will require a power acting parallel to theplane greater than the weight drawn; and every obstacle whoseheight bears a smaller proportion to that of the nave, must beovercome by a smaller power. Again, let a wheel of four feetdiameter be represented by the circle in fig. 6, and supposed tobe moved along the plane PQ, and an obstacle of twelve inchesheight be placed before it, the real lever will then be representedby the lines LOG; which being reduced to the imaginary onesMON, shews that the power is greater than the weight. By thesame rule, if an obstacle of three inches be placed in the way of awheel, as in fig. 7, the power required to move the wheel will beconsiderably less than the weight, though it is plain that the pro-portion of power must always be according to the size of thewheel, the height of the obstacle, and the direction in which thecarriage is drawn. For instance, if the line of traction in fig. 7,be raised into the direction CS, the power required to move thecarriage over it will be to the real weight as the line CO is to theline ON; and inconsequence of thus altering the direction, wegain as much as the length of the line CO exceeds that of CN.This view of the manner in which the wheels of carriages act, willserve to elucidate the question, whether large or small w heels arepreferable for carriages: let the circle, (fig. 8,) represent a wheelof two feet diameter, and the obstacle in its way 7 03 inches inheight; then will the true lever be represented by the lines COL,to be reduced to the imaginary ones MON. In this case, thepow er required to draw the carriage must be to its weight as NOis to OM, which is more than double ; and thus the advantage oflarge wheels over small ones is evident. In this, however, as inall other cases where wheels act as mechanical powers, vve mustremember that the same doctrine applies to them as to the powersthemselves when used in any other manner, viz. that as much aswe gain in power we lose in time; and therefore, though a wheelof twice tlie diameter may be raised over an obstacle of any givenheight with twice the ease that would be required for one of oncethe diameter; yet the large w heel would require twice the timeto move over it that tin: small one does. Hitherto we have con-sidered tlie carriage as being drawn in a direction parallel, ornearly so, to the plane on which the wheels move, which line issupposed to be horizontal; but the case will be different when wesuppose them to move upon an inclined plane ; for then, eventhough tlie line of traction be parallel to the ascending plane, andthough the wheels act as levers, we shall find that the action of theweight will increase with tlie power gained by tlie increase of sizein the wheels ; and consequently, that tiie increased size of thelatter will be of no farther use than that of diminishing tiie fric-tion in the same manner as is done upon horizontal planes. Toillustrate this, suppose the larger circle in fig. 9, to represent awheel of four feet diameter, and the smaller circle a wheel of onlytwo, both of which are made to ascend the inclined plane LM, bypowers applied in tlie directions GI and ES parallel to tlie eleva-tion of tlie plane, which is 45 degrees; it will then be found, thatby describing the lever as in the former case, though the arm oftlie lever to which the power is applied be double the length in tlielarge wheel that it is in the small, the other is augmented in thesame proportion. Neither will tlie powers be augmented byvarying the direction of tlie line of traction; for while these arekept parallel to one another, their relative [lowers must alwayskeep tlie same proportion to one another. From these consider-ations, Mr. Anstice draws the following conclusions: 1. That ina carriage placed upon an horizontal plane, nothing more is re-quired to produce motion than to overcome the friction whichtakes places between it and tlie plane. 2. By tlie application ofwheels to a carriage, the friction is lessened in the proportion ofthe diameters of tlie axles and hollow parts of tlie naves to those oftlie wheels. 3. In the draught of a carriage without wheels tip aregular plain -ascent, tlie friction must not only be overcome, butthere is a power likewise to be applied sufficient to lift such a pro-portion of the weight of the carriage as the perpendicular part ofthe ascending plane bears to that portion of tlie plane. 4. Ifwheels of any size be applied to the carriage in such circum-

^-5

stances, they have only the advantage of lessening the friction ;for though they really act as levers, yet as each ami of tlie leveris lengthened in proportion to the increase of size in the wheels,the power can be no farther augmented than as the ascent mayact as a mechanical power for raising up tlie wheels, carriage, &c.to the top. 5. Large wheels have tlie advantage over small one*in overcoming obstacles, because they act as levers in proportionto their various sizes. 6. Tlie line of traction, or that in thedirection of which tlie carriage is drawn, should always, if possi-ble, be parallel to that in which tire plane lies; for when this is(lie case, the arm of the lever to which tlie power is applied willbear tlie longest proportion possible to the other. This alwaystakes place when the line of traction is perpendicular to that spokeof the wheel which points to the obstacle. As it may not alwaysbe possible, however, to alter tlie direction of tlie line of tractionto this position, it will be most proper to fix upon some mediumbetwixt that which commonly occurs and that which requires thegreatest exertion to overcome tlie obstacle; that is, betwixt alevel line and one rising perpendicular to the spoke of the wheelwhich points to the obstacle it is likely to meet with. The greaterattention ought to be paid to this at last, that all wheels, but espe-cially small ones, are liable to sink into the groud over whichthey pass, and tints produce a constant obstacle to their own pro-gress. 'I'be line of traction, it must also be observed, is not animaginary one drawn from that part of the animal, to which tlietraces or chains are attached to tiie axle of the wheel, but tlie realdirection of tlie traces to whatever part ot tlie carriage they areattached ; for the effort will be instantly communicated in tliesame direction in one part of the carriage to all tlie rest, byreason of the whole being fastened together, and in one piece.Carriages with four wheels, as waggons or coaches, are muchmore advantageous than carriages with two wheels, as carts andchaises; for with two wheels it is plain the tiller-horse carries partof. tlie weight, in one way or other; in going down hill, tlieweight hears upon tlie horse ; and in going up hill, tlie weightfalls the other way, and lifts the horse, which is still worse. Be-sides as the wheels sink into the holes in the roads, sometimes oi»one side, sometimes on the other, tlie shafts strike against tlie til-ler’s sides, which destroys many horses: moreover, when one ofthe wheels sinks into a hole or rut, half the weight falls that way,which endangers tlie overturning of tlie carriage. It would hemuch more advantageous lo make tlie four wheels of a coach orwaggon nearly of a height, than to make the fore wheels of onlyhalt tiie diameter of the hind-wheels, as is used in many places.1 lie fore-wheels have commonly been made of a less sizethan tlie hind ones, both on account of turning short, and toavoid cutting tlie braces. Crane-necks have also been invent-ed for turning yet shorter; and tlie fore-wheels have beenlowered, so as to go quite under tlie bend of (lie crane-neck.It has been considered as an object of tlie utmost importance intlie construction of wheel-carriages to remove as much as possiblethe friction which is occasioned by tlie weight; this has beenattempted by means of friction-w heels or rollers, which may he ap-plied in as great numbers, and in as great a variety of w ays as weplease. The best method of applying them, according lo Mr.Anstice, is to have the wheels and axle fixed lo one another, sothat botli may turn together. Two friction-wheels a little over-lapping each other, must then he fixed on each side of (lie body ottlie carriage, so that it may bear on tlie axle in tlie intersection ottlie wlieeis, as is represented in Plate CLXXXI. fig- 5. HereABCD represents the body of the carriage, tlie large circle oneof tlie wlieeis fixed to tlie axle E. The circumference of each otlie friction-wheels F and G is supposed to be three feet, and iaof their axles three inches. As the large wheel then revolves ytlie motion of the carriage, and tints transfers the friction bom tcircumference lo its axle; so tiie friction of tlie axle itself is now-transferred from tlie circumference of tlie friction-wheels to memaxles. Every revolution of the great wheel, therefore, duringwhicli it passes over eighteen feet of ground by the motion ot 'axle, puts the less wheels round one sixth part ot their cucle ; aconsequently their axles are moved through the same part ot iecircumference, tlie friction being thus reduced to that uponsmall part; which being no more than half an inch, becomestimes less than it would have been on tlie large wheel withou J

motion on an axle, and twelve times less by means of the 111C .