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wheels than without them. The axles on both sides indeed are inmotion, but the calculation must be made as if only one moved:for the greater number of wheels there are, the more will the fric-tion be divided among them. An objection of considerable weightarises to this method of fixing the wheels and axles together, thatthus the wheels are prevented from moving with different veloci-ties as they ought to do, when the carriage moves out of a rightline ; but this may be obviated by leaving the friction-wheels looseupon their axles, by which means they will be at liberty to movewith different velocities, at the same time that they will have theadvantages of friction-wheels always as to one wheel of the car-riage, and generally as to both. But the contrivance of Mr. Gar-rett of Bristol, who obtained a patent for it, is much superior.Between the axle and nave a hollow space is left to be filled upby solid equal rollers nearly touching each other. These are fur-nished with axles inserted into a circular ring at each end, bywhich their relative distances are preserved ; and they are keptparallel by wires fastened to the rings between the rollers, andwhich are rivetted to them. To understand the effect of this ma-chinery we must consider, that if, when plane surfaces move witha roller between them, if the under one be fixed, the upper planewill put the rollers forward but with half the quantity of its ownmotion. This is owing to the reaction of the stationary plane,which causes the roller to move backward upon itself as much asthe other causes it to move forward. Thus, let CD, (PlateCLXXXI. fig. 6,) be a fixed surface, and AB a moveable one,with a roller E between them; if B be moved forward to G, itwill cause the roller to move to F, which is but half the distancethat AB has moved ; because it has rolled in a retrograde directionas far against the surface BA as it has gone forward upon the other.This is entirely owing to the resistance it meets with from CD ;for if it did not touch that surface, but was attached by any othermeans to AB, it would be carried along with it through the wholespace without any rolling motion. Hence it is clear, that if aroller be placed between the axle and nave of a wheel, and thelatter be turned round, the roller will move with a retrograde mo-tion upon the axle; and in order to carry it quite round, the navemust be turned as much beyond a whole revolution as is equal onits inner circumference to the whole of lire circumference of theaxle. To exemplify this, let ABCD, (fig. 7,) represent the nave ofthe wheel E, the inner circumference of which is eighteen inches,and the axle,so small that it may he considered as a point. LetF and G be two rollers closely fitted between them : if then thewheel be turned round, the rollers will also be carried along with itround the point which we consider as an axle , for theie can ueither be rolling nor friction against a mere point. But if the axlebe of any sensible size, for instance, one inch circumference, thenmust each roller move round by the motion of the nave against it,and the resistance of the angle on the opposite side. But in orderto do this, it must roll in a retrograde direction upon the nave, andconsequently the latter must go as far beyond a revolution as isequal to the circumference of the axle upon it, before the rollercan go once round the axle, which in this case is by one-eighteenthpart of thp circumference. Should the circumference of the axlebe nine inches, and that of the inner part of the nave remain as be-fore, the wheel must perform one revolution and an half beforethe roller could be moved once round, and so on in proportion:but as the circumference of an axle must always be less than theinner part of a nave turning upon it with rollers between them, itnever can amount to two revolutions of the wheel round the axle,however nearly it may approach to it; for no segment of a circlecan ever be a straighUine. It will now be apparent, that if severalrollers be placed all round between the nave and axle, which everway the wheel be turned there cannot be any real friction, butmerely a rolling of the rollers. If likewise these rollers be all ofone size, and very nicely fitted to the cavity, they will keep theirplaces without shifting, and very effectually answer the purpose ofdestroying friction. As such tollers, however, were very liable tobe displaced by accident, the use of them was neglected, till Mr.Garnett suggested the improvement represented in fig. 8. HereABCD represents a piece of metal to be inserted into the nave ofa wheel, of which E is the axle, and 1 , 1 , 1 , &c. rollers of metalhaving axes inserted into the brazen circle which passes throughtheir centres ; and both circles being rivetted together by boltspassing between the rollers from one Side of the nave to the other;vouiv.— no. 216 .

they are always kept separate and parallel. By this method, in-1 deed, some friction unavoidably tikes place betwixt the axles ofthe rollers and their sockets in the bra.s-rings; luit as the quantityof friction depends principally on the force by which the rubbingsurfaces are pressed upon each other, and as in this case there isbut the slight pressure occasioned by those accidental circum-stances which would bring the rollers together, the friction mustbe too trifling to be noticed. Mr. Edgeworth concludes his ob-servations with some remarks on the use of springs, which greatlyfacilitate the draught of carriages. “ Whatever (says he) permitsthe load to rise gradually over an obstacle without obstructing thevelocity of the carriage, will tend to facilitate its draught; and theapplication of springs has this effect to a very considerable degree-:the same weight of four pounds being drawn over the same obsta-cles, when springs were put between the load and the carriage, by-four pounds instead of fourteen. This remarkable differencepoints out the great advantage of springs in rough roads; an ad-vantage which might be obtained for heavy waggons, as well asfor other carriages, by a judicious application of the same means.The reason why springs so much facilitate the draught of carriagesseems to be, not only that they allow the wheels to pass more gra-dually over the obstacles, as Mr. Edgeworth says, but that bytheir elasticity they make the carriage bound upwards every mo-ment for a small way. Thus its gravity is for that moment in agreat measure counteracted, and the progressive motion which ithas already acquired i: at liberty to act more freely }n pushing itforward ; for were it possible very suddenly to take away thehorses from a carriage mounted on springs, and moving with con-siderable velocity, it would continue sometime lo move of itself;tile weight in this case acting as a fly upon any mechanical'engine,by means of which the machine accumulates a certain quantity ofpower, and will keep itself in motion for a considerable time afterthe hand is taken away from it. The weight of all carriages in-deed lias some effect o'f this kind, otherwise the draught would re-quire an intolerable exertion of strength. By means of wheels,some people have contrived carriages to go without horses, or anyother moving power than what was given by the passengers, bythe wind, &c. One of these is represented by ABCD, (PlateCLXXXI. hg. 9.) It is moved by the footman behind it; andthe fore-wheels, which act as a rudder, are guided by (he personwho sits in the carriage. It was invented by M. Richard, a phy.sician of Rochelle, and was exhibited at Paris in the seventeethcentury. It is described by M. Ozanam in his Recreations Ma-theinatiques. Between the hind-wheels is placed a box, in whichis concealed the machinery that moves the carriage. A A, (fig. 10,)is a small axis fixed into the box. B is a pulley, over which runs arope, whose two ends are fastened to the ends of the two levers ortreddles CD, whose other ends are fixed in such a manner in thepiece E, which is joined to the box, that they can easily move upand down. F, F, are two fiat pieces of iron that are joined to thetreddles, and take tlie teeth of the two wheels H, H, which arefixed on the same axis with the hind-wheels of the carriage, I, 1.It is evident, that when the footman behind presses down one ofthe treddles, suppose C, with his foot, he must bring down one ofthe pieces of iron F, and consequently turn the wheel H that isnext lo it; and at the same time, by means of the rope that goesover the pulley, he must raise the other treddle D, together withits piece F, which being thrust down will turn the other wheel H ;and so alternately : and as the great wheels are fixed on thesame axis, they must necessarily move at the same time. If theends of the treddles next E, instead of being placed behind thecarriage, were turned the opposite way, so as lo come under thefeet of the person who sits it it, he might move it with equal, qreven greater, facility than the footman, as it would then be charg-ed with the weight of one person only. A machine of this kindwill afford a salutary recreation in a garden or park, or on anyplain ground ; but in a rough or deep road must be attended withmore pain than pleasure. Another contrivance for being carriedwithout draught, is by means of a sailing chariot or boat fixed onfour wheels, and AB, (Plate CLXXXI. fig, 1 i,) which is drivenbefore the wind by the sails CD, and guided by the rudder E.In a chariot of this kind, the wheels should be farther asunder,and the axle-trees longer, than in other carriages, to prevent over-turning. A machine of this sort was constructed in the seven-teenth century by Stephinus, at SchevtTing in Holland, and is ce-10 K. - lebrated