made but one revolution in the fame time, there has been only a fliding of the parts equal to the circumference of the hole in the nave here suppofed to be about fix inches, fo that the friction is leffened about as one to thirty-fix; befides, the advantage gained by confining it to fo fmall a furface, whereby the parts are more cafily kept fmooth and fitted to each other, and fubftances applied and retained to leffen the remaining friction.* By the application of wheels to a carriage, the friction is leffened in proportion of the diameters of the axis, and concave part of the naves to thofe of the wheels. When a carriage is drawn up hill, or any regular plane afcent without wheels, you have not only the friction to overcome, but the power muft alfo be fufficient to overcome that proportion of the weight of the carriage, that the perpendicular part of the inclined plane bears to that portion of the plane. Wheels applied to a carriage moving up a regular plane of afcent appear only to act as removing the friction, for though they may be confidered as levers, yet as each arm of the lever is lengthened in proportion to the fize of the wheels, the power will be only augmented as far as the afcent can be confidered as a mechanical power for raifing the wheels, carriage, &c. to the top of the hill. Large wheels have the advantage of fmall ones in overcoming obstacles, because they act as levers in proportion to their fizes. That in general the center of gravity fhould be as near as may be to the axis of the wheel; and where fafety is particularly confidered, the nearer that center is to the ground the better. A a 3 If Artice's Remarks on the comparative Advantages of Wheel Carriages, p. 21, 40, 41, 42, &c. If the fifpenfion be below and the body be turned forwards, (as is the cafe with two wheeled carriages defcending hills) then will the greater part of the weight be thrown before the axis, and must be partly borne up by the horse that draws; in afcending, the fame proportion will be thrown backwards and tend to lift the animal. If the body be fufpended above the center of gravity, the difadvantages will be equal, but the effect will be reverfed. The latest experiments on this fubject have been made by the Rev. Mr. Vince. Some refults thereof, which have been published in his excellent "Plan of a Courfe of Lectures on the Principles of Natural Philofophy," I fhall now lay before you; befides thefe, there are feveral curious obfervations on this fubject by Mr. L. Edgworth, published in the "Tranfactions of the Royal Irifh Academy," which are well worth your attention, of which, however, I fhall only mention that which relates to the ufe of fprings when applied to car riages. MR. VINCE ON WHEEL-CARRIAGES, ON PLAIN If the wheels be all equal and narrow, it re-. quires the fame weight to draw the carriage, whether it be loaded before or behind. If broad wheels be put on of the fame fize and weight, it requires the fame weight to draw the carriage as for the narrow wheels, at whatever part it is loaded. If two wheels be low and two high, it requires a greater weight to draw the carriage than when all are high. In this cafe it makes no fenfible difference which go before. The common opinion therefore that that the high wheels drive on the lower when they go forward is not true. If the wheels be all equal, it requires a greater weight to draw the carriage, the lefs the wheels are. The difadvantage of finall wheels arifes from hence, that the refiftance of the ground, which turns the wheels about, more eafily overcomes the friction at the axle in a large than a small wheel, because it acts at a greater distance. For the mechanical advantage of wheels is, that the refiftance which must be overcome by a force more than equivalent to it if the wheels could not turn, is overcome by a lefs force in the proportion of the radius of the wheel to the radius of the axle, when the wheels do turn. Hence the disadvantage of laying the load upon the low wheels, as it increases the friction where there is the leaft power to overcome it. Where the load is but fmall, and confequently the friction but fmall, there is but a small difference between the fmall and large wheels; but when the load is great the difference becomes confiderable. ON HARD GROUND WITH OBSTACLES If W be the weight of the carriage, and the center of gravity be in the middle; alfo if r the radius of the wheel and the height of the obftacle, then the power P acting parallel to the horizon which is juft fufficient to ballance the carriage at the obftacle without drawing it overWX √2rx-x2 2r-2x For the power may be conceived to be draw ing a weight up an inclined plane, which is a tangent to the circle at the point where it touches the obftacle; and as when that end rifes, the other refts upon the horizontal plane, the power has to elevate a weight only equal to W. Experiments of this kind are fubject to inaccuracies which cannot be accounted for. The power will fometimes hang for fome time without moving the carriage, and then it will fuddenly draw the carriage over the obftacle. Sometimes there will be a difference of half an ounce out of about ten ounces in drawing the fame carriage over the fame obftacle, although every care is taken to have all the circumflances accurately the fame. Many of the experiments however anfwer very nearly to the theory, nor do any of them differ from it very materially. The ufe of high wheels in going over obftacles is very manifeft from this propofition, and as carriages are continually going over obstacles, high wheels will always have the advantage. Moreover in finking into holes they have a double advantage, first, they do not fink fo deep as low ones would; and fecondly, after finking, they afcend again with lefs power. As, when the center of gravity is in the middle of the carriage, the power has but half it's weight to elevate in going over an obstacle, therefore when the load is not in the middle, it throws the center of gravity towards one end, and therefore when that end goes over an obftacle the power has more than half the weight to raife, the preflure upon each wheel being inverfely as the distance of the center of gravity from them. Hence every carriage fhould be loaded moft towards the higheft wheels, by which means lefs than half the weight will be thrown upon the lower wheels, and thus each pair of wheels may be made to require the fame power to draw them over an obftacle. The fame power, however, that may be neceffary for one obftacle will not be fufficient for another. If the height of the obstacle be inconfiderable in respect to the radius of the wheel, which is the cafe with the common obftacles, as ftones, &c. which carriages ufually meet with, then P= W X Now as each pair of wheels has the fame obstacles to go over, x is given, and that P may be given, or that it may require the fame power for each pair, W muft vary as ; now the weight fupported by each wheel is inverfely as it's distance from the center of gravity. Hence to overcome fmall obftacles, the diftance of the center of gravity from the great wheels; it's diftance from the fmall the fquare root of the radius of the fmall wheel the fquare root of the radius of the large wheel. The radii of the wheels of a common waggon are about 5 ft. 8 in. and 4 ft. 8 in. and the distance of the wheels, when narrow, about 6 ft. 6 in.; hence the center of gravity of the load of a waggon ought to be about 3, 6 in. nearer to the higher than to the lower wheels. For a broad wheel waggon, where the distance of the wheels is about 7 ft. 10 in. the center of gravity ought to be about 4, 2 in. nearer to the higher than to the lower. It appears alfo that when Wand x are given and x is very small, P varies inverfely as the fquare root of the radius of the wheel. Hence the advantage of a wheel to overcome a small obstacle varies as the fquare root of the radius of the wheel. This refiflance of the obftacle caufes the wheel to turn, but this refiftance is not friction; for friction arifes from the rubbing of the parts of one body against thofe of another, whereas there the wheel only turns upon a point; the friction therefore only takes place at the axle, where the parts rub one against another. There is therefore no fric-. tion at the ground, unless when the wheels flide, which is the cafe when they are chained together, which |