If carriages had always to move along perfectly smooth roads, such as a tramway of wood, iron, or stone, the use of wheels in overcoming friction would be their sole utility, and the height of the wheels would be of small consequence. But as carriages are drawn along roads with loose stones and uneven surfaces, wheels are further useful in mounting over these obstacles, and it is plain that a high wheel does this more easily than a low one. To demonstrate this, let us suppose a shallow ditch or gulley of a foot wide and two inches deep, a wheel two feet high would sink into this and touch the bottom, but a wheel three feet high would only sink an inch, and a wheel four feet six inches high would sink only half an inch, on account of their greater diameters. Consequently, whilst the large wheel would have to be lifted by force of pulling only half an inch, the smallest wheel must be lifted two inches, and with the wheel must also be lifted a portion of the load of the entire carriage. Again, the long spoke acts as a longer lever, the point of draught being the axle, which is higher from the ground in the higher wheel, and again assists in overcoming the obstacle, as the angle of incidence is so much less. To learn that the leverage power of a high wheel is very great we need only consider the advantages gained by a large wheel in locomotives and in bicycles. In practice we find that wheels from 4 feet to 5 feet are sufficient for large carriages, and from 3 feet upwards for ordinary vehicles.