In rack railways a cog-wheel on the engine engages in a toothed rack which forms part of the permanent way.
In this way smoothness of working is ensured, the cog-wheel being constantly in action with the rack.
Racks of this type usually become impracticable for gradients steeper than 1 in 4, partly because of the excessive weight of the engine required and partly because of the tendency of the cog-wheel to mount the rack.
The Puerto Cabello and Valencia line (34 m.) is another British undertaking and carries a good traffic. A part of this line is built with a central cog-rail.
Up the steep slope of Mount Washington runs a cog railway.
Among these are many funicular cog-wheel lines, climbing up to considerable heights, so up to Marren (5368 ft.), over the Wengern Alp (6772 ft.), up to the Schynige Platte (6463 ft.), and many others still in the state of projects.
The epicycloid was so named by Ole Romer in 1674, who also demonstrated that cog-wheels having epicycloidal teeth revolved with minimum friction (see Mechanics: Applied); this was also proved by Girard Desargues, Philippe de la Hire and Charles Stephen Louis Camus.