In 1902, Henry Sturmey and James Archer in England devised a three speed rear hub based on an epicyclic gearbox. The middle speed was determined by the tooth ratio between the chain wheel and the rear sprocket, and the gear box could give a 'high' gear 25% higher than this and a 'low' gear 20% lower than the center value.

From: G. Apps, "The Bicycle Book," Smithmark (1996)

In the 1930's the Derailleur gear was introduced to permit gear changes during riding so as to enhance hill climbing capability. A 1934 model is illustrated. Chain transfer between cogs on the rear hub gave rise to the ratio change

From: Sloan, "Sloane's Complete Book of Bicycling," Simon & Schuster (1995)