rate of the clock. The first clocks in northern Europe used foliots, while those in southern Europe used balance wheels. As clocks were made smaller, first as bracket clocks and lantern clocks and then as the first large watches after 1500, balance wheels began to be used in place of foliots. Since more of its weight is located on the rim away from the axis, a balance wheel could have a larger moment of inertia than a foliot of the same size, and keep better time. The wheel shape also had less air resistance, and its geometry partly compensated for thermal expansion error due to temperature changes. Addition of balance spring These early balance wheels were crude timekeepers because they lacked the other essential element: the balance spring. Early balance wheels were pushed in one direction by the escapement until the verge flag that was in contact with a tooth on the escape wheel slipped past the tip of the tooth ("escaped") and the action of the escapement reversed, pushing the wheel back the other way. In such an "inertial" wheel, the acceleration is proportional to the drive force. In a clock or watch without balance spring, the drive force provides both the force that accelerates the wheel and also the force that slows it down and reverses it. If the drive force is increased, both acceleration and deceleration are increased, this results in the wheel getting pushed back and forth faster. This made the timekeeping strongly dependent on the force applied by the escapement. In a watch the drive force provided by the mainspring, applied to the escapement through the timepiece's gear train, declined during the watch's running period as the mainspring unwound. Without some means of equalizing the drive force, the watch slowed down during the running period between windings as the spring lost force, causing it to lose time. This is why all pre-balance spring watches required fusees (or in a few cases stackfreeds) to equalize the force from the mainspring reaching the escapement, to achieve even minimal accuracy. Even with these devices, watches prior to the balance spring were very inaccurate. The idea of the balance spring was inspired by observations that springy hog bristle curbs, added to limit the rotation of the wheel, increased its accuracy. Robert Hooke first applied a metal spring to the balance in 1658 and Jean de Hautefeuille and Christiaan Huygens