Introduction to the Problem of the Isochronous Hairspring

Deviations from isochronism for the system of hairspring and balance wheel are treated by a method due to Haag. The results are given a geometrical interpretation. It is shown that the deviations are related to the displacement of the end point of the hairspring in a set-up in which this end point is free to move keeping its tangent constant in direction. Such an arrangement can be realized with Bouasse's pendulum. For the so-called ``helical'' spring a more accurate solution than Phillips' has been found for the shape of the terminals. Extensive numerical calculations have been made for flat spiral springs, and a new simple terminal has been designed.