In 1659 Christiaan Huygens invented the pendulum clock and realizing the lack of isochronism in a simple pendulum, he mounted it between cycloidal cheeks. After many years of trying to adapt this clock to seagoing vessels to determine longitude, he suggested, in 1675, the use of a balance wheel with an elastic wire to control oscillation. At this time the “theory of elasticity” was not sufficiently developed to analyze his balance arrangement.
The first successful effort to establish the laws of isochronism for a balance governed by spiral springs was made by Phillips (Annales des Mines, Tome XX, 1861). However, he did not discuss the problems raised by the use of regulator pins.
The present paper deals with the isochronal balance as influenced by the functioning of spiral springs equipped with regulator pins. To insure isochronal motion of a balance, the inner end of spiral regulator must act on the balance with a pure torque (a moment unaccompanied by any linear reactions), and this torque must be linearly proportional to the angular displacement of the balance. The design of terminals with regulator pins resolves itself to the problem of finding its shape so as to insure isochronal motion.
