This is at the very heart of it all. It was Galileo Galilei who first noticed it, in a cathedral in Florence. He watched a chandelier swinging, propelled by the draughts, and saw that it seemed to be going much faster when the swings were wider. So he timed them, counting probably ten or twenty swings, and using his own pulse as a time reference. He saw that whatever the amplitude of swing, the time for each swing remained the same. This is called isochronism, derived from the Greek for “equal time.” In a watch, it applies to the balance spring, which is attached at its inner extremity to the axis of the balance and at its outer extremity to the cock. It provides the returning force that keeps the balance oscillating back and forth. This oscillation should ideally have the same frequency whatever the amplitude of the balance – the angle of rotation. The amplitude is greatest when the watch is fully wound. As the spring runs down, the amplitude decreases, and frequency of oscillation changes, because of the differing effects of friction, air resistance and gravity. So, in a watch, isochronism refers to constancy of balance frequency as the mainspring runs down.
A Breguet balance spring, image courtesy of Breguet
Isochronism can be improved by modifying the shape of the balance spring, and in particular the terminal coils, the inner and outer extremities. Breguet’s overcoil was an invention that improved isochronism, with the last coil raised and given a lower curvature.
A balance spring in silicium with Breguet overcoil, photo courtesy of Breguet
Below, a graph showing (very approximately) how the deviation of a wristwatch increases as the mainspring runs down:
