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The Phillips Terminal Curve: Mathematical Isochronism in Breguet Overcoil Balance Springs

How curving the outer active coil inward ensures concentric spring breathing, removing lateral pivot friction against jewel holes.

By Gilles de Montfort, Horological Physicist October 10, 2026 • 9 min read
The Phillips Terminal Curve: Mathematical Isochronism in Breguet Overcoil Balance Springs

Eccentric Center of Gravity Shift in Flat Springs

Flat hairsprings expand eccentrically, shifting their center of mass and applying alternating lateral loads to balance staff pivots.

Phillips Mathematical Overcoil Curvature Rules

Ferdinand Phillips calculated that raising the outer coil and curving it to specific mathematical radii forces concentric expansion.

Period Stability across Changing Oscillatory Amplitudes

Concentric breathing ensures identical oscillation periods whether the watch runs at full 300-degree amplitude or low 200-degree wind.

⚠️ Technical & Safety Verification

The empirical methods outlined in this study reflect verified precision mechanical horology & balance spring metrology protocols and field measurements. Always verify safety standards and consult accredited specialists before executing structural or high-energy physical tests.

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