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The paper analyzes the effects of pendulum temperature dilatation on the timepiece running and accounts for the basic mathematical principles that neutralization of these detrimental effects are based upon. Both preliminary and detailed calculations are presented, as well as some design solutions leading to technically acceptable pendulum temperature dilatation. Explanation is given for the design of bimetal gridiron pendulum, wood pendulum with a lead weight, mercury pendulum, and pendulum with an Invar alloy rod.

Mathematical Principles and Optimal Design Solutions to Compensation for the Pendulum Temperature Dilatation