Practical method for thermal compensation of long-period compound pendulum

The methods for compensation of the clock pendulum thermal dilatation presented in literature are based on combined analytical and experimental procedures. As a rule, the mass center position is always compensated analytically with sufficiently large factor of safety, while the refinements are obtained experimentally. An analytical method has been studied for the pendulum thermal compensation which considers not only the mass center but also the pendulum mass moments of inertia of the first and the second order. Fast and efficient mathematical method as well as the practical constructive solutions are presented which allow the technically acceptable thermal compensation of the long period compound pendulum. The proposed calculation procedures are iterative and fast converging, which make them suitable not only for the design of vintage "wood rod - lead bob" pendulums, but also for the modern pendulums which feature rods thermally compensated by invar alloy. Moreover, the proposed principles and methods are useful in all scientific measurements where the effect of thermal noise must be minimized or even eliminated.