Detailed Explanation and Analysis of Actual Effect on Timekeeping Accuracy of the Theory of Hairspring by Édouard Phillips

Abstract

  Édouard Phillips, a theoretician of 19th century, advocated the conditions of inner and outer end of Archimedes spiral, which is referred to as Conditions of Phillips. However, Phillips developed the expression for conditions using approximation, actual effect has not been adequately evaluated. We conduct holomorphic computation and it is realized that conditions of Phillips improve significantly not only isochronism of horizontal position but also that of vertical position.