Superbly adjusted Swiss watches of the period, and particularly those of Patek Philippe, were signed "EXTRA" or "SPECIAL".Guillaume balanceAnibal (acier au nickel pour balanciers), an alloy invented by Dr. Charles Edouard Guillaume, exhibits unusual properties, both in terms of thermal expansion and changes in elasticity. These properties are very different from those of two other famous alloys invented by Guillaume, Invar and Elinvar. At the end of the 1800's, Guillaume attempted to eliminate the so-called Middle Temperature Error caused by the fact that the change of rate in a timekeeper with a steel-brass bimetallic balance is aproximately a linear function of temperature, while the modifications caused by change in elasticity of a balance-spring are approximately a quadratic function. Thus, it equals zero at only two temperatures, causing secondary error. Countless attempts were made to eliminate Middle Temperature Error, usually by means of auxiliary compensation devices. In 1899, Guillaume noticed that steel with an addition of 44.4% nickel had a negative square coefficient of thermal expansion. This, combined withrass in bimetallic lamina, makes its expansion close to quadratic. Balances with bimetallic rims made of anibal and brass are usually called Guillaume balances, or, as their inventor called them, integral balances. When combined with special balance-springs, they exhibit remarkable temperature stability, on occasion not exceeding 1/50 second per day at 1oC.Engraving the movement twice with the serial number usually indicates that the watch was destined for an observatory trial.