Establishing the length of the meter

Reading the Rapport sur le choix d'une unité de mesure [2] we have been surprised not to find the expected value for the new unit of length. All looks as its length was unknown and it had to be determined by the campaign of measurements outlined in the document. The seconds pendulum has the same omission. But we imagine that the members of the National Assembly, to which the document had to be finally read, were curious to know the rough length of the unit they were going to decree. Instead, the commission provides only an estimate of the size of the unit that would result from the ideal, 7.4 million kilometer long pendulum that beats the day. Therefore, it seems reasonable to believe that the length of the seconds pendulum and of the fourth-millionth part of the meridian were already known rather well, and that there was no need to specify their value. This was our first guess. Actually, the question looks a bit more subtle at a closer look: though those values were well known to scientists, the académiciens kept them `secret' or, at least, they were reluctant to provide an official best estimate of the new unit of length to the politicians [10]. It seems to us that the reason of this reserve is closely related to the preference of the meridian over the pendulum. But let us proceed with order.

The seconds pendulum has been reviewed in section 3. Comparing Cassini's and Newton's value, we can safely take an approximated value of the seconds pendulum at $45^o$ of 440.4 lignes (99.35cm). Let us now see how well the `meter' was known at the time of the March 1791 report [2]. We shall then go through the recommendations of the commission for a more accurate determination of the unit of length and through the resulting meridian expedition.