Interplay of pendulum and the meridian based standard

As we have remarked several times, officially it seems that the meter was invented `out of nothing', apparently only stemming from the slogan ``ten million meters from the pole to the equator'' [41]. A pendulum had been considered as a possible candidate as unit of length, but it had been rejected to avoid a unit of length depending on a unit of time. However, in listing the necessary operations in order to realize the reform of measures, a unitary pendulum is taken into account, as a kind of secondary standard to reproduce the meter:

The operations that are necessary to carry out this work are the following: ...
4th To make some observations in latitude forty-fifth degree to verify the number of oscillations that a simple pendulum, which corresponds to the ten millionth part of the arc of a meridian, would accomplish within a day, in the vacuum, at sea level, at freezing point, so that, after having learned that number, this measure could be found again through the observations of the pendulum. In this way the advantages of the system that we have chosen are joined to the advantages that would be obtained by taking the length of the pendulum as a unit. It is possible to accomplish these observations before learning this ten millionth part. Actually, if the number of the oscillations of a pendulum having a determined length are known, it will be sufficient to learn the relation between this length and the ten millionth part to infer undoubtedly the investigated number.³⁵ (Ref. [2], p. 9)

Therefore, while in the first part of the report the one-second pendulum was ruled out, a one-meter pendulum³⁶ appears in the second part.

The fact that the meter pendulum had to be considered an important tool to carry out the entire project can be easily inferred from the response of the President of the National Assembly to a memory of Borda [42] on the metric system of weights and measures in 1792:

You took your theory from the nature: among all the determined lengths you chose the two unique lengths whose combined result was the most absolute, the measure of the pendulum and above all the measure of the meridian; and by so relating the first to the second with as much zeal as sagacity, the double comparison of time and Earth through a mutual confirmation, you will have the honor to have discovered this permanent unit for all the world, this beneficent truth that is going to become a new advantage to the nations and one of the most useful conquest of the equality. (Ref. [42], p. 9)

And, again, in the July 1793 proposal of decree, it is stated that

the academy has judged that its works were quite well advanced, and that the arc of meridian, as well as the length of the seconds pendulum, the weights of a cubic pied of distilled water, were known at this moment, both from previous observations as well as from those on which the members of the commission have been working, with the accuracy sufficient to the ordinary usages of the society and the commerce (Ref. [14], p. 4)

Therefore, while in the first quote of this section (Ref. [2], p. 9) the commission generically speaks of a ``a pendulum of a determined length'', it is here clear that the referred pendulum was the seconds pendulum, and not a pendulum based on a previous unit of length, like a one-toise pendulum. We see clearly the advantage of that choice. Since the seconds pendulum was quite well known, including the dependence of its period with latitude, once the oscillation time of the meter $t_m$ was known, the unitary length would have been easily determined as $u_m = l_{sp} t_m^2$, where $l_{sp}$ indicates the length of the seconds pendulum and $t_m$ is expressed in seconds. However, it was never stated that the seconds pendulum and one-meter pendulum are very close in length, though their closeness makes easier the intercalibration procedure.