It is by no means only the introduction of arbitrary subdivisions (mere arithmetical adjustment) that removes the “natural” unit of length from nature. No, the Earth itself refuses to sanction the aspirations of the founders of the metric system.
Since the 17th century it has been known that the length of a pendulum beating seconds varies with its location on the Earth; specifically, with the latitude. This is because the constant of proportionality between time and the square root of length depends on the acceleration of gravity g—the rate at which the speed of a freely falling body increases—and g varies with latitude. Hence if the pendulum is to deliver a unit of length, the arbitrary choice of the second of time must be supplemented by something still less justifiable: the selection of a place on the Earth to put the pendulum.
The place chosen ought to be acceptable to everyone, for even if a measure cannot be truly natural, it must aim to become universal, and this requires rising above local prejudice. One would not choose some existing measure and seek to impose it on all peoples; no more should the location of the pendulum be decided on parochial grounds. Since it is with the latitude that g is observed to vary, a point on the unique equator suggests itself. La Condamine, “the apostle of the universal Metric System,” favors Quito, in Ecuador, where (among other places) he has swung pendulums; so there, Favre tells, “he has a bronze rule cast, which will preserve the length of the pendulum at that place, has it sealed in marble, and upon this marble, destined to be placed on the outer wall of the Jesuits’ church, ‘the finest of the town,’ he has these words engraved, traced by his own hand:
‘Penduli simplicis Æquinoctialis, unius Minuti Secundi temporis medii, in altitudine soli Quitensis, Archetypus
[here interposes the bronze rule]
(Mensuræ Naturalis Exemplar, utinam et Universalis!)'”
“Of an Equinoctial simple Pendulum, of one Second of a Minute of mean time, at the altitude of the soil of Quito, Archetype
[here interposes the bronze rule]
(Exemplar of a Natural Measure, would that it were also Universal!)”
There is a great deal more Latin on the plaque, the noble whole of which is shown in the photograph that forms Favre’s frontispiece. From the part of the inscription given here, it may be suspected that altitude affects g, and one naturally wonders whether the quantity is independent of longitude. Truth to tell, La Condamine himself doubted that it was. Anyway, not everyone cared for the equator; some thought the pendulum belonged on the 45th parallel, halfway to the pole—the north 45th, of course, situated “in the midst of countries where the Sciences flourish,” and happily chancing to pass through France (not England).
What of the other candidate for the unit, a fraction of the circumference of the spherical Earth? Not so fast: the Earth is not quite spherical, and the sign of this is precisely that g varies with the latitude. In fact it was the variation of the pendulum that led to the discovery that the Earth is flattened at the poles, forming not a sphere but an oblate spheroid—roundish but not truly round. For the pendulum beating seconds grows longer as you move from the equator towards a pole; that is, g increases, which means that you are drawing closer to the center of mass of the Earth, which is very near its geometrical center; hence the upper latitudes must be pressed in towards the center.
With the perfect sphericity of the Earth vanishes the ideal great circle from which to derive a unit of length. Circumferences differ, so if one is to be used, it must be chosen. Which shall it be? The equator? A meridian of longitude? Which meridian? The Commission of the Academy of Sciences “prefers the length of the Meridian to that of the Equator … among other reasons, because it can be said that each people belongs to one of the Earth’s meridians, but only a part lies under the Equator. A reason [Favre observes] which justifies the choice made only if the meridians are equal.” And the Commission admits that it doesn’t know that to be the case.
Well, in the event a fraction of a meridian, rather than the length of a pendulum, was chosen as the basic measure—contrary to the desire of Thomas Jefferson, among others. Against the pendulum it was argued that one should not appeal to considerations of time and weight, which are irrelevant to the measure of length. But the real reason seems to have been the opportunity of gaining glory for the Academy, by measuring the Earth more accurately than had been done before, with the aid of a superior angle-measuring instrument constructed by an academician, one Borda. And what meridian was measured? The one through Dunkirk and Barcelona, to start with—an arc of it, that is; but to deduce its length from that of the arc required taking account of the flattening of the Earth. “The flattening they had hoped to derive from the measurement itself; but the result having appeared doubtful, they will prefer to derive it from the comparison of the Dunkirk-Barcelona arc to the one ‘of Peru,’ necessarily taken along another meridian! If then all the meridians are not equal, the one from which the meter is deduced is quite indeterminate: the only way, after all, of being universal!”
So the measurements were taken and the mathematics done. And “scarcely had the true and definitive meter been adopted than Delambre, going over the calculations, established that it would be still truer and more worthy of being definitive if it were 1/30 of a ligne [i.e., some 75 millionths of a meter] longer!”