Montjuïc

Pierre Méchain made his famous calculation error in determining the meter during his measurements in and around Barcelona, specifically here from the fortress on Montjuïc hill. While determining the exact latitude of this southern endpoint of the French meridian arc, he discovered discrepancies in his astronomical observations, which he attempted to conceal or correct, but which caused him considerable mental strain and led to an error in the final measurement. This error—a small deviation of about 0.2 millimeters per meter—still remains in the definition of the original meter.

The measurement on Montjuïc was a crucial part of the 18th-century expedition to define the meter as a standard of length based on a natural phenomenon. This was part of determining the length of the meridian arc between the northern point in Dunkirk (northern French coast) and the southern point near Barcelona, which was to form the basis for the new international standard of length.

Here's how the Montjuïc measurement fit into this process:

1. Objective of the expedition:
   French scientists Jean-Baptiste Delambre and Pierre Méchain were tasked with measuring the length of the meridian arc between Dunkirk (northern France) and the southern border with Spain. By determining the arc's length over a known angle of the globe (a latitude difference of one degree), they could calculate the length of a full meridian—this subsequently served as the basis for defining the meter.

2. Role of Montjuïc in Barcelona:
   Montjuïc, a hill in Barcelona, was used as the southern, finely marked reference point or "benchmark" for measuring the meridian arc. This point was the southernmost point of the geodesic line they wanted to measure. Méchain and his team used astronomical observations on Montjuïc to accurately determine the latitude, allowing them to precisely determine the distance between this spot and the northern reference point.

3. The measuring method:
   The idea was to determine the triangular network of points between north and south using angle measurements with theodolites and other measuring instruments, ultimately determining the distance between the two latitudes. By accurately knowing the geographical position of Montjuïc and taking measurements, the length of the arc between Montjuïc and the northern point could be calculated.

4. Effect on the meter definition:
   Once this length was determined, the meter was defined as one ten-millionth of the distance from the North Pole to the equator along the meridian through Paris—the line of which Montjuïc was the southernmost point. The Montjuïc measurements were therefore essential for establishing the total length of this meridian arc and thus determining the scale of the meter.

5. Problem with the measurement:
   Méchain encountered difficulties with astronomical observations at Montjuïc, which later led to a measurement error that slightly affected the meter's final value. This error caused controversy but was never fully corrected.

Pascal Brackman