The first original definition of the metre, presented by the French Academy of Sciences in 1795 is:

The length of the metre is one ten-millionth of the Earth quadrant, the distance from the North Pole to the Equator, measured along a meridian through Paris.

Roughly speaking, this definition is equivalent to the following one:

The length of the metre is 1/40,000,000'th of the circumference of the Earth.

It makes sense sense to define the length of the metre in terms of the entire circumference of the Earth, not its one-fourth, with the deiniftion only featuring a "pure" power of 10 like 100,000,000.

Why was the original definition for the metre chosen? If the original definition is just the paraphrased second definition, the question becomes: where does the '4' come from?

  • $\begingroup$ Is this question like why a ¼ slice of pie is a ½π? $\endgroup$ Commented Oct 29, 2021 at 12:56

1 Answer 1

  1. Strictly speaking the first and second definition are not equivalent, but there was no mean at that time to measure the whole meridian directly, so they assumed central symmetry, in which case the distance from the N pole to the equator along the Paris meridian would be 1/4 of the whole meridian. (To be sure, the distance from the N pole to the equator also cannot be measured directly, so they measured some arcs of it, and used a mathematical model for the shape of the Earth. Besides many precise measurements in Europe, they organized two major expeditions: one to Lapland another to S America).

  2. The reason why they took the length to be 40,000 kilometers is the following. French revolutionary government also introduced decimal measure of angles and time. With these measures the right angle was 100 degrees (round decimal number and somewhat close to the usual 90 degrees). Then the whole circumference was 400 decimal degrees. Each decimal degree was divided into 100 decimal minutes. This is how they arrived to 40,000 decimal minutes, and decided to define kilometer as a decimal minute. So it is similar to the (nautical) mile which is defined as 1 usual minute.

They introduced similar measure of time, with day+night =20 decimal hours (close to 24), and each decimal hour=100 decimal time-minutes.

Then decimal measures for angles and time were abolished (under Napoleon), while meters and kilometers remain. You can still see sometimes in museums (and on e-bay) clocks and angle measuring instruments graduated in these decimal hours, degrees and minutes.

  • $\begingroup$ Scientific calculators still have three modes for angular measure: degrees, radians, and grads. 100 grads = 90 degrees. $\endgroup$ Commented Oct 30, 2021 at 11:42

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