By the end of this video, I hope you will see the "IKEA metre" differently.
It has taken an amazing 7-year-long journey for 2 scientists
to travel through France and Spain to measure the Earth
in the middle of the French Revolution so as to define how long 1 metre should be.
This mission required three elements:
(1) Perserverance for a 7-year-long work,
(2) extremely precise refracting telescopes,
(3) secondary school trigonometry... plus a couple more things.
In spite of all of these efforts combined, it is a human error that accounts for the fact
that the metre is still too short by 0.2mm.
250,000.
That's how many units of measure were found in France in the 1790's
to measure weights and distances.
With that many units of measurement, conversions were almost impossible.
They would lead to fraud, injustice and obviously major difficulties for people to collaborate.
At that time, the marketplace was growing and promising -
and the state wouldn't mind collecting some more taxes.
It becomes necessary to establish a single unit of measurement
to allow everyone to communicate
and to establish an equal relationship between the consumers and the taxpayers.
In 1791, the Académie des Sciences decides to create a new measurement system:
the metric system.
The Academy know the approximate length they would like one metre to be
but they also want to define it using elements that remain unchanging anytime or anywhere
so that the measure would be the same from one village to the other
and from one year to the other.
At that time, the only unchanging thing they know is the Earth.
They decide that one metre will be equal to one 1/10,000th of a quarter of a meridian.
A meridian is an imaginary line that circles the Earth.
There are 360 meridians: one for each degree.
The Academy already have a rough idea of how long a meridian is
and they think that 1/10,000th of 1/4 of a meridian must be a nice enough length to base their measures on.
But with the ambition to create a universal unit of measurement comes the need for extreme precision.
They try to attain it by measuring a portion of a meridian - rounded to two decimal places,
a feat that the old measurement units could not match.
Of course, it's unrealistic to seek to measure an entire meridian:
it's a humongous task,
not to mention that there's some water in the way.
So they go and measure a portion of the meridian.
They estimate that this portion will be long enough between Dunkirk and Barcelona
The Académie des Sciences appoints Jean Delambre and Pierre Méchain, both renowed astronomers,
to roam about the roads of France and Spain, armed with amazingly precise astronomical instruments.
But how, in the 18th century and with no GPS, did they measure such a long distance with that much precision?
If there's one thing they do well at that time, it is measuring angles.
Sailors use many optical instruments, such as sextants, to navigate when at sea.
Adding to the command of angle measurement some simple notions of trigonometry,
the astronomers of the time got fascinating results.
The meridian that was to be measured is represented by this line.
The distance can't be measured from the ground as the Earth's irregularities would distort the results.
The amount of corrections needed would be unfathomable.
Instead the surveyors measure triangles that go across the meridian.
Each vertex needs to be a tall building that can be seen from afar; a bell tower, a telegraph...
Check out my video on optical telegraphs here!
The surveyors had to be able to see the other 2 vertices of the triangle.
At each vertex, the surveyors would measure angles:
the angles within the triangle + the angles between each station and the North line.
At first, Delambre would even get his assistant to start a fire at one of the vertices to see it extra well.
But during the Revolution, starting a fire at the top of a bell tower wasn't the best idea.
So they scraped that method pretty quickly.
Once they have measured the 90 triangles, they move on to measure the triangles' base.
That's one side of one triangle.
With the measurements of all the angles and one side,
it's easy to determine the length of the other two sides of the triangle
thanks to the law of sines.
We have all this info about the triangles that go across the meridian,
but not the length of the actual meridian.
In order to calculate this portion of the meridian,
we create an imaginary right triangle.
We know that the angle between the North line and the line perpendicular to the meridian is 90°.
Thanks to this angle, we can figure out the one between the imaginary line and the first station.
So we've deduced one angle thanks to the length of the triangle base + an angle.
Now we only need to apply the rules of trigonometry to calculate this portion of the meridian.
The calculations for the length of the meridian are then reproduced using every triangle along the way.
What portion of the meridian did the astronomers measure?
10%? 20 or 30%?
It's crucial to know in order to be able to extrapolate the findings to the entire meridian.
There are two last measures to make for this:
the latitudes of Dunkirk and Barcelona.
This calculation is again very simple:
they measure the angle between a faraway star and the vertical line.
Supposing that the star they based their measurements upon is very far away,
the Dunkirk-star line and the Barcelona-star are pretty much parallel to one another.
With the help of basic trigonometry rules, they deduced that the portion of the meridian they measured
is the difference between the 2 angles (Dunkirk-star and Barcelona-star).
Knowing the portion of the meridian they measured, it is easy enough to know 1/4 of a meridian
then divide that by 10,000 and thus end up with...
the metre.
So logically, 1/4 of a meridian should be exactly 10,000 km long.
But actually it is 10,002 km.
2 km of error equals 0.2 mm of error for 1 metre.
Obviously that's an incredibly precise measure for the time,
but with the instruments they had and the knowledge they possessed,
they could have had even more accurate measures.
Where does this 0.2 mm of error come from?
Error...exactly.
Find out about it in Part 2!