Scientific methods – degree measuring was based on astronomy and triangulation
The mission of the expedition had two parts. They had to use astronomical methods to measure the difference latitude between two points on the same longitude. In addition, a chain of survey triangulations had to be formed between these points to calculate the distance between them.
The expedition began by creating a triangulation network between Tornio and Pello.
They knew beforehand that the distance between the sites was about one degree and that they were on roughly the same north-south line, i.e. the same meridian arc.
Once the triangulation was complete, the expedition took astronomical measurements at the ends of the chain to determine the exact latitude difference between the points.
Triangulation was an established method of surveying
Triangulation was developed in the Netherlands in the 16th century. By the 18th century, it was already established as a working method for surveyors and cartographers.
The principle of triangulation is simple. Once the length of one side of one triangle in a chain of triangles (the baseline) is known, the rest can be calculated trigonometrically by measuring the angles between the sides.
A quadrant was used to measure the angles. With the help of the quadrant, the height difference between the measurement points could also be taken into account.
The original plan of the expedition was to set up a chain of survey triangulations on the islands of the coast of the Bay of Bothnia. The islands proved to be too low right from the start of the expedition.
Anders Celsius suggested that they wait for winter and measure the approximately 110-kilometre long degree directly on the ice of the Bay of Bothnia without a triangle network. Locals’ knowledge of sea ice conditions made the expedition reject the proposal.
They also considered clearing a uniform line of sight to the forest near the coast, but it was found to be impossible.
Maupertuis had been on a reconnaissance mission around the Torne and had found that the hills near the river could serve as suitable measurement points for the triangulation network.
Johan Wegelius, the schoolmaster and curate from Tornio, was able to tell the expedition that Tornio and Pello were located on the same meridian, i.e. longitude. This information influenced the choice of the measurement area.
In addition, the Torne provided easy access and travel from one measurement point to another. It also provided a flat platform for measuring the baseline.
Angular measurements from one marker to another
The markers of the triangulation network were built in the shape of a cone from large peeled tree trunks.
The light-coloured cones were clearly visible for tens of kilometres. Visibility from one measurement point to the next was ensured by cutting down a large amount of trees from the top of the hills.
The exact locations of the markers were marked by carving marks into the rocks or by hammering stakes into the ground. In addition, the distance from the centre of the marker to nearby trees and rocks was measured. All this was carefully recorded in the observation journal.
The actual angular measurements were also carefully taken. The observer pointed the instrument, the quadrant, at the marker on the neighbouring hill and reported the bearing reading to the recorder. The readings were carefully recorded in the observation journal. The measurements were repeated several times to avoid errors.
In addition to their own servants, the academics were assisted by twenty local soldiers from the Västerbotten Regiment’s Tornio company.
Their help was invaluable so that the expedition members could set up the markers and clear the lines of sight from one hill to another. In addition, the soldiers knew the area and were able to move through the forests without getting too lost.
The baseline measurement was an essential part of the triangulation
Triangulation is based on the fact that one of the lines of the measurement network is physically measured in the terrain. Once the length of one side of a triangle is known, the rest can be calculated trigonometrically by measuring the angles between the sides.
The side of the triangle measured in terrain is called the baseline.
Alexis Clairaut and Charles Camus plotted the position of the baseline in August. Measurements on the ice of the Torne were made over a period of just over a week in December. The frost was severe and there was a lot of snow on the river.
The northern end of the baseline was a little north of the mouth of the Tengeliönjoki River on the eastern bank of the Torne. The southern end was about 14 kilometres further south, on the west side of the Torne, at the mouth of the Armasjoki River, in the village of Niemis.
Erik Brunnius the Younger (1706–1783), who was the vicar of Ylitornio, made eight straight spruce poles and supporting posts for them for the expedition. The French themselves finished the poles to exactly the right dimensions.
The length of one pole was five toises, or fathoms. The toise is the French unit of measurement in use at the time, which is 1.949 metres in modern measurements.
The rods were therefore approximately 10 metres long. They were measured using an iron toise measure imported from France.
The measure was kept in a room whose temperature was fixed to correspond to the spring temperature of Paris. This was done to eliminate the effect of cold temperatures on the length of the measure, as the iron gauge could become shorter in freezing temperatures.
With a baseline of about 14.4 kilometres measured with 9.745-metre-long rods, the rods could be placed one after the other 1,478 times in a row.
The baseline measurement had to be as accurate as possible. A small error could add up to a significant error in the triangulation calculations. Therefore, the baseline was measured by two groups. Their measurements differed by about four inches, or less than 11 centimetres.
Degree measuring to find out the shape of the Earth
Latitude indicates the location on a north-south longitude on a different meridian. The Equator is zero degrees, while the South and North Pole are 90. The degree of position X is therefore the angle between the rays from the centre of the Earth to the Equator and position X.
The degree latitude was determined by using the stars.
In Pello and Tornio, the height of the same star was measured relative to the highest point in the sky, the zenith. The star chosen was as close as possible to the zenith of the starry sky. Measuring a star closer to the horizon would have been less accurate due to the refraction of light.
As their fixed star, the expedition chose the δ, delta, Draconis. By comparing the measurements from different locations, the difference in degree between the sites could be determined.
If the Earth were perfectly round, the meridian arc of one degree would have the same length at every point on the meridian.
The Maupertuis expedition had the length of a degree of the meridian arc, 57,060 toises, or fathoms, which was measured in northern France. It had been measured in separate measurements by the astronomers and surveyors Jean Picard (1620–1682) and Jacques Cassini (1677–1756).
If the length of a degree measured at the Arctic Circle were longer or shorter, it would prove that the Earth is not perfectly round but either elongated or flattened at the poles.
If the Earth were elongated at the poles, the length of the degree would be shorter closer to the poles. If it were flattened – as we now know it to be – the arc of one degree would lengthen as it moved towards the poles.