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# Delambre-Mechain Geodetic Survey Essay

## Introduction

Delambre-Mechain geodetic survey was one of the most important surveys that defined meter as a standard unit of measurements. According to Wise (1995), that path towards developing this unit measurement by the two scientists was not only tedious, but also marred by political arrests and errors in the units of the measurements that were used. It is important to appreciate the fact that this survey was done at a time when a variety of units were used to measure distance. For instance, while a section of the mathematicians preferred the use of degrees as the standard measurement, others considered toises while another group considered feet to be more appropriate. This condition was worsened by the fact that these units were not universally accepted as they had massive differences.

For instance, the use of feet was considered unreliable because of regional differences. A unit toise was an equivalent of 6.39 English feet or 6 Paris feet. This alone demonstrates how inaccurate the unit of feet was at this time. A distance of one foot in English units would not be equivalent to a distance of one foot in Paris Units. The work of Delambre and Mechian was to develop a unit that would be universally acceptable and more accurate in measuring distance. This essay is focused on analyzing Delambre-Mechain geodetic survey which started in 1792 and was finally published in 1810.

## Delambre-Mechain Geodetic Survey

The geodetic survey by Delambre and Mechian, which begun in 1792, is one of modern scientific surveys whose results have defined the current units of measurements. It would be important to understand the definition of a geodetic survey in order to bring to focus activities that the two scientists were involved in during this process. Alde (2002, 36) defines geodetic survey as, “The scientific discipline of surveying the earth with regards to its shape and size, which include mapping the earth’s gravitational field, tides and the movement of the earth’s crust among others.” The emphasis of this definition is on the study of the earth with regard to its size and shape.

This is what the two scientists were involved in for a period of 20 years, although Mechain did not live long enough to witness the completion of their survey. Mechain has been described by many who studied his work as a meticulous astronomer who was keen on precision and accuracy. He had gained fame for his keen eyes when conducting measurements. This was one of the main reasons why he was assigned to this task. Delambre on the other hand was a historian who had transformed to become a renowned mathematician in the French empire. He had won many prizes due to his ability to determine the size of different planets, especially Jupiter. The two were considered appropriate to conduct this geodetic survey that covered an expansive area.

This geodetic survey was part of French revolution which many considered was a way of ushering in modernity. The history of this geodetic survey can be traced back to 1788 when the French Academy of Sciences, under instructions from Talleyrand, decided to develop a universal decimal measurement system based on invariable natural base to be used in place of the diverse measurements that were common in the entire Europe. The academy was concerned of the inconsistency of the measurements that were in use at that time, and believed that developing a new system based on invariable natural base would be the solution to the existing problem. Meter, a unit that was supposed to be based on natural invariable base, was proposed to be a tenth-millionth of the distance between the Equator and the terrestrial pole (Ariel & Berger, 2006).

The geodetic survey was therefore, a complex process that was supposed to measure this distance. In 1790, Assemblée nationale approved this project and awarded it enough funds that would help in its successful completion. The French Academy of Sciences was tasked with finding experts who will be able to conduct this geodetic survey. In 1792, Delambre and Mechain were finally appointed to undertake the project after a long and competitive process. The academy believed that a combination of the two skills would be vital in coming up with accurate measurements that would be universally acceptable.

Delambre and Mechain were tasked with a project that would survey the Meridian arc that passed through Dunkirk and Barcelona in Spain. They started their work June 25, 1792, soon after their appointment was approved by the academy and government officials. The two split their work into two in order to shorten the duration of the project. Mechain was assigned to cover a distance of 170,000 toises that was running from Rodez to Barcelona, while Delambre was assigned 380,000 toises from Dunkirk to Rodez (Wise, 1995). This way, the two would be able to complete the task within a shorter period than taking the same route at the same time.

Delambre was assigned a distance that was twice what Mechain would cover. This was so because the distance that was to be covered by Mechain had never been explored before, while the distance that Delambre was covering had been explored by previous scientists. Moreover, Mechain was expected to meet a lot of political challenges because part of the region he was to cover was under Spain, a country that had strained relationship with France. When they finally started their assignments, both believed that the Journey to be taken by Mechain through arduous country would be more eventful, and it was expected to take a longer period.

Delambre took his journey heading north, while Mechain headed south. However, Delambre was the first of the two scientists to run into trouble within his own country. His work was seriously affected by militia that associated him with monarch. They associated him with the monarch’s leadership that the society was trying to eliminate. He was imprisoned in various camps that were under tight security of the militiamen. He had to convince the militia that his work was part of the revolution. According to Alde (2002), the explanation given by Delambre that his mission was focused on revolutionizing unit of measurements were pleasing to the militia.

In fact he informed them that the monarch was forced to sign the credentials against his wish. He was released from the militia’s prison in the late 1792. He journeyed further north. However, he was not lucky once again because he was abducted at Saint-Denis by a mob that believed he was an aristocrat. The revolutionists hated aristocrats as they associated them with the problems they were experiencing. It would be important to be analytical to understand the circumstances under which Delambre was arrested in the two occasions.

As mentioned before, French revolution was taking shape during this time, and the fact that he had some relations with the monarch was not acceptable before many of the groups he met on his journey. In both occasions, he had to prove that his mission was meant to revolutionize the field of Mathematics and sciences in general. These arrests slowed the pace of his measurements towards the north. However, he was released and continued with his journey towards the north. Other issues also affected Delambre’s geodetic survey towards the north.

This long journey was characterized by unprecedented ambushes from criminals and other groups of people who were suspicious of his mission. In his report, Delambre noted that there were instances where he would be arrested by criminal gangs who wanted money from him, mistaking him for a rich merchant. In other cases, there were attempts by some individuals to take away his instruments mistaking them for new sophisticate weapons. In all these cases, he had to use the power of communication to convince these people that he meant no harm, and that his journey was a pure scientific survey meant to benefit his country and the world at large.

Some understood and appreciated his work, while others were adamant and he had to escape from their camps. Konvitz (1987) says that these are some of the important factors that should be factored in when analyzing the geodetic study conducted by Mechain. Although many people praised him a lot for the efficiency in his survey, the commissioned never questioned the possibility that he could also have some errors. Given that he was not a perfectionist, he was able to make some guesses to estimate some of the distances he could not cover because of volatility, and because of his level of intelligence, his guesses were near accurate. Alde (2002) has also argued that the massive success that Delambre had on his survey to the north could be attributed to the fact that there were other previous surveys that had been conducted in this region.

It would be easy to determine the patterns taken in these previous research, determine the level of error that they could have been associated with, and come up with a near accurate data without having to cover every distance of the of the journey. However, these arguments have been refuted by Wise (1995), who says that although some of the modern researches have faulted a number of issues with the survey done by the two scientists, their findings were near accurate and formed the basis of the standard meter that is in use to date. Their error could easily be attributed to the poor instruments they had to use, and the harsh environment they were subjected to during the process of conducting the survey.

On his journey to the south, Mechain met numerous hurdles as he measured the distance that had been assigned to him. After covering about a third of his distance, he was arrested at Essone, by a group that believed that he was engaged in activities that were meant to give more power to the monarch. His weapons were mistaken to be some weapons meant to fight revolutionists. It took him some time to cross over to Spain. When he entered Spain, he was further frustrated by the fact that France and Spain was at war. They detained him for several months. He was finally released and he continued with his exploration.

When he reached Barcelona, he conducted a measurement of Barcelona’s latitude and realized that he had an error of 3 degrees because of refraction from the atmosphere (Ariel & Berger, 2006). He realized his error in 1794 when he had covered a greater part of his journey. Upon realizing this error, he decided to extend his journey to Balearic Islands instead of retaking the measurements once again. The increase in distance was supposed to conceal the error that he made all the way from Rodez. This meant that he had to eliminate Barcelona from his grid completely. According to Wise (1995), Mechain was a perfectionist, and could not withstand the fact that he had errors in his measurements that jeopardized his results.

Some scientists have been focused in analyzing some of the issues that made such a great astronomer with a keen eye on precision to make an error in measurement all the way from Rodez to Barcelona without knowing of it. Some have associated these misfortunes to his preoccupation during the journey. He was supposed to cover a shorter distance than what was assigned to Delambre, but it had numerous challenges. This could have preoccupied his mind so much that he never realized that refraction effect of the atmosphere could affect the accuracy of his measurements.

He was finally released from Spain to sail further to Balearic Islands to continue with his measurements. However, he received unfortunate news that the Committee of Public Safety had already cancelled their meridian project (Hahn, 2005). This was in the late 1794. He fled to Genoa to seek refuge. The committee restated the meridian project, and he was recalled to Paris, but fearing for his life, he fled to Marseille. All these events had serious negative consequences on the measurements that Mechain was making. His instruments were getting affected as time went by, and these further jeopardized his accuracy in this geodetic survey. In 1795, he decided to continue with the survey to the new location he had set, but he was not successful enough because of a number of issues that affected his survey. He arrived with his data in Paris in the late 1802, but the issue of accuracy of his data made him conceal them from anyone.

In the meantime, Delambre had completed his survey and his report was ready for publishing. In fact, he had shared his data with Mechain, who did not share his findings with him. He believed that his findings were erroneous, hence not worth sharing with others. According to Alde (2002), Mechain was suffering from a perfectionist syndrome. These reports have indicated that the measurements that were made during the first geodetic survey to the south were not far from the truth. They had level of accuracy that could be considered worth the survey given the hardships that Mechain underwent during the process of collecting data.

Mechain was very much concerned of his data that he went to Napoleon to ask for permission to redo the work. He was granted his request and in 1803, he set forth on another geodetic survey to the south. After completing part of his work, Mechain contracted yellow fever, and succumbed to it at Castellon de la Plana (Ariel & Berger, 2006). The responsibility was left to Delambre who was assigned the task by the committee responsible for the project. The process of measuring arc of meridian was characterized by a lot of complication because of the instruments used, and environmental forces. The process of converting the degrees to the newly developed centesimal units was not only complex but also time consuming. This was further complicated by the need to have high degree of precision and accuracy in the measurements.

He had to ensure that his data was converted to be compatible with the new tables of logarithms and trigonometric functions to enhance further analysis. Another factor that Delambre had to observe was time. The period within which, the survey was to take had passed, and he was now working on an extra time. His partner in this survey had died, and this meant that he had to do all the analysis and compilation of the report alone. A year later after taking over the works of Mechain, Delambre was able to complete the task and hand over the findings- Base du système Métrique- to the emperor. His findings were handed over to foreign scientists and a commission of French for further development. The foreign scientists and government committees used these findings to determine the unit of length, which has become the standard meter (Ariel & Berger, 2006).

This geodetic survey, also known as math history, defined some of the current measurements that have been considered very reliable when measuring the distance. It took the two scientists over 20 years to complete the survey, but their findings were approved by foreign scientists and a French commission that studied the report when it was finally delivered to them by the emperor. An analysis was also conducted on the results that were obtained from Mechain in his initial survey, and according to Wise (1995) there was a high degree of accuracy in the data, especially in his initial data. The discrepancy that was witnessed came after Mechain had been subjected to a series of arrests and other interference by the militia. Given the nature of the instruments they used, modern scientists have praised the two, and blamed Mechain for his perfectionist character.

## Conclusion

The geodetic survey conducted by Delambre and Mechain from 1790 to 1810 was a tedious and complex process that was met by numerous challenges. The mathematician and the astronomer were expected to conduct geodetic survey that would help develop universal mathematical units to replace the units that were in use during that time. The two scientists were expected to measure the distance between the Equator and the terrestrial pole. This meant that they had to determine the distance between Dunkirk and Barcelona in Spain. This was a complex process because they had to journey into kingdoms that were not friendly to their own country. Their survey was made complex by the fact that they had to conduct their measurements using the old units of degrees, and concert this into units compatible with the new tables of logarithms and trigonometric functions to enhance further analysis. However, their research was a success, and today we enjoy their fruits of hard labor, by using standard meter as a unit measure of distance.

## References

Alde, K. (2002). The Measure of All Things: The Seven-Year Odyssey and Hidden Error That Transformed the World. New York: Simon and Schuster. Web.

Ariel, A., & Berger, N. A. (2006). Plotting the globe: Stories of meridians, parallels, and the international date line. Westport: Cengage. Web.

Hahn, R. (2005). Pierre Simon Laplace 1749-1827: A determined scientist. Cambridge: Harvard University Press. Web.

Konvitz, J. W. (1987). Cartography in France, 1660-1848: Science, engineering, and statecraft. Chicago: University of Chicago Press. Web.

Wise, M. N. (1995). The values of precision. Princeton: Princeton University Press. Web.

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