Baron Gaspard Clair François Marie Riche de Prony (22 July 1755 – 29 July 1839) was a French mathematician and engineer, who worked on hydraulics. He was born at Chamelet, Beaujolais, France and died in Asnières-sur-Seine, France.
Education and early works
He was Engineer-in-Chief of the École Nationale des Ponts et Chaussées.
The trigonometric and logarithmic tables of the cadastre
In 1791, de Prony embarked on the task of producing logarithmic and trigonometric tables for the French Cadastre. The effort was sanctioned by the French National Assembly, which, after the French Revolution wanted to bring uniformity to the multiple measurements and standards used throughout the nation. In particular, his tables were intended for precise land surveys, as part of a greater cadastre effort. The tables were vast, calculating logarithms from 1 to 200,000, with values calculated to between fourteen and twenty-nine decimal places, (which de Prony recognized was excessively precise).
Inspired by Adam Smith's Wealth of Nations, de Prony divided up the labor into three levels, bragging that he "could manufacture logarithms as easily as one manufactures pins."
The first level consisted of five or six high-ranking mathematicians with sophisticated analytical skills, including Adrien-Marie Legendre and Lazare Carnot. This group chose the analytical formulas most suited to evaluation by numerical methods, and specified the number of decimals and the numerical range the tables were to cover.
The second group of lesser mathematicians, seven or eight in number, were known as the "planners" and had previous experience as computers in the cadastre, mainly with experience having to do with practical mathematics. The planners combined analytical and computational skills, with this group calculating the pivotal values using the formulas provided and the sets of starting differences. They also prepared templates for the human computers, and the first worked row of calculations, as well as the instructions for the computers to carry the sequence to completion. Finally, this group was tasked with verifying all the calculations made by the human computers. Since recalculating every value would have nullified the use of the lowest level computers since their tasks would have been completely repeated, the planners used a method knows as "differencing," where they compared adjacent values in the tables, checking for any discrepancies.
The third group consisted of sixty to ninety human computers. These had no more than a rudimentary knowledge of arithmetic and carried out the most laborious and repetitive part of the process. Many were out-of-work hairdressers, because, with the guillotining of the aristocracy, the hairdressing trade, which had tended the elaborate hairstyles of the elite, was in recession.Due to their lack of experience, they only had to calculate simple problems of addition and subtraction. In addition, this group did not operate under a factory-like model, instead opting to work from home, sending their results and receiving their new tasks from the planners in a non-centralized manner. These calculators could produce an average of around 700 calculations a day.
Importance for mapping
The tables developed by de Prony's team were doubly important for French metric cartography. Firstly, at the time, sailors needed logarithms for math pertaining to spherical geometry, because this was needed to quickly and accurately position themselves to guarantee safe and efficient travel across the seas. However, the implementation of the new French Revolutionary metric system would make the old logarithmic tables would be obsolete, and French sailors would be unwilling to switch measurement systems since it would have rendered positional calculations significantly more difficult and less precise. Thus, de Prony, by making new logarithmic tables for the new metric system, would have facilitated the transition, enabling sailors to adopt the system. The second key element was that trigonometric values were needed for cadastral measures. Thus, for accurate mapping of the French territory and its subdivisions all the way down to the lowest levels of property ownership, de Prony needed to complete the trigonometric tables. These were both seen as crucial for Revolutionary pride considering the importance of naval prowess at the time and the need for administrative efficiency.