The initiator of these tables was Marquis du Prony (known form Signal
Processing) and not Legendre and triggered by the French revolution. It
was a 3-level hierarchy, were at the highest level there would be
mathematicians who would provide the equations (and Legendre indeed was
hired by du Prony). At the second level there would be analysts that would
transform the equations in a sequence of very simple operations (not unlike
computer programs).
At the lowest level there would be a massive number of low-skilled people
who know only to compute additions and/or differences.
Babbage's idea of doing "calculation by steam" was highly influenced by
Prony's work.
The above information is from the collection of papers collected by
Babbage's son (Henry) which has been republished by the Babbage institute.
Andrei Heilper