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Proceedings of the Royal Society 
ance for the system, had not the non-publication of the requisite 
canon prevented all progress in this direction. 
Notwithstanding many solicitations, and even the offer by 
the English Gfovernment to defray a share of the expense, the 
tables computed in the Bureau du Cadastre remain unpublished; 
and the fact of their existence remains a discouragement to other 
computers. 
Now, fifty years ago, having fallen upon a method of approxi- 
mating very rapidly to the roots of numerical equations, published 
in 1829 under the title, “Solution of Algebraic Equations of all 
Orders,” I applied it to the quinquisection of an arc, and thus 
obtained directly the sine of any proposed decimal division of the 
quadrant. After proceeding a short way in the construction of the 
canon by this method, I laid it aside, from the conviction that the 
labour could, at best, only produce a repetition of what had already 
been accomplished. 
Many years ago, after having felt for long the want of a table 
of logarithms more extensive than any existing, I designed a 
nine-place table up to one million ; and having carried the manu- 
script fifteen-place table up to 300 000, laid it before this Society, 
whose Council did me the exceedingly great favour of presenting to 
Government a memorial soliciting aid in the completion and publi- 
cation. 
One of our scientific periodicals, in noticing this memorial, 
supplied to Government a most potent reason for not acceding to 
the request, in this, that the labours of Prony in the Bureau du 
Cadastre had already anticipated and surpassed all that can be 
done in future in this department of calculation. 
Forced thus into a critical examination of the Cadastre Tables, 
so far as that could be accomplished by help of published docu- 
ments, I arrived at most unexpected conclusions. 
In the first place, the fundamental table, that of the Logarithms 
of the Prime Numbers, as given by Legendre in his work on 
Elliptic Functions, was found to be correct up to 2000; that is, as far 
as Abraham Sharp and other ancient computers had gone. But of 
the primes between 2000 and 10 000 computed in the Bureau, only 
five have their logarithms correctly given, while almost all of the 
other logarthims err on one side. 
