424 Proceedings of the Royal Society 
of those already printed, . . . . ” and I have now to thank, very 
cordially, the author of the note for having mentioned the labours 
of M. Lefort, and so put me in the way of obtaining very startling 
and very important information in regard to Prony’s Tables. 
Concerning the errors in Ylacq, the author of the note says, 
“Almost all the errors, found by Mr Sang by means of this table 
are among those there given by Lefort,” and deduces from this fact, 
in accordance with the well-established axiom that the part is 
greater than the whole — the futility of this or of any other new 
table. Not having yet mastered the first principles of this system 
of logic, I shall not venture to discuss any of the opinions of its 
inventor, and shall only look at the wisdom of his conclusion. 
The studious investigator living in Iceland, in Terra del Fuego, 
or even here in Edinburgh, where logarithms had their birth, 
needing an extensive table of logarithms, must apply to his book- 
seller for Ylacq ; the book has been “ out of print ” for two hun- 
dred years; if found at all, its price is antiquaries’ price. Having 
succeeded, his next business is to procure a copy of the volume of 
the “ Annales de l’Observatoire.” I myself have tried the libraries 
here in vain, so that “without much expenditure of trouble,” I 
have not made my copy of Ylacq “ all but free from error, — much 
more accurate than any new table could possibly be.” Even after 
I shall have effected the correction by help of Lefort’s list, there 
will remain a great uncertainty, arising from the fact that two 
copies of Vlacq may not be in accordance with each other. To 
understand this, we may turn to the Errata printed on page 64 of 
Taylor’s Tables. There we find, among others, the following 
remarks : — 
“In about 100 copies; in about 120 copies; doubtful whether 
a few copies are erroneous or not ; in about half the impression ; 
only in one copy ; and so on.” 
The movable types had been drawn out by the inking dabber, 
and erroneously replaced by the pressman. But in this case there 
is another uncertainty. Complaints were made of pirated editions, 
fac simile of the original Ylacq. 
The search for the list of errors mentioned in the above note, 
led me to find two papers by M. F. Lefort. The first of these, 
coutained in the “ Comptes Rendus,” tome xliv. page 1097, was 
