427 
of Edinburgh, Session 1874 - 75 . 
a double mark when the divergence was more. Moreover, since 
perusing M. Lefort’s note, I have caused the same readers to 
examine the tenth thousand, and 1 exhibit the book itself with 
their pencil marks. On counting these, it is found that consider- 
ably over forty per cent, of Briggs’ final figures are in error. 
When we consider that Briggs used only fifteen decimals in his 
“ Tabula inventioni Logarithmorum inserviens,” we can hardly 
expect a smaller proportion of errors than this among his final 
figures; and the examination exhibits in a very strong light the 
scrupulous care bestowed by him upon the work. But M. Prony’s 
coadjutors of the second section carried their operations to nine- 
teen decimals — that is, to one hundred thousand times the exacti- 
tude aimed at by Briggs, and not one of his errors should have 
escaped detection. It becomes, then, quite a mystery how MM. 
Letellier et Gfuyetant should have allowed upwards of four thousand 
errors to escape their notice. 
To resume. Having accomplished this first part of their labour, 
the members of the second section computed 2° “ the logarithms 
from 10,000 to 200,000 by intervals of 200 to 14 decimals, and 
with four, five, and even six orders of differences. The number of 
decimals was successively augmented by two for each order; so 
that, for example, the sixth difference was written with 26 
decimals;” and this seems to have concluded their labours so far 
as the logarithmic table is concerned. The results were handed 
over to the third section. 
Again, leaving for a while the course of M. Lefort’s details con- 
cerning the preparation of the ruled sheets, I shall begin in 
earnest the computation of the final table. The logarithm of 
10,000, and the differences of the successive orders, are inscribed 
on the upper horizontal line of a sheet, as in the annexed example. 
Our business is to add the first difference to the accompanying 
logarithm ; to take the second difference from the first p^the third 
from the second, and so on ; and this has to be repeated 255 times, 
until we reach the number 10,200, whose logarithm, with its differ- 
ences, ought to agree with what has been prepared for the second 
sheet. There are then to be performed two hundred additions and 
one thousand subtractions of large numbers before the calculator 
of the third section arrive at a check on, or can know anything of, 
