^8- Mr Babbage on Machinery for calculating 
8. Tbe logarithm of the ratios of the sines to their arcs of the 
first 50QO of the lOOjOOOths of the quadrant calculated to four- 
teen decimals with three orders of differences. 
4l The logarithmic tangents corresponding to the logarithmic 
sines calculated to the same extent. 
5. The logarithms of the ratios of the tangents to their arcs 
calculated in the same manner as the logarithms of the ratios of 
the sines to their arcs. 
6. The logarithms of numbers from 1 to 10,000 calculated to 
nineteen decimals. 
7. The logarithms of all numbers from 10,000 to 200,000 
calculated to fourteen figures with five orders of differences. 
Such are the tables which have been calculated, occupying in 
their present state seventeen large folio volumes. It will be ob- 
served, that the trigonometrical tables are adapted to the decimal 
system,, which has not been generally adopted even by the 
French, and which has not been at all employed in this country. 
But, notwithstanding this objection, such was the opinion enter- 
tained of their value, that a distinguished member of the English 
Board of Longitude, was not long since commissioned by our 
Government to make a proposal to the Board of Longitude of 
France^ to print an abridgment of these tables at the joint ex- 
pence of the two countries ; and L. 5000 were named as the sum 
our Government was willing to advance for this purpose. It is 
gratifying to record this disinterested offer, so far above those 
little jealousies which frequently interfere between nations long 
rivals, and manifesting so sincere a desire to render useful to 
mankind the best materials of science in whatever country they 
might be produced. Of the reasons why this proposal was de- 
clined by our neighbours, I am at present uninformed ; but, 
from a personal acquaintance with many of the distinguished 
foreigners to whom it was referred, I am convinced that it was 
received with the same good feelings as those which dictated it. 
I will now endeavour shortly to state the manner in which 
this enormous mass of computation was executed ; one table 
of which (that of the. logarithms of numbers), must contain 
about eight millions of figures. 
The calculators were divided into three sections. The first 
section comprised five or six mathematicians of the highest me” 
