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quickly; you look up the log of each of your two numbers, added them together, then

look up the total; bingo! Teams of people working laboriously by hand had succeeded
in filling 17 really huge hand-written books of log tables with their calculations, but
errors could never be eradicated. These hand-made tables went up to 6 digits, i.e.
200,000. They were still in use by the French army when the Germans invaded in
1940!

This inspired Babbage to design his first computer, the Difference Engine, which could
produce log tables free of any error. Babbage reckoned he could design one to do

calculations on numbers up to 30 digits long and print them out. His weren’t the first
th
calculating machines; in the 17 century, the mathematicians Pascal and Leibnitz
worked on their design and construction, but produced nothing workable.

By part-building his Difference Engine, Babbage created a working mechanical
calculator with towers of precision cog-wheels turned by a single handle. He had to
overcame considerable conceptual and technical difficulties and only built about one-

seventh of his whole design. The same would be true of his later, much more
ambitious, Analytical Engine, which he believed superceded the first.

Ada’s mother, Lady Byron, who was interested in maths, wrote an account of her and
Ada’s visit to see the Difference Engine. As one of the marvels of the age, it made a
great impression on her: “We both went to see the thinking machine (for such it
rd
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seems) last Monday. It raised several Nos. to the 2 and 3 powers, and extracted
the roots of a quadratic equation. I had but faint glimpses of the principles by which it
worked. Babbage said it had given him notions with respect to general laws which
were never before presented to his mind. For instance, the machine would go on
counting regularly, 1,2,3,4 &c to 10,000 and then pursue its calculation according to a
new ration. He said indeed that the exceptions which took place in the operation of
his Machine and which were not to be accounted for by any errors or derangement of
structure, would follow a greater number of uniform experiences than the world had

known of days & nights. There was a sublimity in the views thus opened of the
ultimate results of intellectual power.”

The Difference Engine
Right from the start, Ada’s perception of the proto-computer was different to
Babbage’s. He conceived his machine as a “mechanised servant of mankind”. But to
Ada it was in itself “a new area of discovery with its own mysteries”. As biographer
James Essinger says, “his scientific imagination was ultimately more prosaic and less
incandescent than hers”.