which the Difference Engine tabulates for values of
only up to 7. In this case the cards would order the mechanism to go through that succession of operations which would tabulate
where
might be any number whatever.
These cards, however, have nothing to do with the regulation of the particular numerical data. They merely determine the operations[16] to be effected, which operations may of course be performed on an infinite variety of particular numerical values, and do not bring out any definite numerical results unless the numerical data of the problem have been impressed on the requisite portions of the train of mechanism. In the above example, the first essential step towards an arithmetical result, would be the substitution of specific numbers for
, and for the other primitive quantities which enter into the function.