This is a technique to calculate mathematical tables by repeated regular additions of the ‘differences’ between successive items in a mathematical series. A mathematical series is a set of terms in ordered succession, the value of each being determined by a specific relation to adjacent terms. Mathematical series can be generated by a mathematical formula. To take a simple example, the numbers 1, 2, 3, 4, 5, and so on, to infinity comprise the mathematical series requiring 1 to be added to each previous term. Mathematical tables such as logarithmic tables can also be generated by a mathematical formula. 72 The Difference Engine The beauty of the Method of Differences is that it simplifies the process of calculating a long and complex mathematical series. In essence, it allows otherwise difficult multiplications to be replaced by numerous straightforward but monotonous additions. But, of course, if a machine is carrying them out, their monotony does not matter. Interestingly, Babbage’s approach to calculating mathematical tables was basically the same as that chosen by Gaspard de Prony.
