<Li> Step 3 . This is like Step 1, except it is odd columns (3, 5, 7) added to even columns (2, 4, 6), and column one has its values transferred by a sector gear to the print mechanism on the left end of the engine . Any even column value that passes from "9" to "0" activates a carry lever . The column 1 value, the result for the polynomial, is sent to the attached printer mechanism . </Li> <Li> Step 4 . This is like Step 2, but for doing carries on even columns, and returning odd columns to their original values . </Li> <P> The engine represents negative numbers as ten's complements . Subtraction amounts to addition of a negative number . This works in the same manner that modern computers perform subtraction, known as two's complement . </P> <P> The principle of a difference engine is Newton's method of divided differences . If the initial value of a polynomial (and of its finite differences) is calculated by some means for some value of X, the difference engine can calculate any number of nearby values, using the method generally known as the method of finite differences . For example, consider the quadratic polynomial </P>

Who developed the mechanical calculator called the difference engine