The Solution of Equations by the use of Proportional Differences

Extract

Nowadays every Fifth Form pupil uses logarithm tables. A discussion of the construction of the difference columns, with graphical illustration, would prepare him for the methods to be described below, of an iterative process for the approximate solution of any equation. Incidentally it would help him to realise more fully than he usually does to what degree of accuracy his logarithmic work is reliable. The method of obtaining logarithms by using powers of 1·1, as described in the Algebra Beport, uses the same principle of proportional parts, and, properly treated, helps to establish the general principle that, when the differences for unit increments in the entries used are constant, results obtained by proportional interpolation are accurate to the same number of figures as the entries.