A method of series summation and its application to the electric force in sphere-gaps

The paper sets out a simple procedure of general application whereby any function represented by a power series may be replaced by a sequence of rational functions, the advantage of such representation being that in many cases the rational functions converge much more rapidly than does the series. It often happens that the rational-function form continues to represent the given function accurately for values of the argument which make the series form diverge. The procedure is illustrated with a worked example, and the method is then applied to determine a simple expression for the maximum electric intensity between two equal charged spheres, when the sphere-gap is small compared with the diameters.