A spline function is a function defined by piecewise polynomial arcs joined so that derivatives are continuous everywhere up to and including the order one less than the degree of polynomials used. Various aspects of interpolation by spline functions have been considered by a number of writers. The problem under consideration is that of inter polating for a function of one variable between a number of data points not necessarily equally spaced obtained with sufficient accuracy so that errors of measurement can be considered negligible in comparison with the error involved in interpolation. If the physical system or process which gave rise to the measurements is highly complex, it may be impractical to determine explicitly or to calculate values of the underlying function. The advantages of spline-function interpolation in such situations have been previously pointed out. Continuity of low-order derivatives is secured while largely or wholly avoiding the spurious undulations that commonly result from the use of a polynomial of sufficiently high degree to fit all data points exactly.