Textbook in PDF format This Dover edition, first published in 2006, is an unabridged republication of the second edition of the work originally published in 1950 by Chelsea Publishing Company, New York. The first edition was published in 1927 by The Williams & Wilkins Company, Baltimore. In the mathematical subfield of numerical analysis, interpolation is a procedure that assists in "reading between the lines" in a set of tables by constructing new data points from existing points. This rigorous presentation employs only formulas for which it is possible to calculate error limits. Table of contents: 1. Introduction 2. Displacement-Symbols and Differences 3. Divided Differences 4. Interpolation-Formulas 5. Some Applications 6. Factorial Coefficients 7. Numerical Differentiation 8. Construction of Tables 9. Inverse Interpolation 10. Elementary Methods of Summation 11. Repeated Summation 12. Laplace's and Gauss's Summation-Formulas 13. Bernoulli's Polynomials 14. Euler's Summation-Formula 15. Lubbock's and Woolhouse's Formulas 16. Mechanical Quadrature 17. Numerical Integration of Differential Equations 18. The Calculus of Symbols 19. Interpolation with Several Variables 20. Mechanical Cubature Appendix