For the student of mathematics this book is intended to furnish an introduction to some of the applications of the exact sciences and their relation to the "practical" sciences and useful arts, and is primarily intended to give him a knowledge of facts and methods, but without neglecting the accurate exercise of his reasoning powers. For the student of physical science it is intended especially to emphasize general considerations of measurement, theory of errors, general methods of procedure, quantitative accuracy, adjustment of observations, etc. - topics that are often merely mentioned in the introduction or appendix of a laboratory manual, but that need laboratory work and drill quite as much as the measurements of the individual quantities that the student will take up in his later work.