The Differential Analyzer. a New Machine for Solving Differential Equations

I. This paper will describe a new machine for the solution of ordinary differential equations recently placed in service at the Massachusetts Inst i tute of Technology. First, there will be outlined some of the objectives in view, and the general philosophy underlying the development of this type of analyzing device. Various serious mechanical problems have of necessity been met in the effort to produce a machine which is versatile and accurate, and the means by which these have been at tacked will be treated. The general method of placing an equation on the machine will be presented and illustrated. Finally, a brief discussion will be given of a method of successive approximations for obtaining solutions of high accuracy, a method for avoiding difficulties due to singularities in coefficients, and a t rea tment of the problem of obtaining critical values of a parameter in an equation. 2. The handling of the processes of ari thmetic by mechanical computa t ion has recently revolutionized business accounting methods. The use in mechanical analysis of more advanced mathematical processes will ul t imately be of comparable importance in scientific research and its applications in engineering. This idea is far from original, for Leibnitz envisaged it comprehensively over two hundred years ago. The far-reaching project of utilizing complex mechanical interrelationships as substi tutes for intricate processes of reasoning owes its inception to an inventor of the calculus itself. I Leibnitz lived in an age when any comprehensive