The Exploration and Exploitation of Response Surfaces: An Example of the Link between the Fitted Surface and the Basic Mechanism of the System

This is a sequel to an article which recently appeared in this journal 1 and had the same general title. The previous article described a number of applications of newly developed techniques 2 for the study of response surfaces. The present article shows how study of the form of the empirical surface can throw important light on the basic mechanism operating and can thus make possible developments in the fundamental theory of a process. This idea is illustrated in some detail with an example previously discussed only from the empirical standpoint. A theoretical surface, based on reaction kinetics is now derived, rate constants are estimated from the data and the theoretical surface is compared with the empirical surface previously obtained. It is then shown how the canonical variables of the empirical surface can relate to the basic physical laws controlling the system. In this connection the problem of suitable choice of metrics for the variables is discussed. In a final section some general remarks on the process of scientific investigation are appended.